Control of coupled oscillator networks with application to microgrid technologies
Skardal, Per Sebastian; Arenas, Alex
2015-01-01
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions—a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself. PMID:26601231
Control of coupled oscillator networks with application to microgrid technologies.
Skardal, Per Sebastian; Arenas, Alex
2015-08-01
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent research into smart grid technologies, we study the control of synchronization and consider the important case of networks of coupled phase oscillators with nonlinear interactions-a paradigmatic example that has guided our understanding of self-organization for decades. We develop a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state. The amount of control, that is, number of oscillators, required to stabilize the network is primarily dictated by the coupling strength, dynamical heterogeneity, and mean degree of the network, and depends little on the structural heterogeneity of the network itself.
Coupled Self-Oscillating Systems:. Theory and Applications
NASA Astrophysics Data System (ADS)
Guerra, Francesco
We review the structure of self-oscillating dynamical systems, and point out the numerous applications that they can have. In the case of coupled self-oscillating systems, the typical features of complexity show up, in a completely dynamical setting. This general scheme goes well beyond Fourier analysis, and allows to consider modes at the various time scale levels in a frame where non-linearity plays an essential role. We discuss some basic applications to speech generation, hydrodynamic instabilities, volcanic tremor. Possible lines of development are pointed out.
Phase patterns of coupled oscillators with application to wireless communication
Arenas, A.
2008-01-02
Here we study the plausibility of a phase oscillators dynamical model for TDMA in wireless communication networks. We show that emerging patterns of phase locking states between oscillators can eventually oscillate in a round-robin schedule, in a similar way to models of pulse coupled oscillators designed to this end. The results open the door for new communication protocols in a continuous interacting networks of wireless communication devices.
Saturation in coupled oscillators
NASA Astrophysics Data System (ADS)
Roman, Ahmed; Hanna, James
2015-03-01
We consider a weakly nonlinear system consisting of a resonantly forced oscillator coupled to an unforced oscillator. It has long been known that, for quadratic nonlinearities and a 2:1 resonance between the oscillators, a perturbative solution of the dynamics exhibits a phenomenon known as saturation. At low forcing, the forced oscillator responds, while the unforced oscillator is quiescent. Above a critical value of the forcing, the forced oscillator's steady-state amplitude reaches a plateau, while that of the unforced oscillator increases without bound. We show that, contrary to established folklore, saturation is not unique to quadratically nonlinear systems. We present conditions on the form of the nonlinear couplings and resonance that lead to saturation. Our results elucidate a mechanism for localization or diversion of energy in systems of coupled oscillators, and suggest new approaches for the control or suppression of vibrations in engineered systems.
Dynamics of three coupled van der Pol oscillators with application to circadian rhythms
NASA Astrophysics Data System (ADS)
Rompala, Kevin; Rand, Richard; Howland, Howard
2007-08-01
In this work we study a system of three van der Pol oscillators. Two of the oscillators are identical, and are not directly coupled to each other, but rather are coupled via the third oscillator. We investigate the existence of the in-phase mode in which the two identical oscillators have the same behavior. To this end we use the two variable expansion perturbation method (also known as multiple scales) to obtain a slow flow, which we then analyze using the computer algebra system MACSYMA and the numerical bifurcation software AUTO. Our motivation for studying this system comes from the presence of circadian rhythms in the chemistry of the eyes. We model the circadian oscillator in each eye as a van der Pol oscillator. Although there is no direct connection between the two eyes, they are both connected to the brain, especially to the pineal gland, which is here represented by a third van der Pol oscillator.
Covariant harmonic oscillators and coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
1995-01-01
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
Coupled opto-electronic oscillator
NASA Technical Reports Server (NTRS)
Yao, X. Steve (Inventor); Maleki, Lute (Inventor)
1999-01-01
A coupled opto-electronic oscillator that directly couples a laser oscillation with an electronic oscillation to simultaneously achieve a stable RF oscillation at a high frequency and ultra-short optical pulsation by mode locking with a high repetition rate and stability. Single-mode selection can be achieved even with a very long opto-electronic loop. A multimode laser can be used to pump the electronic oscillation, resulting in a high operation efficiency. The optical and the RF oscillations are correlated to each other.
Zhu, Yenan; Hsieh, Yee-Hsee; Dhingra, Rishi R.; Dick, Thomas E.; Jacono, Frank J.; Galán, Roberto F.
2013-01-01
Interactions between oscillators can be investigated with standard tools of time series analysis. However, these methods are insensitive to the directionality of the coupling, i.e., the asymmetry of the interactions. An elegant alternative was proposed by Rosenblum and collaborators [M. G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. E 65, 041909 (2002); M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. E 64, 045202 (2001)] which consists in fitting the empirical phases to a generic model of two weakly coupled phase oscillators. This allows one to obtain the interaction functions defining the coupling and its directionality. A limitation of this approach is that a solution always exists in the least-squares sense, even in the absence of coupling. To preclude spurious results, we propose a three-step protocol: (1) Determine if a statistical dependency exists in the data by evaluating the mutual information of the phases; (2) if so, compute the interaction functions of the oscillators; and (3) validate the empirical oscillator model by comparing the joint probability of the phases obtained from simulating the model with that of the empirical phases. We apply this protocol to a model of two coupled Stuart-Landau oscillators and show that it reliably detects genuine coupling. We also apply this protocol to investigate cardiorespiratory coupling in anesthetized rats. We observe reciprocal coupling between respiration and heartbeat and that the influence of respiration on the heartbeat is generally much stronger than vice versa. In addition, we find that the vagus nerve mediates coupling in both directions. PMID:23496550
NASA Astrophysics Data System (ADS)
Zhu, Yenan; Hsieh, Yee-Hsee; Dhingra, Rishi R.; Dick, Thomas E.; Jacono, Frank J.; Galán, Roberto F.
2013-02-01
Interactions between oscillators can be investigated with standard tools of time series analysis. However, these methods are insensitive to the directionality of the coupling, i.e., the asymmetry of the interactions. An elegant alternative was proposed by Rosenblum and collaborators [M. G. Rosenblum, L. Cimponeriu, A. Bezerianos, A. Patzak, and R. Mrowka, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.65.041909 65, 041909 (2002); M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.64.045202 64, 045202 (2001)] which consists in fitting the empirical phases to a generic model of two weakly coupled phase oscillators. This allows one to obtain the interaction functions defining the coupling and its directionality. A limitation of this approach is that a solution always exists in the least-squares sense, even in the absence of coupling. To preclude spurious results, we propose a three-step protocol: (1) Determine if a statistical dependency exists in the data by evaluating the mutual information of the phases; (2) if so, compute the interaction functions of the oscillators; and (3) validate the empirical oscillator model by comparing the joint probability of the phases obtained from simulating the model with that of the empirical phases. We apply this protocol to a model of two coupled Stuart-Landau oscillators and show that it reliably detects genuine coupling. We also apply this protocol to investigate cardiorespiratory coupling in anesthetized rats. We observe reciprocal coupling between respiration and heartbeat and that the influence of respiration on the heartbeat is generally much stronger than vice versa. In addition, we find that the vagus nerve mediates coupling in both directions.
Coupled oscillators on evolving networks
NASA Astrophysics Data System (ADS)
Singh, R. K.; Bagarti, Trilochan
2016-12-01
In this work we study coupled oscillators on evolving networks. We find that the steady state behavior of the system is governed by the relative values of the spread in natural frequencies and the global coupling strength. For coupling strong in comparison to the spread in frequencies, the system of oscillators synchronize and when coupling strength and spread in frequencies are large, a phenomenon similar to amplitude death is observed. The network evolution provides a mechanism to build inter-oscillator connections and once a dynamic equilibrium is achieved, oscillators evolve according to their local interactions. We also find that the steady state properties change by the presence of additional time scales. We demonstrate these results based on numerical calculations studying dynamical evolution of limit-cycle and van der Pol oscillators.
Symmetries of coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.
1993-01-01
It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).
Period variability of coupled noisy oscillators
NASA Astrophysics Data System (ADS)
Mori, Fumito; Kori, Hiroshi
2013-03-01
Period variability, quantified by the standard deviation (SD) of the cycle-to-cycle period, is investigated for noisy phase oscillators. We define the checkpoint phase as the beginning or end point of one oscillation cycle and derive an expression for the SD as a function of this phase. We find that the SD is dependent on the checkpoint phase only when oscillators are coupled. The applicability of our theory is verified using a realistic model. Our work clarifies the relationship between period variability and synchronization from which valuable information regarding coupling can be inferred.
Coupling functions in networks of oscillators
NASA Astrophysics Data System (ADS)
Stankovski, Tomislav; Ticcinelli, Valentina; McClintock, Peter V. E.; Stefanovska, Aneta
2015-03-01
Networks of interacting oscillators abound in nature, and one of the prevailing challenges in science is how to characterize and reconstruct them from measured data. We present a method of reconstruction based on dynamical Bayesian inference that is capable of detecting the effective phase connectivity within networks of time-evolving coupled phase oscillators subject to noise. It not only reconstructs pairwise, but also encompasses couplings of higher degree, including triplets and quadruplets of interacting oscillators. Thus inference of a multivariate network enables one to reconstruct the coupling functions that specify possible causal interactions, together with the functional mechanisms that underlie them. The characteristic features of the method are illustrated by the analysis of a numerically generated example: a network of noisy phase oscillators with time-dependent coupling parameters. To demonstrate its potential, the method is also applied to neuronal coupling functions from single- and multi-channel electroencephalograph recordings. The cross-frequency δ, α to α coupling function, and the θ, α, γ to γ triplet are computed, and their coupling strengths, forms of coupling function, and predominant coupling components, are analysed. The results demonstrate the applicability of the method to multivariate networks of oscillators, quite generally.
de Poel, Harjo J.
2016-01-01
Coupled oscillators provide a pertinent model approach to study between-person movement dynamics. While ample literature in this respect has considered the influence of external/environmental constraints and/or effects of a difference between the two agents' individual component dynamics (e.g., mismatch in natural frequency), recent studies also started to more directly consider the interaction per-se. The current perspective paper sets forth that while movement coordination dynamics has mainly been studied alongside a model in which the coupling is considered isotropic (i.e., symmetrical; both oscillators coupled to same degree) or strictly unidirectional (e.g., for moving to a given external rhythm), between-agent coupling involves a natural anisotropy: components influence each other bidirectionally to different degrees. Furthermore, recent research from different areas has considered so-called antagonistic or “competitive” coupling, which refers to the idea that one component is positively coupled to the other (attractive interaction), while the coupling in the other direction is negative (repulsive interaction). Although the latter would be rather tricky to address in within-person coordination, it does have strong applications and implications for between-person dynamics, for instance in the study of competitive interactions in sports situations (e.g., attacker-defender) and conflicting social (movement) interactions. The paper concludes by offering a conceptual framework and perspectives for future studies on the dynamic anisotropic nature of the interaction in between-person contexts. PMID:28066280
NASA Astrophysics Data System (ADS)
Nana, B.; Woafo, P.
2011-04-01
Data encryption has become increasingly important for many applications including phone, internet and satellite communications. Considering the desirable properties of ergodicity and high sensitivity to initial conditions and control parameters, chaotic signals are suitable for encryption systems. Chaotic encryption systems generally have high speed with low cost, which makes them better candidates than many traditional ciphers for multimedia data encryption. In this paper, analytical and numerical methods as well as experimental implementation are used to prove partial and complete synchronized states in a ring of four autonomous oscillators in their chaotic states. Application to secure communication is discussed.
Magnetically Coupled Magnet-Spring Oscillators
ERIC Educational Resources Information Center
Donoso, G.; Ladera, C. L.; Martin, P.
2010-01-01
A system of two magnets hung from two vertical springs and oscillating in the hollows of a pair of coils connected in series is a new, interesting and useful example of coupled oscillators. The electromagnetically coupled oscillations of these oscillators are experimentally and theoretically studied. Its coupling is electromagnetic instead of…
Coupled oscillators with parity-time symmetry
NASA Astrophysics Data System (ADS)
Tsoy, Eduard N.
2017-02-01
Different models of coupled oscillators with parity-time (PT) symmetry are studied. Hamiltonian functions for two and three linear oscillators coupled via coordinates and accelerations are derived. Regions of stable dynamics for two coupled oscillators are obtained. It is found that in some cases, an increase of the gain-loss parameter can stabilize the system. A family of Hamiltonians for two coupled nonlinear oscillators with PT-symmetry is obtained. An extension to high-dimensional PT-symmetric systems is discussed.
Emergence of amplitude and oscillation death in identical coupled oscillators.
Zou, Wei; Senthilkumar, D V; Duan, Jinqiao; Kurths, Jürgen
2014-09-01
We deduce rigorous conditions for the onset of amplitude death (AD) and oscillation death (OD) in a system of identical coupled paradigmatic Stuart-Landau oscillators. A nonscalar coupling and high frequency are beneficial for the onset of AD. In strong contrast, scalar diffusive coupling and low intrinsic frequency are in favor of the emergence of OD. Our finding contributes to clearly distinguish intrinsic geneses for AD and OD, and further substantially corroborates that AD and OD are indeed two dynamically distinct oscillation quenching phenomena due to distinctly different mechanisms.
Markovian evolution of strongly coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Joshi, Chaitanya; Öhberg, Patrik; Cresser, James D.; Andersson, Erika
2014-12-01
We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.
Collective phase response curves for heterogeneous coupled oscillators
NASA Astrophysics Data System (ADS)
Hannay, Kevin M.; Booth, Victoria; Forger, Daniel B.
2015-08-01
Phase response curves (PRCs) have become an indispensable tool in understanding the entrainment and synchronization of biological oscillators. However, biological oscillators are often found in large coupled heterogeneous systems and the variable of physiological importance is the collective rhythm resulting from an aggregation of the individual oscillations. To study this phenomena we consider phase resetting of the collective rhythm for large ensembles of globally coupled Sakaguchi-Kuramoto oscillators. Making use of Ott-Antonsen theory we derive an asymptotically valid analytic formula for the collective PRC. A result of this analysis is a characteristic scaling for the change in the amplitude and entrainment points for the collective PRC compared to the individual oscillator PRC. We support the analytical findings with numerical evidence and demonstrate the applicability of the theory to large ensembles of coupled neuronal oscillators.
Reentrant transition in coupled noisy oscillators
NASA Astrophysics Data System (ADS)
Kobayashi, Yasuaki; Kori, Hiroshi
2015-01-01
We report on a synchronization-breaking instability observed in a noisy oscillator unidirectionally coupled to a pacemaker. Using a phase oscillator model, we find that, as the coupling strength is increased, the noisy oscillator lags behind the pacemaker more frequently and the phase slip rate increases, which may not be observed in averaged phase models such as the Kuramoto model. Investigation of the corresponding Fokker-Planck equation enables us to obtain the reentrant transition line between the synchronized state and the phase slip state. We verify our theory using the Brusselator model, suggesting that this reentrant transition can be found in a wide range of limit cycle oscillators.
Pulse-coupled BZ oscillators with unequal coupling strengths.
Horvath, Viktor; Kutner, Daniel J; Chavis, John T; Epstein, Irving R
2015-02-14
Coupled chemical oscillators are usually studied with symmetric coupling, either between identical oscillators or between oscillators whose frequencies differ. Asymmetric connectivity is important in neuroscience, where synaptic strength inequality in neural networks commonly occurs. While the properties of the individual oscillators in some coupled chemical systems may be readily changed, enforcing inequality between the connection strengths in a reciprocal coupling is more challenging. We recently demonstrated a novel way of coupling chemical oscillators, which allows for manipulation of individual connection strengths. Here we study two identical, pulse-coupled Belousov-Zhabotinsky (BZ) oscillators with unequal connection strengths. When the pulse perturbations contain KBr (inhibitor), this system exhibits simple out-of-phase and complex oscillations, oscillatory-suppressed states as well as temporally periodic patterns (N : M) in which the two oscillators exhibit different numbers of peaks per cycle. The N : M patterns emerge due to the long-term effect of the inhibitory pulse-perturbations, a feature that has not been considered in earlier works. Time delay was previously shown to have a profound effect on the system's behaviour when pulse coupling was inhibitory and the coupling strengths were equal. When the coupling is asymmetric, however, delay produces no qualitative change in behaviour, though the 1 : 2 temporal pattern becomes more robust. Asymmetry in instantaneous excitatory coupling via AgNO3 injection produces a previously unseen temporal pattern (1 : N patterns starting with a double peak) with time delay and high [AgNO3]. Numerical simulations of the behaviour agree well with theoretical predictions in asymmetrical pulse-coupled systems.
Entrainment in coupled salt-water oscillators
NASA Astrophysics Data System (ADS)
Miyakawa, Kenji; Yamada, Kazuhiko
1999-03-01
The properties of coupling between two salt-water oscillators were studied. Two salt-water oscillators were coupled through the window of the partition wall. With an increase of the area of the window, the quasi-periodic mode, the in-phase mode, the bistable mode, and the out-of-phase mode appeared successively. A phase diagram of coupling was obtained in the plane of the area of the window and the diameter of the orifice of the cup. Furthermore, the effect of viscosity on coupling behaviors was investigated. In the boundary region between quasi-periodic coupling and in-phase coupling, the mode coupled with the phase difference of approximately π/4 was found. The experimental results were reproduced by the numerical simulation using coupled non-linear differential equations.
Arrays of coupled chemical oscillators
NASA Astrophysics Data System (ADS)
Forrester, Derek Michael
2015-11-01
Oscillating chemical reactions result from complex periodic changes in the concentration of the reactants. In spatially ordered ensembles of candle flame oscillators the fluctuations in the ratio of oxygen atoms with respect to that of carbon, hydrogen and nitrogen produces an oscillation in the visible part of the flame related to the energy released per unit mass of oxygen. Thus, the products of the reaction vary in concentration as a function of time, giving rise to an oscillation in the amount of soot and radiative emission. Synchronisation of interacting dynamical sub-systems occurs as arrays of flames that act as master and slave oscillators, with groups of candles numbering greater than two, creating a synchronised motion in three-dimensions. In a ring of candles the visible parts of each flame move together, up and down and back and forth, in a manner that appears like a “worship”. Here this effect is shown for rings of flames which collectively empower a central flame to pulse to greater heights. In contrast, situations where the central flames are suppressed are also found. The phenomena leads to in-phase synchronised states emerging between periods of anti-phase synchronisation for arrays with different columnar sizes of candle and positioning.
Arrays of coupled chemical oscillators
Forrester, Derek Michael
2015-01-01
Oscillating chemical reactions result from complex periodic changes in the concentration of the reactants. In spatially ordered ensembles of candle flame oscillators the fluctuations in the ratio of oxygen atoms with respect to that of carbon, hydrogen and nitrogen produces an oscillation in the visible part of the flame related to the energy released per unit mass of oxygen. Thus, the products of the reaction vary in concentration as a function of time, giving rise to an oscillation in the amount of soot and radiative emission. Synchronisation of interacting dynamical sub-systems occurs as arrays of flames that act as master and slave oscillators, with groups of candles numbering greater than two, creating a synchronised motion in three-dimensions. In a ring of candles the visible parts of each flame move together, up and down and back and forth, in a manner that appears like a “worship”. Here this effect is shown for rings of flames which collectively empower a central flame to pulse to greater heights. In contrast, situations where the central flames are suppressed are also found. The phenomena leads to in-phase synchronised states emerging between periods of anti-phase synchronisation for arrays with different columnar sizes of candle and positioning. PMID:26582365
Adaptive coupling and enhanced synchronization in coupled phase oscillators
NASA Astrophysics Data System (ADS)
Ren, Quansheng; Zhao, Jianye
2007-07-01
We study the dynamics of an adaptive coupled array of phase oscillators. The adaptive law is designed in such a way that the coupling grows stronger for the pairs which have larger phase incoherence. The proposed scheme enhances the synchronization and achieves a more reasonable coupling dynamics for the network of oscillators with different intrinsic frequencies. The synchronization speed and the steady-state phase difference can be adjusted by the parameters of the adaptive law. Besides global coupling, nearest-neighbor ring coupling is also considered to demonstrate the generality of the method.
Explosive oscillation death in coupled Stuart-Landau oscillators
NASA Astrophysics Data System (ADS)
Bi, Hongjie; Hu, Xin; Zhang, Xiyun; Zou, Yong; Liu, Zonghua; Guan, Shuguang
2014-12-01
Recently, explosive phase transitions, such as explosive percolation and explosive synchronization, have attracted extensive research interest. So far, most existing works have investigated Kuramoto-type models, where only phase variables are involved. Here, we report the occurrence of explosive oscillation quenching in a system of coupled Stuart-Landau oscillators that incorporates both phase and amplitude dynamics. We observe three typical scenarios with distinct microscopic mechanism of occurrence, i.e., ordinary, hierarchical, and cluster explosive oscillation death, corresponding to different frequency distributions of oscillators. We carry out theoretical analyses and obtain the backward transition point, which is shown to be independent of the specific frequency distributions. Numerical results are consistent with the theoretical predictions.
Synchronization of coupled Boolean phase oscillators
NASA Astrophysics Data System (ADS)
Rosin, David P.; Rontani, Damien; Gauthier, Daniel J.
2014-04-01
We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bidirectional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of the large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.
Synchronization of coupled nonidentical genetic oscillators
NASA Astrophysics Data System (ADS)
Li, Chunguang; Chen, Luonan; Aihara, Kazuyuki
2006-03-01
The study of the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lur'e form by exploiting the special structure of biological systems. By using a control theory approach, we provide a theoretical method for analysing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.
Mode coupling in spin torque oscillators
Zhang, Steven S. -L.; Zhou, Yan; Li, Dong; Heinonen, Olle
2016-09-15
A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Here, our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. In conclusion, the acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.
Mode coupling in spin torque oscillators
Zhang, Steven S. -L.; Zhou, Yan; Li, Dong; ...
2016-09-15
A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Here, our resultsmore » show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. In conclusion, the acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.« less
Oscillator death induced by amplitude-dependent coupling in repulsively coupled oscillators.
Liu, Weiqing; Xiao, Guibao; Zhu, Yun; Zhan, Meng; Xiao, Jinghua; Kurths, Jürgen
2015-05-01
The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression.
Oscillator death induced by amplitude-dependent coupling in repulsively coupled oscillators
NASA Astrophysics Data System (ADS)
Liu, Weiqing; Xiao, Guibao; Zhu, Yun; Zhan, Meng; Xiao, Jinghua; Kurths, Jürgen
2015-05-01
The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression.
Enhancing energy harvesting by coupling monostable oscillators
NASA Astrophysics Data System (ADS)
Peña Rosselló, Julián I.; Wio, Horacio S.; Deza, Roberto R.; Hänggi, Peter
2017-02-01
The performance of a ring of linearly coupled, monostable nonlinear oscillators is optimized towards its goal of acting as energy harvester - through piezoelectric transduction - of mesoscopic fluctuations, which are modeled as Ornstein-Uhlenbeck noises. For a single oscillator, the maximum output voltage and overall efficiency are attained for a soft piecewise-linear potential (providing a weak attractive constant force) but they are still fairly large for a harmonic potential. When several harmonic springs are linearly and bidirectionally coupled to form a ring, it is found that counter-phase coupling can largely improve the performance while in-phase coupling worsens it. Moreover, it turns out that few (two or three) coupled units perform better than more.
Susceptibility of large populations of coupled oscillators
NASA Astrophysics Data System (ADS)
Daido, Hiroaki
2015-01-01
It is an important and interesting problem to elucidate how the degree of phase order in a large population of coupled oscillators responds to a synchronizing periodic force from the outside. Here this problem is studied analytically as well as numerically by introducing the concept of susceptibility for globally coupled phase oscillators with either nonrandom or random interactions. It is shown that the susceptibility diverges at the critical point in the nonrandom case with Widom's equality satisfied, while it exhibits a cusp in the most random case.
Mode coupling in solar spicule oscillations
NASA Astrophysics Data System (ADS)
Fazel, Zahra
2016-01-01
In a real medium which has oscillations, the perturbations can cause an energy transfer between different modes. A perturbation, which is interpreted as an interaction between the modes, is inferred to be mode coupling. The mode coupling process in an inhomogeneous medium such as solar spicules may lead to the coupling of kink waves to local Alfvén waves. This coupling occurs in practically any conditions when there is smooth variation in density in the radial direction. This process is seen as the decay of transverse kink waves in the medium. To study the damping of kink waves due to mode coupling, a 2.5-dimensional numerical simulation of the initial wave is considered in spicules. The initial perturbation is assumed to be in a plane perpendicular to the spicule axis. The considered kink wave is a standing wave which shows an exponential damping in the inhomogeneous layer after the mode coupling occurs.
An Agile Beam Transmit Array Using Coupled Oscillator Phase Control
NASA Technical Reports Server (NTRS)
Pogorzelski, Ronald S.; Scaramastra, Rocco P.; Huang, John; Beckon, Robert J.; Petree, Steve M.; Chavez, Cosme
1993-01-01
A few years ago York and colleagues suggested that injection locking of voltage controlled oscillators could be used to implement beam steering in a phased array [I]. The scheme makes use of the fact that when an oscillator is injection locked to an external signal, the phase difference between the output of the oscillator and the injection signal is governed by the difference between the injection frequency and the free running frequency of the oscillator (the frequency to which the oscillator is tuned). Thus, if voltage controlled oscillators (VCOs) are used, this phase difference is controlled by an applied voltage. Now, if a set of such oscillators are coupled to nearest neighbors, they can be made to mutually injection lock and oscillate as an ensemble. If they are all tuned to the same frequency, they will all oscillate in phase. Thus, if the outputs are connected to radiating elements forming a linear array, the antenna will radiate normal to the line of elements. Scanning is accomplished by antisymmetrically detuning the end oscillators in the array by application of a pair of appropriate voltages to their tuning ports. This results in a linear phase progression across the array which is just the phasing required to scan the beam. The scan angle is determined by the degree of detuning. We have constructed a seven element one dimensional agile beam array at S-band based on the above principle. Although, a few such arrays have been built in the past, this array possesses two unique features. First, the VCO MMICs have buffer amplifiers which isolate the output from the tuning circuit, and second, the oscillators are weakly coupled to each other at their resonant circuits rather than their outputs. This results in a convenient isolation between the oscillator array design and the radiating aperture design. An important parameter in the design is the so called coupling phase which determines the phase shift of the signals passing from one oscillator to its
Locally and globally coupled oscillators in muscle.
Sato, Katsuhiko; Kuramoto, Yoshiki; Ohtaki, Masako; Shimamoto, Yuta; Ishiwata, Shin'ichi
2013-09-06
At an intermediate activation level, striated muscle exhibits autonomous oscillations called SPOC, in which the basic contractile units, sarcomeres, oscillate in length, and various oscillatory patterns such as traveling waves and their disrupted forms appear in a myofibril. Here we show that these patterns are reproduced by mechanically connecting in series the unit model that explains characteristics of SPOC at the single-sarcomere level. We further reduce the connected model to phase equations, revealing that the combination of local and global couplings is crucial to the emergence of these patterns.
Locally and Globally Coupled Oscillators in Muscle
NASA Astrophysics Data System (ADS)
Sato, Katsuhiko; Kuramoto, Yoshiki; Ohtaki, Masako; Shimamoto, Yuta; Ishiwata, Shin'ichi
2013-09-01
At an intermediate activation level, striated muscle exhibits autonomous oscillations called SPOC, in which the basic contractile units, sarcomeres, oscillate in length, and various oscillatory patterns such as traveling waves and their disrupted forms appear in a myofibril. Here we show that these patterns are reproduced by mechanically connecting in series the unit model that explains characteristics of SPOC at the single-sarcomere level. We further reduce the connected model to phase equations, revealing that the combination of local and global couplings is crucial to the emergence of these patterns.
Synchronization Dynamics of Coupled Chemical Oscillators
NASA Astrophysics Data System (ADS)
Tompkins, Nathan
The synchronization dynamics of complex networks have been extensively studied over the past few decades due to their ubiquity in the natural world. Prominent examples include cardiac rhythms, circadian rhythms, the flashing of fireflies, predator/prey population dynamics, mammalian gait, human applause, pendulum clocks, the electrical grid, and of the course the brain. Detailed experiments have been done to map the topology of many of these systems and significant advances have been made to describe the mathematics of these networks. Compared to these bodies of work relatively little has been done to directly test the role of topology in the synchronization dynamics of coupled oscillators. This Dissertation develops technology to examine the dynamics due to topology within networks of discrete oscillatory components. The oscillatory system used here consists of the photo-inhibitable Belousov-Zhabotinsky (BZ) reaction water-in-oil emulsion where the oscillatory drops are diffusively coupled to one another and the topology is defined by the geometry of the diffusive connections. Ring networks are created from a close-packed 2D array of drops using the Programmable Illumination Microscope (PIM) in order to test Turing's theory of morphogenesis directly. Further technology is developed to create custom planar networks of BZ drops in more complicated topologies which can be individually perturbed using illumination from the PIM. The work presented here establishes the validity of using the BZ emulsion system with a PIM to study the topology induced effects on the synchronization dynamics of coupled chemical oscillators, tests the successes and limitations of Turing's theory of morphogenesis, and develops new technology to further probe the effects of network topology on a system of coupled oscillators. Finally, this Dissertation concludes by describing ongoing experiments which utilize this new technology to examine topology induced transitions of synchronization
Inference of Stochastic Nonlinear Oscillators with Applications to Physiological Problems
NASA Technical Reports Server (NTRS)
Smelyanskiy, Vadim N.; Luchinsky, Dmitry G.
2004-01-01
A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of dynamical models. We illustrate the main ideas of the technique by inferencing a model of five globally and locally coupled noisy oscillators. Specific modifications of the technique for inferencing hidden degrees of freedom of coupled nonlinear oscillators is discussed in the context of physiological applications.
Synchronization in Networks of Coupled Chemical Oscillators
NASA Astrophysics Data System (ADS)
Showalter, Kenneth; Tinsley, Mark; Nkomo, Simbarashe; Ke, Hua
2014-03-01
We have studied networks of coupled photosensitive chemical oscillators. Experiments and simulations are carried out on networks with different topologies and modes of coupling. We describe experimental and modeling studies of chimera and phase-cluster states and their relation to other synchronization states. Networks of integrate-and-fire oscillators are also studied in which sustained coordinated activity is exhibited. Individual nodes display incoherent firing events; however, a dominant frequency within the collective signal is exhibited. The introduction of spike-timing-dependent plasticity allows the network to evolve and leads to a stable unimodal link-weight distribution. M. R. Tinsley et al., Nature Physics 8, 662 (2012); S. Nkomo et al., Phys. Rev. Lett. 110, 244102 (2013); H. Ke et al., in preparation.
Dynamics of learning in coupled oscillators tutored with delayed reinforcements.
Trevisan, M A; Bouzat, S; Samengo, I; Mindlin, G B
2005-07-01
In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired by the process of learning of birdsongs by oscine birds. An oscillator acts as the generator of a basic rhythm and drives slave oscillators which are responsible for different motor actions. The driving signal arrives at each driven oscillator through two different pathways. One of them is a direct pathway. The other one is a reinforcement pathway, through which the signal arrives delayed. The coupling coefficients between the driving oscillator and the slave ones evolve in time following a Hebbian-like rule. We discuss the conditions under which a driven oscillator is capable of learning to lock to the driver. The resulting phase difference and connectivity are a function of the delay of the reinforcement. Around some specific delays, the system is capable of generating dramatic changes in the phase difference between the driver and the driven systems. We discuss the dynamical mechanism responsible for this effect and possible applications of this learning scheme.
Dynamics of learning in coupled oscillators tutored with delayed reinforcements
NASA Astrophysics Data System (ADS)
Trevisan, M. A.; Bouzat, S.; Samengo, I.; Mindlin, G. B.
2005-07-01
In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired by the process of learning of birdsongs by oscine birds. An oscillator acts as the generator of a basic rhythm and drives slave oscillators which are responsible for different motor actions. The driving signal arrives at each driven oscillator through two different pathways. One of them is a direct pathway. The other one is a reinforcement pathway, through which the signal arrives delayed. The coupling coefficients between the driving oscillator and the slave ones evolve in time following a Hebbian-like rule. We discuss the conditions under which a driven oscillator is capable of learning to lock to the driver. The resulting phase difference and connectivity are a function of the delay of the reinforcement. Around some specific delays, the system is capable of generating dramatic changes in the phase difference between the driver and the driven systems. We discuss the dynamical mechanism responsible for this effect and possible applications of this learning scheme.
Coupled oscillators and Feynman's three papers
NASA Astrophysics Data System (ADS)
Kim, Y. S.
2007-05-01
According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the "rest of the universe" contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.
Predicting synchrony in heterogeneous pulse coupled oscillators
NASA Astrophysics Data System (ADS)
Talathi, Sachin S.; Hwang, Dong-Uk; Miliotis, Abraham; Carney, Paul R.; Ditto, William L.
2009-08-01
Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.
Four mass coupled oscillator guitar model.
Popp, John E
2012-01-01
Coupled oscillator models have been used for the low frequency response (50 to 250 Hz) of a guitar. These 2 and 3 mass models correctly predict measured resonance frequency relationships under various laboratory boundary conditions, but did not always represent the true state of a guitar in the players' hands. The model presented has improved these models in three ways, (1) a fourth oscillator includes the guitar body, (2) plate stiffnesses and other fundamental parameters were measured directly and effective areas and masses used to calculate the responses, including resonances and phases, directly, and (3) one of the three resultant resonances varies with neck and side mass and can also be modeled as a bar mode of the neck and body. The calculated and measured resonances and phases agree reasonably well.
Active Coupled Oscillators in the Inner Ear
NASA Astrophysics Data System (ADS)
Strimbu, Clark Elliott
Auditory and vestibular systems are endowed with an active process that enables them to detect signals as small as a few Angstroms; they also exhibit frequency selectivity; show strong nonlinearities; and can exhibit as spontaneous activity. Much of this active process comes from the sensory hair cells at the periphery of the auditory and vestibular systems. Each hair cell is capped by an eponymous hair bundle, a specialized structure that transduces mechanical forces into electrical signals. Experiments on mechanically decoupled cells from the frog sacculus have shown that individual hair bundles behave in an active manner analogous to an intact organ suggesting a common cellular basis for the active processes seen in many species. In particular, mechanically decoupled hair bundles show rapid active movements in response to transient stimuli and exhibit spontaneous oscillations. However, a single mechanosensitive hair cell is unable to match the performance of an entire organ. In vivo, hair bundles are often coupled to overlying membranes, gelatinous extracellular matrices. We used an in vitro preparation of the frog sacculus in which the otolithic membrane has been left intact. Under natural coupling conditions, there is a strong degree of correlation across the saccular epithelium, suggesting that the collective response of many cells contributes to the extreme sensitivity of this organ. When the membrane is left intact, the hair bundles do not oscillate spontaneously, showing that the natural coupling and loading tunes them into a quiescent regime. However, when stimulated by a pulse, the bundles show a rapid biphasic response that is abolished when the transduction channels are blocked. The active forces generated by the bundles are sufficient to move the overlying membrane.
Spontaneous mode switching in coupled oscillators competing for constant amounts of resources.
Hirata, Yoshito; Aono, Masashi; Hara, Masahiko; Aihara, Kazuyuki
2010-03-01
We propose a widely applicable scheme of coupling that models competitions among dynamical systems for fixed amounts of resources. Two oscillators coupled in this way synchronize in antiphase. Three oscillators coupled circularly show a number of oscillation modes such as rotation and partially in-phase synchronization. Intriguingly, simple oscillators in the model also produce complex behavior such as spontaneous switching among different modes. The dynamics reproduces well the spatiotemporal oscillatory behavior of a true slime mold Physarum, which is capable of computational optimization.
Synchronization using environmental coupling in mercury beating heart oscillators
NASA Astrophysics Data System (ADS)
Singla, Tanu; Montoya, Fernando; Rivera, M.; Tajima, Shunsuke; Nakabayashi, Seiichiro; Parmananda, P.
2016-06-01
We report synchronization of Mercury Beating Heart (MBH) oscillators using the environmental coupling mechanism. This mechanism involves interaction of the oscillators with a common medium/environment such that the oscillators do not interact among themselves. In the present work, we chose a modified MBH system as the common environment. In the absence of coupling, this modified system does not exhibit self sustained oscillations. It was observed that, as a result of the coupling of the MBH oscillators with this common environment, the electrical and the mechanical activities of both the oscillators synchronized simultaneously. Experimental results indicate the emergence of both lag and the complete synchronization in the MBH oscillators. Simulations of the phase oscillators were carried out in order to better understand the experimental observations.
Synchronization in arrays of coupled self-induced friction oscillators
NASA Astrophysics Data System (ADS)
Marszal, Michał; Saha, Ashesh; Jankowski, Krzysztof; Stefański, Andrzej
2016-11-01
We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities.
The effects of dual-channel coupling on the transition from amplitude death to oscillation death
NASA Astrophysics Data System (ADS)
Chen, Jiangnan; Liu, Weiqing; Zhu, Yun; Xiao, Jinghua
2016-07-01
Oscillation quenching including amplitude death (AD) and oscillation death (OD) in addition to the transition processes between them have been hot topics in aspect of chaos control, physical and biological applications. The effects of dual-channel coupling on the AD and OD dynamics regimes, and their transition processes in coupled nonidentical oscillators are explored numerically and theoretically. Our results indicate that an additional repulsive coupling tends to shrink the AD domain while it enlarges the OD domain, however, an additional attractive coupling acts inversely. As a result, the transitions from AD to OD are replaced by transitions from oscillation state (OS) to AD or from OS to OD in the dual-channel coupled oscillators with different frequency mismatches. Our results are helpful to better understand the control of AD and OD and their transition processes.
Amplitude death in coupled robust-chaos oscillators
NASA Astrophysics Data System (ADS)
Palazzi, M. J.; Cosenza, M. G.
2014-12-01
We investigate the synchronization behavior of a system of globally coupled, continuous-time oscillators possessing robust chaos. The local dynamics corresponds to the Shimizu-Morioka model where the occurrence of robust chaos in a region of its parameter space has been recently discovered. We show that the global coupling can drive the oscillators to synchronization into a fixed point created by the coupling, resulting in amplitude death in the system. The existence of robust chaos allows to introduce heterogeneity in the local parameters, while guaranteeing the functioning of all the oscillators in a chaotic mode. In this case, the system reaches a state of oscillation death, with coexisting clusters of oscillators in different steady states. The phenomena of amplitude death or oscillation death in coupled robust-chaos flows could be employed as mechanisms for stabilization and control in systems that require reliable operation under chaos.
Quorum Sensing and Synchronization in Populations of Coupled Chemical Oscillators
NASA Astrophysics Data System (ADS)
Taylor, Annette F.; Tinsley, Mark R.; Showalter, Kenneth
2013-12-01
Experiments and simulations of populations of coupled chemical oscillators, consisting of catalytic particles suspended in solution, provide insights into density-dependent dynamics displayed by many cellular organisms. Gradual synchronization transitions, the "switching on" of activity above a threshold number of oscillators (quorum sensing) and the formation of synchronized groups (clusters) of oscillators have been characterized. Collective behavior is driven by the response of the oscillators to chemicals emitted into the surrounding solution.
Surprises of the Transformer as a Coupled Oscillator System
ERIC Educational Resources Information Center
Silva, J. P.; Silvestre, A. J.
2008-01-01
We study a system of two RLC oscillators coupled through a variable mutual inductance. The system is interesting because it exhibits some peculiar features of coupled oscillators: (i) there are two natural frequencies; (ii) in general, the resonant frequencies do not coincide with the natural frequencies; (iii) the resonant frequencies of both…
Gluing Bifurcations in Coupled Spin Torque Nano-Oscillators
2013-01-01
REPORT Gluing bifurcations in coupled spin torque nano -oscillators 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: Over the past few years it has been...shown, through theory and experiments, that the AC current produced by spin torque nano -oscillators (STNO), coupled in an array, can lead to feedback...Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS Nano -oscillators, symmetry, bifurcations Katherine
Dynamical Recurrence and the Quantum Control of Coupled Oscillators
NASA Astrophysics Data System (ADS)
Genoni, Marco G.; Serafini, Alessio; Kim, M. S.; Burgarth, Daniel
2012-04-01
Controllability—the possibility of performing any target dynamics by applying a set of available operations—is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, such as spin systems, precise criteria to establish controllability, such as the so-called rank criterion, are well known. However, most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems—encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nanomechanical oscillators—governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend the rank criterion to infinite-dimensional quadratic systems. Further, we present a useful application of our finding, by proving indirect controllability of a chain of harmonic oscillators.
Robustness and fragility in coupled oscillator networks under targeted attacks
NASA Astrophysics Data System (ADS)
Yuan, Tianyu; Aihara, Kazuyuki; Tanaka, Gouhei
2017-01-01
The dynamical tolerance of coupled oscillator networks against local failures is studied. As the fraction of failed oscillator nodes gradually increases, the mean oscillation amplitude in the entire network decreases and then suddenly vanishes at a critical fraction as a phase transition. This critical fraction, widely used as a measure of the network robustness, was analytically derived for random failures but not for targeted attacks so far. Here we derive the general formula for the critical fraction, which can be applied to both random failures and targeted attacks. We consider the effects of targeting oscillator nodes based on their degrees. First we deal with coupled identical oscillators with homogeneous edge weights. Then our theory is applied to networks with heterogeneous edge weights and to those with nonidentical oscillators. The analytical results are validated by numerical experiments. Our results reveal the key factors governing the robustness and fragility of oscillator networks.
Spectra of delay-coupled heterogeneous noisy nonlinear oscillators
NASA Astrophysics Data System (ADS)
Vüllings, Andrea; Schöll, Eckehard; Lindner, Benjamin
2014-02-01
Nonlinear oscillators that are subject to noise and delayed interaction have been used to describe a number of dynamical phenomena in Physics and beyond. Here we study the spectral statistics (power and cross-spectral densities) of a small number of noisy nonlinear oscillators and derive analytical approximations for these spectra. In our paper, individual oscillators are described by the normal form of a supercritical or subcritical Hopf bifurcation supplemented by Gaussian white noise. Oscillators can be distinguished from each other by their frequency, bifurcation parameter, and noise intensity. Extending previous results from the literature, we first calculate in linear response theory the power spectral density and response function of the single oscillator in both super- and subcritical parameter regime and test them against numerical simulations. For small heterogeneous groups of oscillators (N = 2 or 3), which are coupled by a delayed linear term, we use a linear response ansatz to derive approximations for the power and cross-spectral densities of the oscillators within this small network. These approximations are confirmed by comparison with extensive numerical simulations. Using the theory we relate the peaks in the spectra of the homogeneous system (identical oscillators) to periodic solutions of the deterministic (noiseless) system. For two delay-coupled subcritical Hopf oscillators, we show that the coupling can enhance the coherence resonance effect, which is known to occur for the single subcritical oscillator. In the case of heterogeneous oscillators, we find that the delay-induced characteristic profile of the spectra is conserved for moderate frequency detuning.
Basin stability measure of different steady states in coupled oscillators
Rakshit, Sarbendu; Bera, Bidesh K.; Majhi, Soumen; Hens, Chittaranjan; Ghosh, Dibakar
2017-01-01
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis. PMID:28378760
Implication of Two-Coupled Differential Van der Pol Duffing Oscillator in Weak Signal Detection
NASA Astrophysics Data System (ADS)
Peng, Hang-hang; Xu, Xue-mei; Yang, Bing-chu; Yin, Lin-zi
2016-04-01
The principle of the Van der Pol Duffing oscillator for state transition and for determining critical value is described, which has been studied to indicate that the application of the Van der Pol Duffing oscillator in weak signal detection is feasible. On the basis of this principle, an improved two-coupled differential Van der Pol Duffing oscillator is proposed which can identify signals under any frequency and ameliorate signal-to-noise ratio (SNR). The analytical methods of the proposed model and the construction of the proposed oscillator are introduced in detail. Numerical experiments on the properties of the proposed oscillator compared with those of the Van der Pol Duffing oscillator are carried out. Our numerical simulations have confirmed the analytical treatment. The results demonstrate that this novel oscillator has better detection performance than the Van der Pol Duffing oscillator.
Symmetry-broken states on networks of coupled oscillators
NASA Astrophysics Data System (ADS)
Jiang, Xin; Abrams, Daniel M.
2016-05-01
When identical oscillators are coupled together in a network, dynamical steady states are often assumed to reflect network symmetries. Here, we show that alternative persistent states may also exist that break the symmetries of the underlying coupling network. We further show that these symmetry-broken coexistent states are analogous to those dubbed "chimera states," which can occur when identical oscillators are coupled to one another in identical ways.
The mutual synchronization of coupled delayed feedback klystron oscillators
NASA Astrophysics Data System (ADS)
Emel'yanov, V. V.; Emelianova, Yu. P.; Ryskin, N. M.
2016-08-01
We report on the results of a numerical investigation of the synchronization of two coupled klystron oscillators with an external feedback circuit. Simulation has been carried out using the particle-in-cell method. We have also considered the results of a numerical analysis of an amplifier klystron and an isolated klystron oscillator, which make it possible to choose the optimal values of parameters of coupled klystrons. The structure of the synchronization domain for various parameters has been analyzed. The possibility of increasing the total output power with an appropriate choice of parameter of coupling between the oscillators has been revealed.
Switching dynamics of single and coupled VO2-based oscillators as elements of neural networks
NASA Astrophysics Data System (ADS)
Velichko, Andrey; Belyaev, Maksim; Putrolaynen, Vadim; Pergament, Alexander; Perminov, Valentin
2017-01-01
In the present paper, we report on the switching dynamics of both single and coupled VO2-based oscillators, with resistive and capacitive coupling, and explore the capability of their application in oscillatory neural networks. Based on these results, we further select an adequate SPICE model to describe the modes of operation of coupled oscillator circuits. Physical mechanisms influencing the time of forward and reverse electrical switching, that determine the applicability limits of the proposed model, are identified. For the resistive coupling, it is shown that synchronization takes place at a certain value of the coupling resistance, though it is unstable and a synchronization failure occurs periodically. For the capacitive coupling, two synchronization modes, with weak and strong coupling, are found. The transition between these modes is accompanied by chaotic oscillations. A decrease in the width of the spectrum harmonics in the weak-coupling mode, and its increase in the strong-coupling one, is detected. The dependences of frequencies and phase differences of the coupled oscillatory circuits on the coupling capacitance are found. Examples of operation of coupled VO2 oscillators as a central pattern generator are demonstrated.
Stable integrated hyper-parametric oscillator based on coupled optical microcavities.
Armaroli, Andrea; Feron, Patrice; Dumeige, Yannick
2015-12-01
We propose a flexible scheme based on three coupled optical microcavities that permits us to achieve stable oscillations in the microwave range, the frequency of which depends only on the cavity coupling rates. We find that the different dynamical regimes (soft and hard excitation) affect the oscillation intensity, but not their periods. This configuration may permit us to implement compact hyper-parametric sources on an integrated optical circuit with interesting applications in communications, sensing, and metrology.
A common lag scenario in quenching of oscillation in coupled oscillators
NASA Astrophysics Data System (ADS)
Suresh, K.; Sabarathinam, S.; Thamilmaran, K.; Kurths, Jürgen; Dana, Syamal K.
2016-08-01
A large parameter mismatch can induce amplitude death in two instantaneously coupled oscillators. Alternatively, a time delay in the coupling can induce amplitude death in two identical oscillators. We unify the mechanism of quenching of oscillation in coupled oscillators, either by a large parameter mismatch or a delay coupling, by a common lag scenario that is, surprisingly, different from the conventional lag synchronization. We present numerical as well as experimental evidence of this unknown kind of lag scenario when the lag increases with coupling and at a critically large value at a critical coupling strength, amplitude death emerges in two largely mismatched oscillators. This is analogous to amplitude death in identical systems with increasingly large coupling delay. In support, we use examples of the Chua oscillator and the Bonhoeffer-van der Pol system. Furthermore, we confirm this lag scenario during the onset of amplitude death in identical Stuart-Landau system under various instantaneous coupling forms, repulsive, conjugate, and a type of nonlinear coupling.
Opto-Electronic Oscillator and its Applications
NASA Technical Reports Server (NTRS)
Yao, X. S.; Maleki, L.
1996-01-01
We present the theoretical and experimental results of a new class of microwave oscillators called opto-electronic oscillators (OEO). We discuss techniques of achieving high stability single mode operation and demonstrate the applications of OEO in photonic communication systems.
Classification of attractors for systems of identical coupled Kuramoto oscillators
Engelbrecht, Jan R.; Mirollo, Renato
2014-03-15
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For N≠3 oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Classification of attractors for systems of identical coupled Kuramoto oscillators.
Engelbrecht, Jan R; Mirollo, Renato
2014-03-01
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For [Formula: see text] oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
Effect of spatial distribution on the synchronization in rings of coupled oscillators
NASA Astrophysics Data System (ADS)
Ma, Hongjing; Liu, Weiqing; Wu, Ye; Yang, Yixian; Xiao, Jinghua
2013-10-01
In this paper, the effects of spatial distribution of coupling on the synchronizability are explored in a ring of diffusively coupled oscillators. We find that the inhomogeneity and spatial arrangements of coupling strength have great impacts on the synchronizability. When the inhomogeneous coupling constants are spatially rearranged, the eigenvalues λ2 (the second largest eigenvalue of the coupling matrixes) for all possible spatial arrangements, which may describe the synchronizability of coupled oscillators, obey a log-normal distribution. The spatial arrangement of period 1 achieves the best synchronizability while that of period 2 has the worst one. In addition, the regimes of the effects of spatial distribution on synchronizability are analyzed by a ring of coupled Rossler systems. The spatial rearrangement of coupling has meaningful applications in the manipulation of self- organization for coupled systems.
Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators
NASA Technical Reports Server (NTRS)
Golubitsky, Martin; Stewart, Ian
1986-01-01
The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.
Coupling between ion-acoustic waves and neutrino oscillations.
Haas, Fernando; Pascoal, Kellen Alves; Mendonça, José Tito
2017-01-01
The work investigates the coupling between ion-acoustic waves and neutrino flavor oscillations in a nonrelativistic electron-ion plasma under the influence of a mixed neutrino beam. Neutrino oscillations are mediated by the flavor polarization vector dynamics in a material medium. The linear dispersion relation around homogeneous static equilibria is developed. When resonant with the ion-acoustic mode, the neutrino flavor oscillations can transfer energy to the plasma exciting a new fast unstable mode in extreme astrophysical scenarios. The growth rate and the unstable wavelengths are determined in typical type II supernova parameters. The predictions can be useful for a new indirect probe on neutrino oscillations in nature.
Coupling between ion-acoustic waves and neutrino oscillations
NASA Astrophysics Data System (ADS)
Haas, Fernando; Pascoal, Kellen Alves; Mendonça, José Tito
2017-01-01
The work investigates the coupling between ion-acoustic waves and neutrino flavor oscillations in a nonrelativistic electron-ion plasma under the influence of a mixed neutrino beam. Neutrino oscillations are mediated by the flavor polarization vector dynamics in a material medium. The linear dispersion relation around homogeneous static equilibria is developed. When resonant with the ion-acoustic mode, the neutrino flavor oscillations can transfer energy to the plasma exciting a new fast unstable mode in extreme astrophysical scenarios. The growth rate and the unstable wavelengths are determined in typical type II supernova parameters. The predictions can be useful for a new indirect probe on neutrino oscillations in nature.
The vertical oscillations of coupled magnets
NASA Astrophysics Data System (ADS)
Kewei, Li; Jiahuang, Lin; Yang, Kang Zi; Liang, Samuel Yee Wei; Wong Say Juan, Jeremias
2011-07-01
The International Young Physicists' Tournament (IYPT) is a worldwide, annual competition for high school students. This paper is adapted from the winning solution to Problem 14, Magnetic Spring, as presented in the final round of the 23rd IYPT in Vienna, Austria. Two magnets were arranged on top of each other on a common axis. One was fixed, while the other could move vertically. Various parameters of interest were investigated, including the effective gravitational acceleration, the strength, size, mass and geometry of the magnets, and damping of the oscillations. Despite its simplicity, this setup yielded a number of interesting and unexpected relations. The first stage of the investigation was concerned only with the undamped oscillations of small amplitudes, and the period of small amplitude oscillations was found to be dependent only on the eighth root of important magnet properties such as its strength and mass. The second stage sought to investigate more general oscillations. A numerical model which took into account magnet size, magnet geometry and damping effects was developed to model the general oscillations. Air resistance and friction were found to be significant sources of damping, while eddy currents were negligible.
Energetics of synchronization in coupled oscillators rotating on circular trajectories
NASA Astrophysics Data System (ADS)
Izumida, Yuki; Kori, Hiroshi; Seifert, Udo
2016-11-01
We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even and odd parts of the coupling function express the effect on collective and relative dynamics, respectively. We reveal that the odd part always decreases the dissipation upon synchronization, while the even part yields a characteristic square-root change of the dissipation near the bifurcation point whose sign depends on the specific system parameters. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that can be interpreted as a simple model of synchronization of coupled oscillators in a biophysical system. We show that the coupled Stokes spheres gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.
Coupling a Bose condensate to micromechanical oscillators
NASA Astrophysics Data System (ADS)
Kemp, Chandler; Fox, Eli; Flanz, Scott; Vengalattore, Mukund
2011-05-01
We describe the construction of a compact apparatus to investigate the interaction of a spinor Bose-Einstein condensate and a micromechanical oscillator. The apparatus uses a double magneto-optical trap, Raman sideband cooling, and evaporative cooling to rapidly produce a 87Rb BEC in close proximity to a high Q membrane. The micromotion of the membrane results in small Zeeman shifts at the location of the BEC due to a magnetic domain attached to the oscillator. Detection of this micromotion by the condensate results in a backaction on the membrane. We investigate prospects of using this backaction to generate nonclassical states of the mechanical oscillator. This work was funded by the DARPA ORCHID program.
Limits to detection of generalized synchronization in delay-coupled chaotic oscillators.
Kato, Hideyuki; Soriano, Miguel C; Pereda, Ernesto; Fischer, Ingo; Mirasso, Claudio R
2013-12-01
We study how reliably generalized synchronization can be detected and characterized from time-series analysis. To that end, we analyze synchronization in a generalized sense of delay-coupled chaotic oscillators in unidirectional ring configurations. The generalized synchronization condition can be verified via the auxiliary system approach; however, in practice, this might not always be possible. Therefore, in this study, widely used indicators to directly quantify generalized and phase synchronization from noise-free time series of two oscillators are employed complementarily to the auxiliary system approach. In our analysis, none of the indices provide the consistent results of the auxiliary system approach. Our findings indicate that it is a major challenge to directly detect synchronization in a generalized sense between two oscillators that are connected via a chain of other oscillators, even if the oscillators are identical. This has major consequences for the interpretation of the dynamics of coupled systems and applications thereof.
Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators
Locatelli, Nicolas; Hamadeh, Abbass; Abreu Araujo, Flavio; Belanovsky, Anatoly D.; Skirdkov, Petr N.; Lebrun, Romain; Naletov, Vladimir V.; Zvezdin, Konstantin A.; Muñoz, Manuel; Grollier, Julie; Klein, Olivier; Cros, Vincent; de Loubens, Grégoire
2015-01-01
Due to their nonlinear properties, spin transfer nano-oscillators can easily adapt their frequency to external stimuli. This makes them interesting model systems to study the effects of synchronization and brings some opportunities to improve their microwave characteristics in view of their applications in information and communication technologies and/or to design innovative computing architectures. So far, mutual synchronization of spin transfer nano-oscillators through propagating spinwaves and exchange coupling in a common magnetic layer has been demonstrated. Here we show that the dipolar interaction is also an efficient mechanism to synchronize neighbouring oscillators. We experimentally study a pair of vortex-based spin transfer nano-oscillators, in which mutual synchronization can be achieved despite a significant frequency mismatch between oscillators. Importantly, the coupling efficiency is controlled by the magnetic configuration of the vortices, as confirmed by an analytical model and micromagnetic simulations highlighting the physics at play in the synchronization process. PMID:26608230
Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators
NASA Astrophysics Data System (ADS)
Locatelli, Nicolas; Hamadeh, Abbass; Abreu Araujo, Flavio; Belanovsky, Anatoly D.; Skirdkov, Petr N.; Lebrun, Romain; Naletov, Vladimir V.; Zvezdin, Konstantin A.; Muñoz, Manuel; Grollier, Julie; Klein, Olivier; Cros, Vincent; de Loubens, Grégoire
2015-11-01
Due to their nonlinear properties, spin transfer nano-oscillators can easily adapt their frequency to external stimuli. This makes them interesting model systems to study the effects of synchronization and brings some opportunities to improve their microwave characteristics in view of their applications in information and communication technologies and/or to design innovative computing architectures. So far, mutual synchronization of spin transfer nano-oscillators through propagating spinwaves and exchange coupling in a common magnetic layer has been demonstrated. Here we show that the dipolar interaction is also an efficient mechanism to synchronize neighbouring oscillators. We experimentally study a pair of vortex-based spin transfer nano-oscillators, in which mutual synchronization can be achieved despite a significant frequency mismatch between oscillators. Importantly, the coupling efficiency is controlled by the magnetic configuration of the vortices, as confirmed by an analytical model and micromagnetic simulations highlighting the physics at play in the synchronization process.
NASA Astrophysics Data System (ADS)
Wan, Yu; Jin, Kai; Ahmad, Talha J.; Black, Michael J.; Xu, Zhiping
2017-03-01
Fluidic environment is encountered for mechanical components in many circumstances, which not only damps the oscillation but also modulates their dynamical behaviors through hydrodynamic interactions. In this study, we examine energy transfer and motion synchronization between two mechanical micro-oscillators by performing thermal lattice-Boltzmann simulations. The coefficient of inter-oscillator energy transfer is measured to quantify the strength of microhydrodynamic coupling, which depends on their distance and fluid properties such as density and viscosity. Synchronized motion of the oscillators is observed in the simulations for typical parameter sets in relevant applications, with the formation and loss of stable anti-phase synchronization controlled by the oscillating frequency, amplitude, and hydrodynamic coupling strength. The critical ranges of key parameters to assure efficient energy transfer or highly synchronized motion are predicted. These findings could be used to advise mechanical design of passive and active devices that operate in fluid.
Coupled domain wall oscillations in magnetic cylindrical nanowires
Murapaka, Chandrasekhar; Goolaup, S.; Purnama, I.; Lew, W. S.
2015-02-07
We report on transverse domain wall (DW) dynamics in two closely spaced cylindrical nanowires. The magnetostatically coupled DWs are shown to undergo an intrinsic oscillatory motion along the nanowire length in addition to their default rotational motion. In the absence of external forces, the amplitude of the DW oscillation is governed by the change in the frequency of the DW rotation. It is possible to sustain the DW oscillations by applying spin-polarized current to the nanowires to balance the repulsive magnetostatic coupling. The current density required to sustain the DW oscillation is found to be in the order of 10{sup 5 }A/cm{sup 2}. Morover, our analysis of the oscillation reveals that the DWs in cylindrical nanowires possess a finite mass.
NASA Astrophysics Data System (ADS)
Yu, Da-ren; Wei, Li-qiu; Ding, Yong-jie; Han, Ke; Yan, Guo-jun; Qi, Feng-yan
2007-11-01
In order to study the physical mechanism of an oscillation newly discovered by the Harbin Institute of Technology Plasma Propulsion Lab (HPPL) in the range of hundreds of kHz to several MHz, Hall thrusters with different magnetic coils are studied by changing one of the following three parameters: discharge voltage, anode flow and coil current, directly measuring the coil current and measuring plasma oscillations related to coil current oscillation with the Langmuir probe. Experimental results indicated that in the discharge process of a Hall thruster the broadband turbulence of the Hall current causes an unstable spatial magnetic field and this field causes the magnetic circuit to resonate as an equivalent high level resistance-inductance-capacitance (RLC) network. As the response of the network, the oscillation of the coil current has a large oscillating component at the natural frequencies of the network. Also, the oscillation of coil current has an effect on the discharge process at the same time, so that they reach a self-consistent equilibrium state. As a result of such a coupling, both coil current and the discharge current exhibit their oscillating component at the natural frequencies of the magnetic circuit. It is therefore concluded that the newly discovered oscillation is caused by the coupling between the magnetic circuit and the discharge circuit.
Birth of oscillation in coupled non-oscillatory Rayleigh-Duffing oscillators
NASA Astrophysics Data System (ADS)
Guin, A.; Dandapathak, M.; Sarkar, S.; Sarkar, B. C.
2017-01-01
We have studied the dynamics of two bilaterally-coupled non-oscillatory Rayleigh-Duffing oscillators (RDOs). With the increase of coupling factor (CF) between RDOs, birth of periodic oscillations observed. For increased values of CF, dynamics becomes chaotic through a quasi-periodicroute but for even higher CF, synchronized stable periodic oscillations in RDOs are found. Taking direct and anti-diffusive coupling cases into consideration, we derive conditions for periodic bifurcation in parameter space analytically and verified them through numerical solution of system equations. Numerical simulation is also used to predict system states in two parameter space involving CF and linear damping parameter of RDOs. It indicates non-oscillatory, periodic, quasi-periodic and chaotic zones of system dynamics. Qualitative explanation of the simulated dynamics is given using homoclinic perturbation theory. Hardware experiment is performed on analog circuits simulating RDO model and obtained results confirm the predictions regarding birth of periodic oscillation and other features of system dynamics. Experimental results examining onset of oscillations in two under-biased bi-laterally coupled X-band Gunn oscillators (which are modelled as RDOs) is presented in support of the analysis.
Link weight evolution in a network of coupled chemical oscillators
NASA Astrophysics Data System (ADS)
Ke, Hua; Tinsley, Mark R.; Steele, Aaron; Wang, Fang; Showalter, Kenneth
2014-05-01
Link weight evolution is studied in a network of coupled chemical oscillators. Oscillators are perturbed by adjustments in imposed light intensity based on excitatory or inhibitory links to other oscillators undergoing excitation. Experimental and modeling studies demonstrate that the network is capable of producing sustained coordinated activity. The individual nodes of the network exhibit incoherent firing events; however, a dominant frequency can be discerned within the collective signal by Fourier analysis. The introduction of spike-timing-dependent plasticity yields a network that evolves to a stable unimodal link weight distribution.
Emergence of a negative resistance in noisy coupled linear oscillators
NASA Astrophysics Data System (ADS)
Quiroz-Juárez, M. A.; Aragón, J. L.; León-Montiel, R. de J.; Vázquez-Medina, R.; Domínguez-Juárez, J. L.; Quintero-Torres, R.
2016-12-01
We report on the experimental observation of an emerging negative resistance in a system of coupled linear electronic RLC harmonic oscillators under the influence of multiplicative noise with long correlation time. When two oscillators are coupled by a noisy inductor, an analysis in the Fourier space of the electrical variables unveils the presence of an effective negative resistance, which acts as an energy transport facilitator. This might constitute a simple explanation of the now fashionable problem of energy transport assisted by noise in classical systems. The experimental setup is based on the working principle of an analog computer and by itself constitutes a versatile platform for studying energy transport in noisy systems by means of coupled electrical oscillator systems.
Enhancing the stability of the synchronization of multivariable coupled oscillators
NASA Astrophysics Data System (ADS)
Sevilla-Escoboza, R.; Gutiérrez, R.; Huerta-Cuellar, G.; Boccaletti, S.; Gómez-Gardeñes, J.; Arenas, A.; Buldú, J. M.
2015-09-01
Synchronization processes in populations of identical networked oscillators are the focus of intense studies in physical, biological, technological, and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of Rössler-like oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.
Dynamics of phase oscillators with generalized frequency-weighted coupling
NASA Astrophysics Data System (ADS)
Xu, Can; Gao, Jian; Xiang, Hairong; Jia, Wenjing; Guan, Shuguang; Zheng, Zhigang
2016-12-01
Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during recent years. In this paper, we extend the Kuramoto model by considering a particular heterogeneous coupling scheme in an ensemble of phase oscillators, where each oscillator pair interacts with different coupling strength that is weighted by a general function of the natural frequency. The Kuramoto theory for the transition to synchronization can be explicitly generalized, such as the expression for the critical coupling strength. Also, a self-consistency approach is developed to predict the stationary states in the thermodynamic limit. Moreover, Landau damping effects are further revealed by means of linear stability analysis and resonance poles theory below the critical threshold, which turns to be far more generic. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings.
Clustering and phase synchronization in populations of coupled phase oscillators
NASA Astrophysics Data System (ADS)
Cascallares, Guadalupe; Gleiser, Pablo M.
2015-10-01
In many species daily rhythms are endogenously generated by groups of coupled neurons that play the role of a circadian pacemaker. The adaptation of the circadian clock to environmental and seasonal changes has been proposed to be regulated by a dual oscillator system. In order to gain insight into this model, we analyzed the synchronization properties of two fully coupled groups of Kuramoto oscillators. Each group has an internal coupling parameter and the interaction between the two groups can be controlled by two parameters allowing for symmetric or non-symmetric coupling. We show that even for such a simple model counterintuitive behaviours take place, such as a global decrease in synchrony when the coupling between the groups is increased. Through a detailed analysis of the local synchronization processes we explain this behaviour.
Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments
NASA Astrophysics Data System (ADS)
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2015-07-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
Chimera states in purely local delay-coupled oscillators.
Bera, Bidesh K; Ghosh, Dibakar
2016-05-01
We study the existence of chimera states in a network of locally coupled chaotic and limit-cycle oscillators. The necessary condition for chimera state in purely local coupled oscillators is discussed. At first, we numerically observe the existence of chimera or multichimera states in the locally coupled Hindmarsh-Rose neuron model. We find that delay time in the nonlinear local coupling reduces the domain of the coherent island in the parameter space of the synaptic coupling strength and time delay, and thus the coherent region can be completely eliminated once the time delay exceeds a certain threshold. We then consider another form of nonlinearity in the local coupling, and the existence of chimera states is observed in the time-delayed Mackey-Glass system and in a Van der Pol oscillator. We also discuss the effect of time delay in local coupling for the existence of chimera states in Mackey-Glass systems. The nonlinearity present in the coupling function plays a key role in the emergence of chimera or multichimera states. A phase diagram for the chimera state is identified over a wide parameter space.
Chimera states in purely local delay-coupled oscillators
NASA Astrophysics Data System (ADS)
Bera, Bidesh K.; Ghosh, Dibakar
2016-05-01
We study the existence of chimera states in a network of locally coupled chaotic and limit-cycle oscillators. The necessary condition for chimera state in purely local coupled oscillators is discussed. At first, we numerically observe the existence of chimera or multichimera states in the locally coupled Hindmarsh-Rose neuron model. We find that delay time in the nonlinear local coupling reduces the domain of the coherent island in the parameter space of the synaptic coupling strength and time delay, and thus the coherent region can be completely eliminated once the time delay exceeds a certain threshold. We then consider another form of nonlinearity in the local coupling, and the existence of chimera states is observed in the time-delayed Mackey-Glass system and in a Van der Pol oscillator. We also discuss the effect of time delay in local coupling for the existence of chimera states in Mackey-Glass systems. The nonlinearity present in the coupling function plays a key role in the emergence of chimera or multichimera states. A phase diagram for the chimera state is identified over a wide parameter space.
Coupled, Active Oscillators and Lizard Otoacoustic Emissions
NASA Astrophysics Data System (ADS)
Bergevin, Christopher; Velenovsky, David S.; Bonine, Kevin E.
2011-11-01
The present study empirically explores the relationship between spontaneous otoacoustic emissions (SOAEs) and stimulus-frequency emissions (SFOAEs) in lizards, an ideal group for such research given their relatively simple inner ear (e.g., lack of basilar membrane traveling waves), diverse morphology across species/families (e.g., tectorial membrane structure) and robust emissions. In a nutshell, our results indicate that SFOAEs evoked using low-level tones are intimately related to underlying SOAE activity, and appear to represent the entrained response of active oscillators closely tuned to the probe frequency. The data described here indicate several essential features that are desirable to capture in theoretical models for auditory transduction in lizards, and potentially represent generic properties at work in many different classes of "active" ears.
Coupling among three chemical oscillators: Synchronization, phase death, and frustration
NASA Astrophysics Data System (ADS)
Yoshimoto, Minoru; Yoshikawa, Kenichi; Mori, Yoshihito
1993-02-01
Various modes in three coupled chemical oscillators in a triangular arrangement were observed. As a well-defined nonlinear oscillator, the Belousov-Zhabotinsky reaction was studied in a continuous-flow stirred tank reactor (CSTR). Coupling among CSTR's was performed by mass exchange. The coupling strength was quantitatively controlled by changing the flow rate of reacting solutions among the three CSTR's using peristaltic pumps between each pair of the reactors. As a key parameter to control the model of coupling, we changed the symmetry of the interaction between the oscillators. In the case of the symmetric coupling, a quasiperiodic state or a biperiodic mode, an all-death mode and two kinds of synchronized modes appeared, depending on the coupling strength. On the other hand, under the asymmetric coupling, a quasiperiodic state or a biperiodic mode, an all death mode and four kinds of synchronized modes appeared. Those modes have been discussed in relation to the idea of ``frustration'' in the Ising spin system, where the three-phase mode appears as a transition from the Ising spin system to the XY spin system.
Quantum synchronization of chaotic oscillator behaviors among coupled BEC-optomechanical systems
NASA Astrophysics Data System (ADS)
Li, Wenlin; Li, Chong; Song, Heshan
2017-03-01
We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.
Internal wave--vorticity coupling for an oscillating disk
NASA Astrophysics Data System (ADS)
Voisin, Bruno; Joubaud, Sylvain; Dauxois, Thierry
2011-11-01
In a density-stratified fluid, viscosity couples internal waves with vertical vorticity. So far this coupling used to be neglected in analytical studies and only the viscous attenuation and spreading of the waves was taken into account, except in a very recent study of the oscillations of a horizontal circular disk. We investigate the relations between the previous analytical approaches of the disk, considering either inviscid or viscous propagation of the waves and either free- or no-slip conditions at the disk, and compare their output with an original approach based on the boundary integral method. In particular, the role of the Stokes number is clarified. The analytical predictions are compared with contact measurements for vertical oscillations and with original PIV measurements and visualizations for both vertical and horizontal oscillations. Supported by grant PIWO of the ANR (France).
Experimental Evidence on Intermittent Lag Synchronization in Coupled Chua's Oscillators
NASA Astrophysics Data System (ADS)
Roy, P. K.; Dana, S. K.
2003-08-01
Phase synchronization (PS) in coupled chaotic oscillators has been investigated numerically in Lorenz, Rossler models and also experimentally in cardiorespiratory systems by many researchers. In non-identical oscillators, which is a reality, complete synchronization (CS) of amplitude and phase is difficult to arrive at. Lag synchronization (LS) is an intermediate step between complete (CS) and PS. PS shows promises in communication, in the context of pulse position modulation, in homoclinic chaotic systems. As has been observed earlier by others in numerical experiments that there is an intermittent region between PS and LS. This intermediate region is defined as the intermittent lag synchronization (ILS). Experimental evidence on both PS and ILS using two coupled Chua's oscillator (non-identical) is reported here.
Raman-Suppressing Coupling for Optical Parametric Oscillator
NASA Technical Reports Server (NTRS)
Savchenkov, Anatoliy; Maleki, Lute; Matsko, Andrey; Rubiola, Enrico
2007-01-01
A Raman-scattering-suppressing input/ output coupling scheme has been devised for a whispering-gallery-mode optical resonator that is used as a four-wave-mixing device to effect an all-optical parametric oscillator. Raman scattering is undesired in such a device because (1) it is a nonlinear process that competes with the desired nonlinear four-wave conversion process involved in optical parametric oscillation and (2) as such, it reduces the power of the desired oscillation and contributes to output noise. The essence of the present input/output coupling scheme is to reduce output loading of the desired resonator modes while increasing output loading of the undesired ones.
Cold atoms coupled with mechanical oscillators
NASA Astrophysics Data System (ADS)
Valencia, Jose; Montoya, Cris; Ranjit, Gambhir; Geraci, Andrew; Eardley, Matt; Kitching, John
2015-05-01
Mechanical resonators can be used to probe and manipulate atomic spins with nanometer spatial resolution and single-spin sensitivity, ultimately enabling new approaches in neutral-atom quantum computation, quantum simulation, or precision sensing. We describe our experiment that manipulates the spin of trapped, cold Rb atoms using magnetic material on a cantilever. Cold atoms can also be used as a coolant for mechanical resonators: we estimate that ground state cooling of an optically trapped nano-sphere is achievable when starting at room temperature, by sympathetic cooling of a cold atomic gas optically coupled to the nanoparticle.
Dynamics of globally coupled oscillators: Progress and perspectives
NASA Astrophysics Data System (ADS)
Pikovsky, Arkady; Rosenblum, Michael
2015-09-01
In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches.
Dynamics of finite-size networks of coupled oscillators
NASA Astrophysics Data System (ADS)
Buice, Michael; Chow, Carson
2010-03-01
Mean field models of coupled oscillators do not adequately capture the dynamics of large but finite size networks. For example, the incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N -> infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model. We also demonstrate this approach with a system of pulse coupled theta neurons and describe the stability of the population activity.
Golden Ratio in a Coupled-Oscillator Problem
ERIC Educational Resources Information Center
Moorman, Crystal M.; Goff, John Eric
2007-01-01
The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.
String-Coupled Pendulum Oscillators: Theory and Experiment.
ERIC Educational Resources Information Center
Moloney, Michael J.
1978-01-01
A coupled-oscillator system is given which is readily set up, using only household materials. The normal-mode analysis of this system is worked out, and an experiment or demonstration is recommended in which one verifies the theory by measuring two times and four lengths. (Author/GA)
Wu, Wei; Chen, Tianping
2009-12-01
Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. In 1990, Mirollo and Strogatz proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact, when transmission delays are introduced, the dynamic behaviors of pulse-coupled networks change a lot. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. A concept of synchronization, named weak asymptotic synchronization, which is weaker than asymptotic synchronization, is proposed. We prove that for pulse-coupled oscillator networks with delayed excitatory coupling, weak asymptotic synchronization cannot occur.
Chou, Chung-Hsien; Yu, Ting; Hu, B L
2008-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.
Three People Can Synchronize as Coupled Oscillators during Sports Activities
Yokoyama, Keiko; Yamamoto, Yuji
2011-01-01
We experimentally investigated the synchronized patterns of three people during sports activities and found that the activity corresponded to spatiotemporal patterns in rings of coupled biological oscillators derived from symmetric Hopf bifurcation theory, which is based on group theory. This theory can provide catalogs of possible generic spatiotemporal patterns irrespective of their internal models. Instead, they are simply based on the geometrical symmetries of the systems. We predicted the synchronization patterns of rings of three coupled oscillators as trajectories on the phase plane. The interactions among three people during a 3 vs. 1 ball possession task were plotted on the phase plane. We then demonstrated that two patterns conformed to two of the three patterns predicted by the theory. One of these patterns was a rotation pattern (R) in which phase differences between adjacent oscillators were almost 2π/3. The other was a partial anti-phase pattern (PA) in which the two oscillators were anti-phase and the third oscillator frequency was dead. These results suggested that symmetric Hopf bifurcation theory could be used to understand synchronization phenomena among three people who communicate via perceptual information, not just physically connected systems such as slime molds, chemical reactions, and animal gaits. In addition, the skill level in human synchronization may play the role of the bifurcation parameter. PMID:21998570
Speech encoding by coupled cortical theta and gamma oscillations
Hyafil, Alexandre; Fontolan, Lorenzo; Kabdebon, Claire; Gutkin, Boris; Giraud, Anne-Lise
2015-01-01
Many environmental stimuli present a quasi-rhythmic structure at different timescales that the brain needs to decompose and integrate. Cortical oscillations have been proposed as instruments of sensory de-multiplexing, i.e., the parallel processing of different frequency streams in sensory signals. Yet their causal role in such a process has never been demonstrated. Here, we used a neural microcircuit model to address whether coupled theta–gamma oscillations, as observed in human auditory cortex, could underpin the multiscale sensory analysis of speech. We show that, in continuous speech, theta oscillations can flexibly track the syllabic rhythm and temporally organize the phoneme-level response of gamma neurons into a code that enables syllable identification. The tracking of slow speech fluctuations by theta oscillations, and its coupling to gamma-spiking activity both appeared as critical features for accurate speech encoding. These results demonstrate that cortical oscillations can be a key instrument of speech de-multiplexing, parsing, and encoding. DOI: http://dx.doi.org/10.7554/eLife.06213.001 PMID:26023831
Cyanobacterial clock, a stable phase oscillator with negligible intercellular coupling
Amdaoud, M.; Vallade, M.; Weiss-Schaber, C.; Mihalcescu, I.
2007-01-01
Accuracy in cellular function has to be achieved despite random fluctuations (noise) in the concentrations of different molecular constituents inside and outside the cell. The circadian oscillator in cyanobacteria is an example of resilience to noise. This resilience could be either the consequence of intercellular communication or the intrinsic property of the built-in biochemical network. Here we investigate the intercellular coupling hypothesis. A short theoretical depiction of interacting noisy phase oscillators, confirmed by numerical simulations, allows us to discriminate the effect of coupling from noise. Experimentally, by studying the phase of concurrent populations of different initial phases, we evaluate a very small upper limit of the intercellular coupling strength. In addition, in situ entrainment experiments confirm our ability to detect a coupling of the circadian oscillator to an external force and to describe explicitly the dynamic change of the mean phase. We demonstrate, therefore, that the cyanobacterial clock stability is a built-in property as the intercellular coupling effect is negligible. PMID:17438272
Collective cell movement promotes synchronization of coupled genetic oscillators.
Uriu, Koichiro; Morelli, Luis G
2014-07-15
Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.
Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators
Uriu, Koichiro; Morelli, Luis G.
2014-01-01
Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns. PMID:25028893
Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect
NASA Astrophysics Data System (ADS)
Li, Xiao-Wen; Zheng, Zhi-Gang
2007-02-01
Phase synchronization of two linearly coupled Rossler oscillators with parameter misfits is explored. It is found that depending on parameter mismatches, the synchronization of phases exhibits different manners. The synchronization regime can be divided into three regimes. For small mismatches, the amplitude-insensitive regime gives the phase-dominant synchronization; When the parameter misfit increases, the amplitudes and phases of oscillators are correlated, and the amplitudes will dominate the synchronous dynamics for very large mismatches. The lag time among phases exhibits a power law when phase synchronization is achieved.
Time Correlations in Mode Hopping of Coupled Oscillators
NASA Astrophysics Data System (ADS)
Heltberg, Mathias L.; Krishna, Sandeep; Jensen, Mogens H.
2017-02-01
We study the dynamics in a system of coupled oscillators when Arnold Tongues overlap. By varying the initial conditions, the deterministic system can be attracted to different limit cycles. Adding noise, the mode hopping between different states become a dominating part of the dynamics. We simplify the system through a Poincare section, and derive a 1D model to describe the dynamics. We explain that for some parameter values of the external oscillator, the time distribution of occupancy in a state is exponential and thus memoryless. In the general case, on the other hand, it is a sum of exponential distributions characteristic of a system with time correlations.
Coupled Langmuir oscillations in 2-dimensional quantum plasmas
Akbari-Moghanjoughi, M.
2014-03-15
In this work, we present a hydrodynamic model to study the coupled quantum electron plasma oscillations (QEPO) for two dimensional (2D) degenerate plasmas, which incorporates all the essential quantum ingredients such as the statistical degeneracy pressure, electron-exchange, and electron quantum diffraction effect. Effects of diverse physical aspects like the electronic band-dispersion effect, the electron exchange-correlations and the quantum Bohm-potential as well as other important plasma parameters such as the coupling parameter (plasma separation) and the plasma electron number-densities on the linear response of the coupled system are investigated. By studying three different 2D plasma coupling types, namely, graphene-graphene, graphene-metalfilm, and metalfilm-metalfilm coupling configurations, it is remarked that the collective quantum effects can influence the coupled modes quite differently, depending on the type of the plasma configuration. It is also found that the slow and fast QEPO frequency modes respond very differently to the change in plasma parameters. Current findings can help in understanding of the coupled density oscillations in multilayer graphene, graphene-based heterojunctions, or nanofabricated integrated circuits.
Zanotto, Simone; Tredicucci, Alessandro
2016-01-01
In this article we discuss a model describing key features concerning the lineshapes and the coherent absorption conditions in Fano-resonant dissipative coupled oscillators. The model treats on the same footing the weak and strong coupling regimes, and includes the critical coupling concept, which is of great relevance in numerous applications; in addition, the role of asymmetry is thoroughly analyzed. Due to the wide generality of the model, which can be adapted to various frameworks like nanophotonics, plasmonics, and optomechanics, we envisage that the analytical formulas presented here will be crucial to effectively design devices and to interpret experimental results. PMID:27091489
NASA Astrophysics Data System (ADS)
Zanotto, Simone; Tredicucci, Alessandro
2016-04-01
In this article we discuss a model describing key features concerning the lineshapes and the coherent absorption conditions in Fano-resonant dissipative coupled oscillators. The model treats on the same footing the weak and strong coupling regimes, and includes the critical coupling concept, which is of great relevance in numerous applications; in addition, the role of asymmetry is thoroughly analyzed. Due to the wide generality of the model, which can be adapted to various frameworks like nanophotonics, plasmonics, and optomechanics, we envisage that the analytical formulas presented here will be crucial to effectively design devices and to interpret experimental results.
Synchronization of two memristively coupled van der Pol oscillators
NASA Astrophysics Data System (ADS)
Ignatov, M.; Hansen, M.; Ziegler, M.; Kohlstedt, H.
2016-02-01
The objective of this letter is to convey two essential principles of biological computing—synchronization and memory—in an electronic circuit with two van der Pol (vdP) oscillators coupled via a memristive device. The coupling was mediated by connecting the gate terminals of two programmable unijunction transistors through a resistance-capacitance network comprising an Ag-TiOx-Al memristive device. In the high resistance state the memristance was in the order of MΩ, which leads to two independent self-sustained oscillators characterized by the different frequencies f1 and f2 and no phase relation between the oscillations. Depending on the mediated pulse amplitude, the memristive device switched to the low resistance state after a few cycles and a frequency adaptation and phase locking were observed. The experimental results are underlined by theoretically considering a system of two coupled vdP equations. This experiment may pave the way to larger neuromorphic networks in which the coupling parameters (through memristive devices) can vary in time and strength and are able to remember the history of applied electrical potentials.
Collective oscillations and coupled modes in confined microfluidic droplet arrays
NASA Astrophysics Data System (ADS)
Schiller, Ulf D.; Fleury, Jean-Baptiste; Seemann, Ralf; Gompper, Gerhard
Microfluidic droplets have a wide range of applications ranging from analytic assays in cellular biology to controlled mixing in chemical engineering. Ensembles of microfluidic droplets are interesting model systems for non-equilibrium many-body phenomena. When flowing in a microchannel, trains of droplets can form microfluidic crystals whose dynamics are governed by long-range hydrodynamic interactions and boundary effects. In this contribution, excitation mechanisms for collective waves in dense and confined microfluidic droplet arrays are investigated by experiments and computer simulations. We demonstrate that distinct modes can be excited by creating specific `defect' patterns in flowing droplet trains. While longitudinal modes exhibit a short-lived cascade of pairs of laterally displacing droplets, transversely excited modes form propagating waves that behave like microfluidic phonons. We show that the confinement induces a coupling between longitudinal and transverse modes. We also investigate the life time of the collective oscillations and discuss possible mechanisms for the onset of instabilities. Our results demonstrate that microfluidic phonons can exhibit effects beyond the linear theory, which can be studied particularly well in dense and confined systems. This work was supported by Deutsche Forschungsgemeinschaft under Grant No. SE 1118/4.
Coexistence of Quantized, Time Dependent, Clusters in Globally Coupled Oscillators
NASA Astrophysics Data System (ADS)
Bi, Hongjie; Hu, Xin; Boccaletti, S.; Wang, Xingang; Zou, Yong; Liu, Zonghua; Guan, Shuguang
2016-11-01
We report on a novel collective state, occurring in globally coupled nonidentical oscillators in the proximity of the point where the transition from the system's incoherent to coherent phase converts from explosive to continuous. In such a state, the oscillators form quantized clusters, where neither their phases nor their instantaneous frequencies are locked. The oscillators' instantaneous speeds are different within the clusters, but they form a characteristic cusped pattern and, more importantly, they behave periodically in time so that their average values are the same. Given its intrinsic specular nature with respect to the recently introduced Chimera states, the phase is termed the Bellerophon state. We provide an analytical and numerical description of Bellerophon states, and furnish practical hints on how to seek them in a variety of experimental and natural systems.
Experimental observation of a transition from amplitude to oscillation death in coupled oscillators
NASA Astrophysics Data System (ADS)
Banerjee, Tanmoy; Ghosh, Debarati
2014-06-01
We report the experimental evidence of an important transition scenario, namely the transition from amplitude death (AD) to oscillation death (OD) state in coupled limit cycle oscillators. We consider two Van der Pol oscillators coupled through mean-field diffusion and show that this system exhibits a transition from AD to OD, which was earlier shown for Stuart-Landau oscillators under the same coupling scheme [T. Banerjee and D. Ghosh, Phys. Rev. E 89, 052912 (2014), 10.1103/PhysRevE.89.052912]. We show that the AD-OD transition is governed by the density of mean-field and beyond a critical value this transition is destroyed; further, we show the existence of a nontrivial AD state that coexists with OD. Next, we implement the system in an electronic circuit and experimentally confirm the transition from AD to OD state. We further characterize the experimental parameter zone where this transition occurs. The present study may stimulate the search for the practical systems where this important transition scenario can be observed experimentally.
Plykin-type attractor in nonautonomous coupled oscillators
NASA Astrophysics Data System (ADS)
Kuznetsov, Sergey P.
2009-03-01
A system of two coupled nonautonomous oscillators is considered. Dynamics of complex amplitudes is governed by differential equations with periodic piecewise continuous dependence of the coefficients on time. The Poincaré map is derived explicitly. With the exclusion of the overall phase, on which the evolution of other variables does not depend, the Poincaré map is reduced to three-dimensional (3D) mapping. It possesses an attractor of Plykin-type located on an invariant sphere. Computer verification of the cone criterion confirms the hyperbolic nature of the attractor in the 3D map. Some results of numerical studies of the dynamics for the coupled oscillators are presented, including the attractor portraits, Lyapunov exponents, and the power spectral density.
Spiral wave chimeras in locally coupled oscillator systems
NASA Astrophysics Data System (ADS)
Li, Bing-Wei; Dierckx, Hans
2016-02-01
The recently discovered chimera state involves the coexistence of synchronized and desynchronized states for a group of identical oscillators. In this work, we show the existence of (inwardly) rotating spiral wave chimeras in the three-component reaction-diffusion systems where each element is locally coupled by diffusion. A transition from spiral waves with the smooth core to spiral wave chimeras is found as we change the local dynamics of the system or as we gradually increase the diffusion coefficient of the activator. Our findings on the spiral wave chimera in the reaction-diffusion systems suggest that spiral chimera states may be found in chemical and biological systems that can be modeled by a large population of oscillators indirectly coupled via a diffusive environment.
Transients in the synchronization of asymmetrically coupled oscillator arrays
NASA Astrophysics Data System (ADS)
Cantos, C. E.; Hammond, D. K.; Veerman, J. J. P.
2016-09-01
We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we show that minimizing the transients requires considering non-symmetric coupling, and that within Ω the computed linear growth in N of the transients is independent of (reasonable) boundary conditions.
Environmental coupling in ecosystems: From oscillation quenching to rhythmogenesis
NASA Astrophysics Data System (ADS)
Arumugam, Ramesh; Dutta, Partha Sharathi; Banerjee, Tanmoy
2016-08-01
How landscape fragmentation affects ecosystems diversity and stability is an important and complex question in ecology with no simple answer, as spatially separated habitats where species live are highly dynamic rather than just static. Taking into account the species dispersal among nearby connected habitats (or patches) through a common dynamic environment, we model the consumer-resource interactions with a ring type coupled network. By characterizing the dynamics of consumer-resource interactions in a coupled ecological system with three fundamental mechanisms such as the interaction within the patch, the interaction between the patches, and the interaction through a common dynamic environment, we report the occurrence of various collective behaviors. We show that the interplay between the dynamic environment and the dispersal among connected patches exhibits the mechanism of generation of oscillations, i.e., rhythmogenesis, as well as suppression of oscillations, i.e., amplitude death and oscillation death. Also, the transition from homogeneous steady state to inhomogeneous steady state occurs through a codimension-2 bifurcation. Emphasizing a network of a spatially extended system, the coupled model exposes the collective behavior of a synchrony-stability relationship with various synchronization occurrences such as in-phase and out-of-phase.
Tune Determination of Strongly Coupled Betatron Oscillations in a Fast-Ramping Synchrotron
Alexahin, Y.; Gianfelice-Wendt, E.; Marsh, W; Triplett, K.; /Fermilab
2012-05-01
Tune identification -- i.e. attribution of the spectral peak to a particular normal de of oscillations -- can present a significant difficulty in the presence of strong transverse coupling when the normal mode with a lower damping rate dominates spectra of Turn-by-Turn oscillations in both planes. The introduced earlier phased sum algorithm helped to recover the weaker normal mode signal from the noise, but by itself proved to be insufficient for automatic peak identification in the case of close phase advance distribution in both planes. To resolve this difficulty we modified the algorithm by taking and analyzing Turn-by-Turn data for two different ramps with the beam oscillation excited in each plane in turn. Comparison of relative amplitudes of Fourier components allows for correct automatic tune identification. The proposed algorithm was implemented in the Fermilab Booster B38 console application and successfully used for tune, coupling and chromaticity measurements.
Chimera and phase-cluster states in populations of coupled chemical oscillators
NASA Astrophysics Data System (ADS)
Tinsley, Mark R.; Nkomo, Simbarashe; Showalter, Kenneth
2012-09-01
Populations of coupled oscillators may exhibit two coexisting subpopulations, one with synchronized oscillations and the other with unsynchronized oscillations, even though all of the oscillators are coupled to each other in an equivalent manner. This phenomenon, discovered about ten years ago in theoretical studies, was then further characterized and named the chimera state after the Greek mythological creature made up of different animals. The highly counterintuitive coexistence of coherent and incoherent oscillations in populations of identical oscillators, each with an equivalent coupling structure, inspired great interest and a flurry of theoretical activity. Here we report on experimental studies of chimera states and their relation to other synchronization states in populations of coupled chemical oscillators. Our experiments with coupled Belousov-Zhabotinsky oscillators and corresponding simulations reveal chimera behaviour that differs significantly from the behaviour found in theoretical studies of phase-oscillator models.
Wu, Wei; Liu, Bo; Chen, Tianping
2010-09-01
In this paper, we investigate the firing behaviors in networks of pulse-coupled oscillators with delayed excitatory coupling according to the coupling strength epsilon and delay tau. We find out that the parameter space A={(epsilon,tau)|0
Synchronization of phase oscillators with frequency-weighted coupling
Xu, Can; Sun, Yuting; Gao, Jian; Qiu, Tian; Zheng, Zhigang; Guan, Shuguang
2016-01-01
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all couplings. A rigorous mean-field analysis is implemented to predict the possible steady states. Furthermore, a detailed linear stability analysis proves that the incoherent state is only neutrally stable below the synchronization threshold. Nevertheless, interestingly, the amplitude of the order parameter decays exponentially (at least for short time) in this regime, resembling the Landau damping effect in plasma physics. Moreover, the explicit expression for the critical coupling strength is determined by both the mean-field method and linear operator theory. The mechanism of bifurcation for the incoherent state near the critical point is further revealed by the amplitude expansion theory, which shows that the oscillating standing wave state could also occur in this model for certain frequency distributions. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings. PMID:26903110
Different kinds of chimera death states in nonlocally coupled oscillators
NASA Astrophysics Data System (ADS)
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2016-05-01
We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multichimera death state, type I periodic chimera death (PCD) state, and type II periodic chimera death state. We also find that the number of periodic domains in both types of PCD states decreases exponentially with an increase of coupling range and obeys a power law under nonlocal coupling. Additionally, we also analyze the structural changes of chimera death states by reducing the system of dynamical equations to a phase model through the phase reduction. We also briefly study the role of nonisochronicity parameter on chimera states, where the existence of a multichimera state with respect to the coupling range is pointed out. Moreover, we also analyze the robustness of the chimera death state to perturbations in the natural frequencies of the oscillators.
Different kinds of chimera death states in nonlocally coupled oscillators.
Premalatha, K; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M
2016-05-01
We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multichimera death state, type I periodic chimera death (PCD) state, and type II periodic chimera death state. We also find that the number of periodic domains in both types of PCD states decreases exponentially with an increase of coupling range and obeys a power law under nonlocal coupling. Additionally, we also analyze the structural changes of chimera death states by reducing the system of dynamical equations to a phase model through the phase reduction. We also briefly study the role of nonisochronicity parameter on chimera states, where the existence of a multichimera state with respect to the coupling range is pointed out. Moreover, we also analyze the robustness of the chimera death state to perturbations in the natural frequencies of the oscillators.
Synchronization of phase oscillators with frequency-weighted coupling
NASA Astrophysics Data System (ADS)
Xu, Can; Sun, Yuting; Gao, Jian; Qiu, Tian; Zheng, Zhigang; Guan, Shuguang
2016-02-01
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all couplings. A rigorous mean-field analysis is implemented to predict the possible steady states. Furthermore, a detailed linear stability analysis proves that the incoherent state is only neutrally stable below the synchronization threshold. Nevertheless, interestingly, the amplitude of the order parameter decays exponentially (at least for short time) in this regime, resembling the Landau damping effect in plasma physics. Moreover, the explicit expression for the critical coupling strength is determined by both the mean-field method and linear operator theory. The mechanism of bifurcation for the incoherent state near the critical point is further revealed by the amplitude expansion theory, which shows that the oscillating standing wave state could also occur in this model for certain frequency distributions. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings.
Stimulus-locked responses of two phase oscillators coupled with delayed feedback.
Krachkovskyi, Valerii; Popovych, Oleksandr V; Tass, Peter A
2006-06-01
For a system of two phase oscillators coupled with delayed self-feedback we study the impact of pulsatile stimulation administered to both oscillators. This system models the dynamics of two coupled phase-locked loops (PLLs) with a finite internal delay within each loop. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. Remarkably, for large coupling strength the two PLLs are completely desynchronized. We study stimulus-locked responses emerging in the different dynamical regimes. Simple phase resets may be followed by a response clustering, which is intimately connected with long poststimulus resynchronization. Intriguingly, a maximal perturbation (i.e., maximal response clustering and maximal resynchronization time) occurs, if the system gets trapped at a stable manifold of an unstable saddle fixed point due to appropriately calibrated stimulus. Also, single stimuli with suitable parameters can shift the system from a stable synchronized state to a stable desynchronized state or vice versa. Our result show that appropriately calibrated single pulse stimuli may cause pronounced transient and/or long-lasting changes of the oscillators' dynamics. Pulse stimulation may, hence, constitute an effective approach for the control of coupled oscillators, which might be relevant to both physical and medical applications.
Multiphysics Application Coupling Toolkit
Campbell, Michael T.
2013-12-02
This particular consortium implementation of the software integration infrastructure will, in large part, refactor portions of the Rocstar multiphysics infrastructure. Development of this infrastructure originated at the University of Illinois DOE ASCI Center for Simulation of Advanced Rockets (CSAR) to support the center's massively parallel multiphysics simulation application, Rocstar, and has continued at IllinoisRocstar, a small company formed near the end of the University-based program. IllinoisRocstar is now licensing these new developments as free, open source, in hopes to help improve their own and others' access to infrastructure which can be readily utilized in developing coupled or composite software systems; with particular attention to more rapid production and utilization of multiphysics applications in the HPC environment. There are two major pieces to the consortium implementation, the Application Component Toolkit (ACT), and the Multiphysics Application Coupling Toolkit (MPACT). The current development focus is the ACT, which is (will be) the substrate for MPACT. The ACT itself is built up from the components described in the technical approach. In particular, the ACT has the following major components: 1.The Component Object Manager (COM): The COM package provides encapsulation of user applications, and their data. COM also provides the inter-component function call mechanism. 2.The System Integration Manager (SIM): The SIM package provides constructs and mechanisms for orchestrating composite systems of multiply integrated pieces.
Pacemakers in large arrays of oscillators with nonlocal coupling
NASA Astrophysics Data System (ADS)
Jaramillo, Gabriela; Scheel, Arnd
2016-02-01
We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be approximated by a continuous nonlocal evolution equation. We concentrate on the case of heterogeneities with positive average and show that steady solutions to the nonlocal problem exist. In particular, we show that these heterogeneities act as a wave source. This effect is not possible in 3 dimensional systems, such as the complex Ginzburg-Landau equation, where the wavenumber of weak sources decays at infinity. To obtain our results we use a series of isomorphisms to relate the nonlocal problem to the viscous eikonal equation. We then use Fredholm properties of the Laplace operator in Kondratiev spaces to obtain solutions to the eikonal equation, and by extension to the nonlocal problem.
Coupled Oscillations and Circadian Rhythms in Molecular Replication Networks.
Wagner, Nathaniel; Alasibi, Samaa; Peacock-Lopez, Enrique; Ashkenasy, Gonen
2015-01-02
Living organisms often display rhythmic and oscillatory behavior. We investigate here a challenge in contemporary Systems Chemistry, that is, to construct "bottom-up" molecular networks that display such complex behavior. We first describe oscillations during self-replication by applying kinetic parameters relevant to peptide replication in an open environment. Small networks of coupled oscillators are then constructed in silico, producing various functions such as logic gates, integrators, counters, triggers, and detectors. These networks are finally utilized to simulate the connectivity and network topology of the Kai proteins circadian clocks from the S. elongatus cyanobacteria, thus producing rhythms whose constant frequency is independent of the input intake rate and robust toward concentration fluctuations. We suggest that this study helps further reveal the underlying principles of biological clocks and may provide clues into their emergence in early molecular evolution.
NASA Astrophysics Data System (ADS)
Castellini, Horacio; Yudiarsah, Efta; Romanelli, Lilia; Cerdeira, Hilda A.
2005-04-01
Animal locomotion employs different periodic patterns known as animal gaits. In 1993, Collins and Stewart recognized that gaits possessed certain symmetries and characterized the gaits of quadrupeds and bipeds using permutation symmetry groups, which impose constraints on the locomotion center called the central pattern generator (CPG) in the animal brain. They modeled the CPG by coupling four nonlinear oscillators and found that it was possible to reproduce all symmetries of the gaits by changing the coupling strength. Here we propose to extend this idea using coupled chaotic oscillators synchronized using the Pyragas method in order to characterize the CPG symmetries. We also evaluate the time series behavior when the foot is in contact with the ground: this has potential robotic applications.
Multistable states in a system of coupled phase oscillators with inertia
Yuan, Di; Lin, Fang; Wang, Limei; Liu, Danyang; Yang, Junzhong; Xiao, Yi
2017-01-01
We investigate the generalized Kuramoto model of globally coupled oscillators with inertia, in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians. We consider the correlation between the coupling strengths of oscillators and the distributions of natural frequencies. Two different types of correlations are studied. It is shown that the model supports multistable synchronized states such as different types of travelling wave states, π state and another type of nonstationary state: an oscillating π state. The phase distribution oscillates in a confined region and the phase difference between conformists and contrarians oscillates around π periodically in the oscillating π state. The different types of travelling wave state may be characterized by the speed of travelling wave and the effective frequencies of oscillators. Finally, the bifurcation diagrams of the model in the parameter space are presented. PMID:28176829
Multistable states in a system of coupled phase oscillators with inertia
NASA Astrophysics Data System (ADS)
Yuan, Di; Lin, Fang; Wang, Limei; Liu, Danyang; Yang, Junzhong; Xiao, Yi
2017-02-01
We investigate the generalized Kuramoto model of globally coupled oscillators with inertia, in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians. We consider the correlation between the coupling strengths of oscillators and the distributions of natural frequencies. Two different types of correlations are studied. It is shown that the model supports multistable synchronized states such as different types of travelling wave states, π state and another type of nonstationary state: an oscillating π state. The phase distribution oscillates in a confined region and the phase difference between conformists and contrarians oscillates around π periodically in the oscillating π state. The different types of travelling wave state may be characterized by the speed of travelling wave and the effective frequencies of oscillators. Finally, the bifurcation diagrams of the model in the parameter space are presented.
Coupled predator-prey oscillations in a chaotic food web.
Benincà, Elisa; Jöhnk, Klaus D; Heerkloss, Reinhard; Huisman, Jef
2009-12-01
Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles are coupled through competition between prey species. Here, we investigate predator-prey oscillations in a long-term experiment with a marine plankton community. Wavelet analysis of the species fluctuations reveals two predator-prey cycles that fluctuate largely in anti-phase. The phase angles point at strong competition between the phytoplankton species, but relatively little prey overlap among the zooplankton species. This food web architecture is consistent with the size structure of the plankton community, and generates highly dynamic food webs. Continued alternations in species dominance enable coexistence of the prey species through a non-equilibrium 'killing-the-winner' mechanism, as the system shifts back and forth between the two predator-prey cycles in a chaotic fashion.
Testing the global flow reconstruction method on coupled chaotic oscillators
NASA Astrophysics Data System (ADS)
Plachy, Emese; Kolláth, Zoltán
2010-03-01
Irregular behaviour of pulsating variable stars may occur due to low dimensional chaos. To determine the quantitative properties of the dynamics in such systems, we apply a suitable time series analysis, the global flow reconstruction method. The robustness of the reconstruction can be tested through the resultant quantities, like Lyapunov dimension and Fourier frequencies. The latter is specially important as it is directly derivable from the observed light curves. We have performed tests using coupled Rossler oscillators to investigate the possible connection between those quantities. In this paper we present our test results.
Transient chaos in two coupled, dissipatively perturbed Hamiltonian Duffing oscillators
NASA Astrophysics Data System (ADS)
Sabarathinam, S.; Thamilmaran, K.; Borkowski, L.; Perlikowski, P.; Brzeski, P.; Stefanski, A.; Kapitaniak, T.
2013-11-01
The dynamics of two coupled, dissipatively perturbed, near-integrable Hamiltonian, double-well Duffing oscillators has been studied. We give numerical and experimental (circuit implementation) evidence that in the case of small positive or negative damping there exist two different types of transient chaos. After the decay of the transient chaos in the neighborhood of chaotic saddle we observe the transient chaos in the neighborhood of unstable tori. We argue that our results are robust and they exist in the wide range of system parameters.
Submillimeter local oscillators for spaceborne heterodyne applications
NASA Technical Reports Server (NTRS)
Petuchowski, S. J.; Durachta, J.
1985-01-01
Existing and prospective submillimeter local oscillator technologies are surveyed and compared with respect to criteria of suitability for application in spaceborne submillimeter heterodyne receivers as those proposed for the Large Deployable Reflector (LDR). Solid-state and plasma devices are considered in terms of fundamental limitations.
Analytical Insights on Theta-Gamma Coupled Neural Oscillators
2013-01-01
In this paper, we study the dynamics of a quadratic integrate-and-fire neuron, spiking in the gamma (30–100 Hz) range, coupled to a delta/theta frequency (1–8 Hz) neural oscillator. Using analytical and semianalytical methods, we were able to derive characteristic spiking times for the system in two distinct regimes (depending on parameter values): one regime where the gamma neuron is intrinsically oscillating in the absence of theta input, and a second one in which gamma spiking is directly gated by theta input, i.e., windows of gamma activity alternate with silence periods depending on the underlying theta phase. In the former case, we transform the equations such that the system becomes analogous to the Mathieu differential equation. By solving this equation, we can compute numerically the time to the first gamma spike, and then use singular perturbation theory to find successive spike times. On the other hand, in the excitable condition, we make direct use of singular perturbation theory to obtain an approximation of the time to first gamma spike, and then extend the result to calculate ensuing gamma spikes in a recursive fashion. We thereby give explicit formulas for the onset and offset of gamma spike burst during a theta cycle, and provide an estimation of the total number of spikes per theta cycle both for excitable and oscillator regimes. PMID:23945442
NASA Astrophysics Data System (ADS)
Kohira, Masahiro I.; Kitahata, Hiroyuki; Magome, Nobuyuki; Yoshikawa, Kenichi
2012-02-01
An oscillatory system called a plastic bottle oscillator is studied, in which the downflow of water and upflow of air alternate periodically in an upside-down plastic bottle containing water. It is demonstrated that a coupled two-bottle system exhibits in- and antiphase synchronization according to the nature of coupling. A simple ordinary differential equation is deduced to interpret the characteristics of a single oscillator. This model is also extended to coupled oscillators, and the model reproduces the essential features of the experimental observations.
EDFA-based coupled opto-electronic oscillator and its phase noise
NASA Technical Reports Server (NTRS)
Salik, Ertan; Yu, Nan; Tu, Meirong; Maleki, Lute
2004-01-01
EDFA-based coupled opto-electronic oscillator (COEO), an integrated optical and microwave oscillator that can generate picosecond optical pulses, is presented. the phase noise measurements of COEO show better performance than synthesizer-driven mode-locked laser.
Link between truncated fractals and coupled oscillators in biological systems.
Paar, V; Pavin, N; Rosandić, M
2001-09-07
This article aims at providing a new theoretical insight into the fundamental question of the origin of truncated fractals in biological systems. It is well known that fractal geometry is one of the characteristics of living organisms. However, contrary to mathematical fractals which are self-similar at all scales, the biological fractals are truncated, i.e. their self-similarity extends at most over a few orders of magnitude of separation. We show that nonlinear coupled oscillators, modeling one of the basic features of biological systems, may generate truncated fractals: a truncated fractal pattern for basin boundaries appears in a simple mathematical model of two coupled nonlinear oscillators with weak dissipation. This fractal pattern can be considered as a particular hidden fractal property. At the level of sufficiently fine precision technique the truncated fractality acts as a simple structure, leading to predictability, but at a lower level of precision it is effectively fractal, limiting the predictability of the long-term behavior of biological systems. We point out to the generic nature of our result.
A discrete dynamics model for synchronization of pulse-coupled oscillators.
Schultz, A; Wechsler, H
1998-01-01
Biological information processing systems employ a variety of feature types. It has been postulated that oscillator synchronization is the mechanism for binding these features together to realize coherent perception. A discrete dynamic model of a coupled system of oscillators is presented. The network of oscillators converges to a state where subpopulations of cells become phase synchronized. It has potential applications to describing biological perception as well as for the construction of multifeature pattern recognition systems. It is shown that this model can be used to detect the presence of short line segments in the boundary contour of an object. The Hough transform, which is the standard method for detecting curve segments of a specified shape in an image was found not to be effective for this application. Implementation of the discrete dynamics model of oscillator synchronization is much easier than the differential equation models that have appeared in the literature. A systematic numerical investigation of the convergence properties of the model has been performed and it is shown that the discrete dynamics model can scale up to large number of oscillators.
NASA Astrophysics Data System (ADS)
Fukuyama, T.; Okugawa, M.
2017-03-01
We have experimentally investigated the dynamic behavior of coupled nonlinear oscillators, including chaos caused by the instability of ionization waves in a glow discharge plasma. We studied the phase synchronization process of coupled asymmetric oscillators with increasing coupling strength. Coherence resonance and phase synchronization were observed in the coupled systems. The phase synchronization process revealed scaling laws with a tendency of Type-I intermittency in the relationships between the coupling strength and the average duration of successive laminar states interrupted by a phase slip. Coupled periodic oscillators changed from a periodic state to chaos caused by the interaction of nonlinear periodic waves at increasing coupling strength.
Oscillation quenching in third order phase locked loop coupled by mean field diffusive coupling
NASA Astrophysics Data System (ADS)
Chakraborty, S.; Dandapathak, M.; Sarkar, B. C.
2016-11-01
We explored analytically the oscillation quenching phenomena (amplitude death and parameter dependent inhomogeneous steady state) in a coupled third order phase locked loop (PLL) both in periodic and chaotic mode. The phase locked loops were coupled through mean field diffusive coupling. The lower and upper limits of the quenched state were identified in the parameter space of the coupled PLL using the Routh-Hurwitz technique. We further observed that the ability of convergence to the quenched state of coupled PLLs depends on the design parameters. For identical systems, both the systems converge to the homogeneous steady state, whereas for non-identical parameter values they converge to an inhomogeneous steady state. It was also observed that for identical systems, the quenched state is wider than the non-identical case. When the system parameters are so chosen that each isolated loop is chaotic in nature, we observe narrowing down of the quenched state. All these phenomena were also demonstrated through numerical simulations.
Oscillation quenching in third order phase locked loop coupled by mean field diffusive coupling.
Chakraborty, S; Dandapathak, M; Sarkar, B C
2016-11-01
We explored analytically the oscillation quenching phenomena (amplitude death and parameter dependent inhomogeneous steady state) in a coupled third order phase locked loop (PLL) both in periodic and chaotic mode. The phase locked loops were coupled through mean field diffusive coupling. The lower and upper limits of the quenched state were identified in the parameter space of the coupled PLL using the Routh-Hurwitz technique. We further observed that the ability of convergence to the quenched state of coupled PLLs depends on the design parameters. For identical systems, both the systems converge to the homogeneous steady state, whereas for non-identical parameter values they converge to an inhomogeneous steady state. It was also observed that for identical systems, the quenched state is wider than the non-identical case. When the system parameters are so chosen that each isolated loop is chaotic in nature, we observe narrowing down of the quenched state. All these phenomena were also demonstrated through numerical simulations.
NASA Astrophysics Data System (ADS)
Dolan, Kevin; Majtanik, Milan; Tass, Peter A.
2005-11-01
Recently extensive work has been done towards developing methods for effective desynchronization of globally coupled phase oscillators (the Kuramoto model), by means of short stimulation pulses, or sequences of pulses. This is of great importance for the treatment of neurological disorders like Parkinson’s disease and essential tremor. As a progressive step towards the goal of being able to apply these desynchronization and phase-resetting techniques medically as a form of treatment, we demonstrate here how these ideas can be generalized and applied to a network of two-dimensional phase oscillators with inertia. This model has been previously presented as a simplification of a neuron with an axon and dendrite, and can be used to account for intrinsic transient behavior often seen experimentally. The stimulation techniques originally developed for the Kuramoto model work on a network of globally coupled inertial phase oscillators in a qualitatively similar way. In both cases desynchronization can be achieved when the stimulation causes nearby trajectories to diverge from each other. However, the mechanism by which this divergence of trajectories is achieved, is substantially different for the network of inertial oscillators. In particular, the addition of inertia results in a broad range of transient dynamics not present in the Kuramoto model. Nevertheless, the basic principles of phase resetting and desynchronization still apply. This suggests a robustness of these techniques which is of extreme importance to the medical applications.
NASA Astrophysics Data System (ADS)
Zheng, Zhigang; Wang, Xingang; Cross, Michael C.
2002-05-01
Generalized synchronization in an array of mutually (bidirectionally) coupled nonidentical chaotic oscillators is studied. Coupled Lorenz oscillators and coupled Lorenz-Rossler oscillators are adopted as our working models. With increasing the coupling strengths, the system experiences a cascade of transitions from the partial to the global generalized synchronizations, i.e., different oscillators are gradually entrained through a clustering process. This scenario of transitions reveals an intrinsic self-organized order in groups of interacting units, which generalizes the idea of generalized synchronizations in drive-response systems.
Properties of Coupled Oscillator Model for Bidirectional Associative Memory
NASA Astrophysics Data System (ADS)
Kawaguchi, Satoshi
2016-08-01
In this study, we consider the stationary state and dynamical properties of a coupled oscillator model for bidirectional associative memory. For the stationary state, we apply the replica method to obtain self-consistent order parameter equations. The theoretical results for the storage capacity and overlap agree well with the numerical simulation. For the retrieval process, we apply statistical neurodynamics to include temporal noise correlations. For the successful retrieval process, the theoretical result obtained with the fourth-order approximation qualitatively agrees with the numerical simulation. However, for the unsuccessful retrieval process, higher-order noise correlations suppress severely; therefore, the maximum value of the overlap and the relaxation time are smaller than those of the numerical simulation. The reasons for the discrepancies between the theoretical result and numerical simulation, and the validity of our analysis are discussed.
Elementary modes of coupled oscillators as whispering-gallery microresonators
NASA Astrophysics Data System (ADS)
Banerjee, Rabin; Mukherjee, Pradip
2015-10-01
We obtain the elementary modes of a system of parity-time reversal (PT)-symmetric coupled oscillators with balanced loss and gain. These modes are used to give a physical picture of the phase transition recently reported [C. M. Bender, M. Gianfreda, B. Peng, S. K. Özdemir and L. Yang, Phys. Rev. A 88, 062111 (2013); L. Yang, S. K. Özdemir and B. Peng, 12th Int. Workshop and Conf. Pseudo-Hermitian Hamiltonians in Quantum Physics, Istanbul, Turkey, July 2013; B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender and L. Yang, Nat. Phys. 10, 394 (2014)] in experiments with whispering-gallery microresonators.
Dynamically Coupled Oscillators: Cooperative Behavior via Dynamical Interaction
NASA Astrophysics Data System (ADS)
Aonishi, Toru; Okada, Masato
2003-06-01
We propose a theoretical framework for studying the cooperative behavior of dynamically coupled oscillators (DCOs) that possess dynamical interactions. Then, to clarify synchronization phenomena in networks of interneurons which possess inhibitory interactions, we propose a DCO model with dynamics of interactions that tend to cause 180^\\circ phase lags. Employing the approach developed here, we demonstrate that although our model displays synchronization at high frequencies, it does not exhibit synchronization at low frequencies because this dynamical interaction does not cause a phase lag sufficiently large to cancel the effect of the inhibition. We interpret the disappearance of synchronization in our model with decreasing frequency as describing the breakdown of synchronization in the interneuron network of the CA1 area below the critical frequency of 20 Hz.
Interplay of coupling and common noise at the transition to synchrony in oscillator populations
Pimenova, Anastasiya V.; Goldobin, Denis S.; Rosenblum, Michael; Pikovsky, Arkady
2016-01-01
There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes. PMID:27922105
Interplay of coupling and common noise at the transition to synchrony in oscillator populations
NASA Astrophysics Data System (ADS)
Pimenova, Anastasiya V.; Goldobin, Denis S.; Rosenblum, Michael; Pikovsky, Arkady
2016-12-01
There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes.
Coupled-oscillator theory of dispersion and Casimir-Polder interactions
Berman, P. R.; Ford, G. W.; Milonni, P. W.
2014-10-28
We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r{sup −4}, a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called “remarkable formula” for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented.
NASA Astrophysics Data System (ADS)
Krylov, S. N.; Smirnov, D. A.; Osipov, G. V.; Bezruchko, B. P.
2015-06-01
To analyze the coupling between oscillating systems by time series, the Granger causality assessment—an improved prognosis of the autoregression model—is widely used. It is known that wrong conclusions regarding the presence of bidirectional coupling can be obtained in the case of unidirectional coupled systems when the sampling interval is rather wide. However, it remains unclear under what conditions the effect of false coupling is significant, and thus criteria of significance to account for this effect in practice are absent. In this work, such conditions were studied and qualitatively formulated for an etalon system of coupled oscillators. In particular, it is shown that this effect is negligible in the case of insufficient data if a "fast" oscillator (with a smaller oscillation period and relaxation time) is driving a "slow" oscillator, while the effect is strong otherwise. If both periods are considerably larger than the sampling interval, the effect increases with relaxation time of the driving oscillator and decreases with increasing relaxation time of the driven one.
Synchronization of phase oscillators with coupling mediated by a diffusing substance
NASA Astrophysics Data System (ADS)
Batista, C. A. S.; Szezech, J. D.; Batista, A. M.; Macau, E. E. N.; Viana, R. L.
2017-03-01
We investigate the transition to phase and frequency synchronization in a one-dimensional chain of phase oscillator "cells" where the coupling is mediated by the local concentration of a chemical which can diffuse in the inter-oscillator medium and it is both secreted and absorbed by the oscillator "cells", influencing their dynamical behavior. This coupling has the advantage of having a tunable parameter which makes it possible to pass continuously from a global (all-to-all) to a local (nearest-neighbor) coupling form. We have verified that synchronous behavior depends on the coupling strength and coupling length.
NASA Astrophysics Data System (ADS)
Duggento, Andrea; Stankovski, Tomislav; McClintock, Peter V. E.; Stefanovska, Aneta
2012-12-01
Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.024101 109, 024101 (2012)] introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time-evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically generated data, data from an analog electronic circuit, and cardiorespiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.
Kuznetsov, Alexey S; Kopell, Nancy J; Wilson, Charles J
2006-02-01
Dopaminergic neurons of the midbrain fire spontaneously at rates <10/s and ordinarily will not exceed this range even when driven with somatic current injection. When driven at higher rates, these cells undergo spike failure through depolarization block. During spontaneous bursting of dopaminergic neurons in vivo, bursts related to reward expectation in behaving animals, and bursts generated by dendritic application of N-methyl-d-aspartate (NMDA) agonists, transient firing attains rates well above this range. We suggest a way such high-frequency firing may occur in response to dendritic NMDA receptor activation. We have extended the coupled oscillator model of the dopaminergic neuron, which represents the soma and dendrites as electrically coupled compartments with different natural spiking frequencies, by addition of dendritic AMPA (voltage-independent) or NMDA (voltage-dependent) synaptic conductance. Both soma and dendrites contain a simplified version of the calcium-potassium mechanism known to be the mechanism for slow spontaneous oscillation and background firing in dopaminergic cells. The compartments differ only in diameter, and this difference is responsible for the difference in natural frequencies. We show that because of its voltage dependence, NMDA receptor activation acts to amplify the effect on the soma of the high-frequency oscillation of the dendrites, which is normally too weak to exert a large influence on the overall oscillation frequency of the neuron. During the high-frequency oscillations that result, sodium inactivation in the soma is removed rapidly after each action potential by the hyperpolarizing influence of the dendritic calcium-dependent potassium current, preventing depolarization block of the spike mechanism, and allowing high-frequency spiking.
Collective dynamics of time-delay-coupled phase oscillators in a frustrated geometry
NASA Astrophysics Data System (ADS)
Thakur, Bhumika; Sharma, Devendra; Sen, Abhijit; Johnston, George L.
2017-01-01
We study the effect of time delay on the dynamics of a system of repulsively coupled nonlinear oscillators that are configured as a geometrically frustrated network. In the absence of time delay, frustrated systems are known to possess a high degree of multistability among a large number of coexisting collective states except for the fully synchronized state that is normally obtained for attractively coupled systems. Time delay in the coupling is found to remove this constraint and to lead to such a synchronized ground state over a range of parameter values. A quantitative study of the variation of frustration in a system with the amount of time delay has been made and a universal scaling behavior is found. The variation in frustration as a function of the product of time delay and the collective frequency of the system is seen to lie on a characteristic curve that is common for all natural frequencies of the identical oscillators and coupling strengths. Thus time delay can be used as a tuning parameter to control the amount of frustration in a system and thereby influence its collective behavior. Our results can be of potential use in a host of practical applications in physical and biological systems in which frustrated configurations and time delay are known to coexist.
NASA Astrophysics Data System (ADS)
Chen, Xiaoxiao; Feng, Xiuqin; Tian, Zuolin; Yao, Zhihai
2016-06-01
We present the control and synchronization of spatiotemporal chaos in the photo-refractive ring oscillator systems with coupling technology. First, we realize the synchronization of spatiotemporal chaos in the two photorefractive ring oscillator systems via mutual coupling by choosing a suitable coupling strength. With the mutual coupling strength enlarging, the two mutual coupling photorefractive ring oscillator systems are controlled into periodic state, period number differs on account of the coupling strength and lattice coordinates. By increasing the coupling strength, the photorefractive ring oscillator is converted into period 8, subsequently it is converted into periods 4 and 2, periodic synchronization of the photorefractive ring oscillator systems is achieved at the same time. Calculation results show that period 1 is impossible by mutual coupling technology. Then, we investigate the influence of noise and parameter deviation on chaotic synchronization. We find that mutual coupling chaotic synchronization method can synchronize two chaotic systems with the weak noise and parameter deviation and has very good robustness. Given that the weak noise and parameter deviation have a slight effect on synchronization. Furthermore, we investigate two dimension control and synchronization of spatiotemporal chaos in the photorefractive ring osillator systems with coupling technology and get successful results. Mutual coupling technology is suitable in practical photorefractive ring oscillator systems.
Phase-flip and oscillation-quenching-state transitions through environmental diffusive coupling
NASA Astrophysics Data System (ADS)
Sharma, Amit; Verma, Umesh Kumar; Shrimali, Manish Dev
2016-12-01
We study the dynamics of nonlinear oscillators coupled through environmental diffusive coupling. The interaction between the dynamical systems is maintained through its agents which, in turn, interact globally with each other in the common dynamical environment. We show that this form of coupling scheme can induce an important transition like phase-flip transition as well transitions among oscillation quenching states in identical limit-cycle oscillators. This behavior is analyzed in the parameter plane by analytical and numerical studies of specific cases of the Stuart-Landau oscillator and van der Pol oscillator. Experimental evidences of the phase-flip transition and quenching states are shown using an electronic version of the van der Pol oscillators.
NASA Astrophysics Data System (ADS)
Čevizović, D.; Petković, S.; Galović, S.; Chizhov, A.; Reshetnyak, A.
2015-10-01
We enlarge our results from the study of the hopping mechanism of the oscillation excitation transport in 1D model of one biologica-likel macromolecular chain to the case of a system composed from two 1D parallel macromolecular chains with consideration of the properties of intramolecular oscillation excitations. We suppose, that due to the exciton interaction with thermal oscillation (generated by mechanical phonon subsystem) of structural elements (consisting of the peptide group) of the chains, the exciton becomes by self trapped and forms the polaron state. We suggest a model which generalizes the modified Holstein polaron model to the case of two macromolecular chains and find that because of the interchain coupling, the exciton energy band is splitted into two subbands. The hopping process of exciton migration along the macromolecular chains is studied in dependence of system parameters and temperature. We pay an special attention to the temperature range (near T = 300 K) in which living cells operate. It is found that for the certain values of the system parameters there exists the abrupt change of the exciton migration nature from practically free (light) exciton motion to an immobile (heavy, dressed by phonon cloud) quasiparticle We discuss an application of the obtained results to the exciton transport both within deoxyribonucleic acid molecule and in the 2D polymer films organized from such macromolecular chains.
NASA Astrophysics Data System (ADS)
Jia, Ji; Shangguan, Zhichun; Li, Haihong; Wu, Ye; Liu, Weiqing; Xiao, Jinghua; Kurths, Jürgen
2016-11-01
Upside-down bottles containing water which are common in our daily life exhibit rich vibration dynamics. Rich dynamic regimes are observed in bottle oscillators by directly measuring the pressure difference between inside and outside of a bottle with the aid of pressure sensors. We observe experimentally that an asymmetrical oscillation process between the outflow of water and the inflow of air is formed in a single bottle oscillator and, in addition, a kind of 2:1 frequency synchronization occurs in a coupled system of two non-identical bottle oscillators. The peak values of the oscillation of pressure differences between inside and outside of the bottle decease as the height of the liquid surface steps down, while the oscillation period increases gradually. The theoretical model of the oscillator is amended to understand the regimes in the experiment by introducing time-dependent parameters related to the asymmetrical oscillation processes. Our numerical results based on the model fit well with the experimental ones.
NASA Astrophysics Data System (ADS)
Zhao, Liyun; Zhou, Jin; Wu, Quanjun
2016-01-01
This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.
Universal control of an oscillator with dispersive coupling to a qubit
NASA Astrophysics Data System (ADS)
Krastanov, Stefan; Heeres, Reinier; Reinhold, Philip; Albert, Victor V.; Shen, Chao; Zou, Chang-Ling; Vlastakis, Brian; Schoelkopf, Robert; Jiang, Liang
2016-05-01
We investigate quantum control of an oscillator mode that dispersively couples to an ancillary qubit. In the strong dispersive regime, we may drive the qubit conditioned on the selected number states of the oscillator, which enables selective number-dependent arbitrary phase (SNAP) operation and universal control of the oscillator. We provide explicit constructions for arbitrary state preparation and arbitrary unitary operation of the oscillator. Moreover, using optimal control techniques, we develop fast and efficient pulse sequences to achieve high fidelity unitary gates. This universal control scheme of the oscillator can readily be implemented using superconducting circuits. Supported by ARO, AFOSR MURI, Sloan Foundation, and Packard Foundation.
Synchronization and quorum sensing in an ensemble of indirectly coupled chaotic oscillators
NASA Astrophysics Data System (ADS)
Li, Bing-Wei; Fu, Chenbo; Zhang, Hong; Wang, Xingang
2012-10-01
The fact that the elements in some realistic systems are influenced by each other indirectly through a common environment has stimulated a new surge of studies on the collective behavior of coupled oscillators. Most of the previous studies, however, consider only the case of coupled periodic oscillators, and it remains unknown whether and to what extent the findings can be applied to the case of coupled chaotic oscillators. Here, using the population density and coupling strength as the tuning parameters, we explore the synchronization and quorum sensing behaviors in an ensemble of chaotic oscillators coupled through a common medium, in which some interesting phenomena are observed, including the appearance of the phase synchronization in the process of progressive synchronization, the various periodic oscillations close to the quorum sensing transition, and the crossover of the critical population density at the transition. These phenomena, which have not been reported for indirectly coupled periodic oscillators, reveal a corner of the rich dynamics inherent in indirectly coupled chaotic oscillators, and are believed to have important implications to the performance and functionality of some realistic systems.
NASA Astrophysics Data System (ADS)
Ghosh, Debarati; Banerjee, Tanmoy
2014-12-01
We report the transitions among different oscillation quenching states induced by the interplay of diffusive (direct) coupling and environmental (indirect) coupling in coupled identical oscillators. This coupling scheme was introduced by Resmi et al. [Phys. Rev. E 84, 046212 (2011), 10.1103/PhysRevE.84.046212] as a general scheme to induce amplitude death (AD) in nonlinear oscillators. Using a detailed bifurcation analysis we show that, in addition to AD, which actually occurs only in a small region of parameter space, this coupling scheme can induce other oscillation quenching states, namely oscillation death (OD) and a novel nontrvial AD (NAD) state, which is a nonzero bistable homogeneous steady state; more importantly, this coupling scheme mediates a transition from the AD state to the OD state and a new transition from the AD state to the NAD state. We identify diverse routes to the NAD state and map all the transition scenarios in the parameter space for periodic oscillators. Finally, we present the first experimental evidence of oscillation quenching states and their transitions induced by the interplay of direct and indirect coupling.
Coupling dynamics of Nb/Nb2O5 relaxation oscillators
NASA Astrophysics Data System (ADS)
Li, Shuai; Liu, Xinjun; Nandi, Sanjoy Kumar; Venkatachalam, Dinesh Kumar; Elliman, Robert Glen
2017-03-01
The coupling dynamics of capacitively coupled Nb/Nb2O5 relaxation oscillators are shown to exhibit rich collective behaviour depending on the negative differential resistance response of the individual devices, the operating voltage and the coupling capacitance. These coupled oscillators are shown to exhibit stable frequency and phase locking states at source voltages as low as 2.2 V, with frequency control in the range from 0.85 to 16.2 MHz and frequency tunability of ∼8 MHz V–1. The experimental realisation of such compact, scalable and low power coupled-oscillator systems is of particular significance for the development and implementation of large oscillator networks in non-Boolean computing architectures.
Coupling dynamics of Nb/Nb2O5 relaxation oscillators.
Li, Shuai; Liu, Xinjun; Nandi, Sanjoy Kumar; Venkatachalam, Dinesh Kumar; Elliman, Robert Glen
2017-03-24
The coupling dynamics of capacitively coupled Nb/Nb2O5 relaxation oscillators are shown to exhibit rich collective behaviour depending on the negative differential resistance response of the individual devices, the operating voltage and the coupling capacitance. These coupled oscillators are shown to exhibit stable frequency and phase locking states at source voltages as low as 2.2 V, with frequency control in the range from 0.85 to 16.2 MHz and frequency tunability of ∼8 MHz V(-1). The experimental realisation of such compact, scalable and low power coupled-oscillator systems is of particular significance for the development and implementation of large oscillator networks in non-Boolean computing architectures.
Chaotic weak chimeras and their persistence in coupled populations of phase oscillators
NASA Astrophysics Data System (ADS)
Bick, Christian; Ashwin, Peter
2016-05-01
Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recently-introduced notion of a weak chimera gives a rigorously testable characterization of chimera states for finite-dimensional phase oscillator networks. In this paper we give some persistence results for dynamically invariant sets under perturbations and apply them to coupled populations of phase oscillators with generalized coupling. In contrast to the weak chimeras with nonpositive maximal Lyapunov exponents constructed so far, we show that weak chimeras that are chaotic can exist in the limit of vanishing coupling between coupled populations of phase oscillators. We present numerical evidence that positive Lyapunov exponents can persist for a positive measure set of this inter-population coupling strength.
Edge Event-Triggered Synchronization in Networks of Coupled Harmonic Oscillators.
Wei, Bo; Xiao, Feng; Dai, Ming-Zhe
2016-08-30
The synchronization problems of networks of coupled harmonic oscillators are addressed by the edge event-triggered approach in this paper. The network dynamics with respect to edge states are presented and a new edge event-triggered control protocol is designed. Combined with the periodic event-detecting and edge event-triggered approach, sufficient conditions that guarantee the synchronization of coupled harmonic oscillators are presented. Two event-detecting rules are given to achieve the synchronization of coupled harmonic oscillators with low resource consumption. Finally, simulations are conducted to illustrate the effectiveness of the edge event-triggered control algorithm.
Control of individual phase relationship between coupled oscillators using multilinear feedback.
Kano, T; Kinoshita, S
2010-02-01
Due to various technological and medical demands, several methods for controlling the dynamical behavior of coupled oscillators have been developed. In the present study, we develop a method to control the individual phase relationship between coupled oscillators, in which multilinear feedback is used to modify the interaction between the oscillators. By carrying out a simulation, we show that the phase relationship can be well controlled by using the proposed method and the control is particularly robust when the target coupling function is selected properly.
Bubbling effect in the electro-optic delayed feedback oscillator coupled network
NASA Astrophysics Data System (ADS)
Liu, Lingfeng; Lin, Jun; Miao, Suoxia
2017-03-01
Synchronization in the optical systems coupled network always suffers from bubbling events. In this paper, we numerically investigate the statistical properties of the synchronization characteristics and bubbling effects in the electro-optic delayed feedback oscillator coupled network with different coupling strength, delay time and gain coefficient. Furthermore, we compare our results with the synchronization properties of semiconductor laser (SL) coupled network, which indicates that the electro-optic delayed feedback oscillator can be better to suppress the bubbling effects in the synchronization of coupled network under the same conditions.
Nicu, Valentin Paul
2016-08-03
Motivated by the renewed interest in the coupled oscillator (CO) model for VCD, in this work a generalised coupled oscillator (GCO) expression is derived by introducing the concept of a coupled oscillator origin. Unlike the standard CO expression, the GCO expression is exact within the harmonic approximation. Using two illustrative example molecules, the theoretical concepts introduced here are demonstrated by performing a GCO decomposition of the rotational strengths computed using DFT. This analysis shows that: (1) the contributions to the rotational strengths that are normally neglected in the standard CO model can be comparable to or larger than the CO contribution, and (2) the GCO mechanism introduced here can affect the VCD intensities of all types of modes in symmetric and asymmetric molecules.
Cross-frequency coupling of brain oscillations in studying motivation and emotion.
Schutter, Dennis J L G; Knyazev, Gennady G
2012-03-01
Research has shown that brain functions are realized by simultaneous oscillations in various frequency bands. In addition to examining oscillations in pre-specified bands, interactions and relations between the different frequency bandwidths is another important aspect that needs to be considered in unraveling the workings of the human brain and its functions. In this review we provide evidence that studying interdependencies between brain oscillations may be a valuable approach to study the electrophysiological processes associated with motivation and emotional states. Studies will be presented showing that amplitude-amplitude coupling between delta-alpha and delta-beta oscillations varies as a function of state anxiety and approach-avoidance-related motivation, and that changes in the association between delta-beta oscillations can be observed following successful psychotherapy. Together these studies suggest that cross-frequency coupling of brain oscillations may contribute to expanding our understanding of the neural processes underlying motivation and emotion.
Carbon nanotube oscillators for applications as nanothermometers
NASA Astrophysics Data System (ADS)
Rahmat, Fainida; Thamwattana, Ngamta; Hill, James M.
2010-10-01
Nanostructures such as carbon nanotubes have a broad range of potential applications such as nanomotors, nano-oscillators and electromechanical nanothermometers, and a proper understanding of the molecular interaction between nanostructures is fundamentally important for these applications. In this paper, we determine the molecular interaction potential of interacting carbon nanotubes for two configurations. The first is a shuttle configuration involving a short outer tube sliding on a fixed inner tube, and the second involves a telescopic configuration for which an inner tube moves both in the region between two outer tubes and through the tubes themselves. For the first configuration we examine two cases of semi-infinite and finite inner carbon nanotubes. We employ the continuum approximation and the 6-12 Lennard-Jones potential for non-bonded molecules to determine the molecular interaction potential and the resulting van der Waals force, and we evaluate the resulting surface integrals numerically. We also investigate the acceptance condition and suction energy for the first configuration. Our results show that for the shuttle configuration with a semi-infinite inner tube, the suction energy is maximum when the difference between the outer and inner tubes radii is approximately 3.4 Å, which is the ideal inter-wall spacing between graphene sheets. For the finite inner tube, the potential energy is dependent on both the inner and outer tube lengths as well as on the inter-wall spacing. In terms of the oscillating frequency, the critical issue is the length of the moving outer tube, and the shorter the length, the higher the frequency. Further, for the telescopic configuration with two semi-infinite outer nanotubes of different radii, we find that the interaction energy also depends on the difference of the tube radii. For two outer nanotubes of equal radii we observe that the shorter the distance between the two outer nanotubes, the higher the magnitude of the
Fast Dynamical Coupling Enhances Frequency Adaptation of Oscillators for Robotic Locomotion Control
Nachstedt, Timo; Tetzlaff, Christian; Manoonpong, Poramate
2017-01-01
Rhythmic neural signals serve as basis of many brain processes, in particular of locomotion control and generation of rhythmic movements. It has been found that specific neural circuits, named central pattern generators (CPGs), are able to autonomously produce such rhythmic activities. In order to tune, shape and coordinate the produced rhythmic activity, CPGs require sensory feedback, i.e., external signals. Nonlinear oscillators are a standard model of CPGs and are used in various robotic applications. A special class of nonlinear oscillators are adaptive frequency oscillators (AFOs). AFOs are able to adapt their frequency toward the frequency of an external periodic signal and to keep this learned frequency once the external signal vanishes. AFOs have been successfully used, for instance, for resonant tuning of robotic locomotion control. However, the choice of parameters for a standard AFO is characterized by a trade-off between the speed of the adaptation and its precision and, additionally, is strongly dependent on the range of frequencies the AFO is confronted with. As a result, AFOs are typically tuned such that they require a comparably long time for their adaptation. To overcome the problem, here, we improve the standard AFO by introducing a novel adaptation mechanism based on dynamical coupling strengths. The dynamical adaptation mechanism enhances both the speed and precision of the frequency adaptation. In contrast to standard AFOs, in this system, the interplay of dynamics on short and long time scales enables fast as well as precise adaptation of the oscillator for a wide range of frequencies. Amongst others, a very natural implementation of this mechanism is in terms of neural networks. The proposed system enables robotic applications which require fast retuning of locomotion control in order to react to environmental changes or conditions. PMID:28377710
Transverse mode coupling and supermode establishment in a free-electron laser oscillator
Pinhasi, Y.; Gover, A.
1995-12-31
A three-dimensional study of transverse mode evolution in a free-electron laser (FEL) oscillator is presented. The total electromagnetic field circulating in the resonator is represented as a superposition of transverse modes of the cavity. Coupled-mode theory is employed to derive a generalized 3-D steady-state oscillation criterion, from which the oscillator supermode is found analytically. The oscillator supermode keeps its transverse features after each round-trip, and it is the eigenmode solution of the oscillator at steady-state. Relations between the oscillator supermode and the amplifier supermode are discussed. It is shown that they are identical only when the feedback process is entirely non-disperssive and non-discriminating. We employ a 3-D, non-linear simulation code to demonstrate the evolvement of transverse modes in the oscillator towards formation of a supermode. The simulation shows that the resulted supermode is identical to that predicted by the analytical approach.
Coupling mechanism in the gate and oscillator model of the SCN
NASA Astrophysics Data System (ADS)
Li, Ying; Liu, Zengrong
2016-09-01
In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus is considered as the master circadian pacemaker. The SCN is divided into two subgroups of gate and oscillator cells: the ventrolateral (VL) neurons, which receive the periodic light-dark (LD) signal, and the dorsomedial (DM) neurons, which are coupled to the VL cells. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to create an integrated pacemaker that can govern behavioral and physiological rhythmicity and be reset by environmental light. The key is that the heterogeneous network formed by the cellular clocks within the SCN must synchronize to maintain timekeeping activity. Based on the structural and functional heterogeneity of the SCN, the authors bring forward a mathematical model including gate cells and oscillator cells with a wide range of periods. The gate neurons offer daily injection to oscillator neurons and the activation of gate is determined by the output of the oscillator neurons. In this model, the authors consider two kinds of coupling: interior coupling among the oscillator cells and exterior coupling from the gate cells to the oscillator cells. The authors mainly analyze the combined effects of these two kinds of coupling on the entrainment of the oscillator cells in the DM part. It is found that the interior coupling is conducive to entrainment, but a stronger coupling is not beneficial to entrainment. The gate mechanism in exterior coupling is more propitious to entrainment than continuous coupling. This study helps to understand collective circadian rhythm in the mammals.
NASA Astrophysics Data System (ADS)
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2017-02-01
We show the existence of chimeralike states in two distinct groups of identical populations of globally coupled Stuart-Landau oscillators. The existence of chimeralike states occurs only for a small range of frequency difference between the two populations, and these states disappear for an increase of mismatch between the frequencies. Here the chimeralike states are characterized by the synchronized oscillations in one population and desynchronized oscillations in another population. We also find that such states observed in two distinct groups of identical populations of nonlocally coupled oscillators are different from the above case in which coexisting domains of synchronized and desynchronized oscillations are observed in one population and the second population exhibits synchronized oscillations for spatially prepared initial conditions. Perturbation from such spatially prepared initial condition leads to the existence of imperfectly synchronized states. An imperfectly synchronized state represents the existence of solitary oscillators which escape from the synchronized group in population I and synchronized oscillations in population II. Also the existence of chimera state is independent of the increase of frequency mismatch between the populations. We also find the coexistence of different dynamical states with respect to different initial conditions, which causes multistability in the globally coupled system. In the case of nonlocal coupling, the system does not show multistability except in the cluster state region.
Optical parametric oscillators for medical applications
NASA Astrophysics Data System (ADS)
Gloster, Lawrie A. W.; Golding, Paul S.; King, Terence A.
1996-04-01
In recent years optical parametric oscillators (OPOs) have undergone a renaissance largely due to the discovery of new nonlinear materials capable of wide continuous tuning ranges spanning from the UV to the near-infrared spectral regions. To date, however, OPOs have not been exploited in the medical field despite their advantages over the dye laser in terms of tuning range and solid state structure. We consider the development of an OPO based on barium borate (BBO) which can be tailored to suit applications in medicine. Converting the maximum number of pump photons to tunable signal and idler photons is of great importance to secure high-fluence radiation necessary for many treatments. With this in mind, we report on an all- solid-state system using BBO which has been optimized by computer modeling with the potential of delivering amplification factors of typically up to 20 over a continuous tuning range of 700 nm to 1000 nm. As an example of its biomedical application, we describe the selective excitation of biomolecules and chromophores for cell destruction using malachite green isothiocyanate labelled bacteria. The potential for development is reviewed towards other medical applications such as diagnostic sensing and phototherapy.
Breakdown of order preservation in symmetric oscillator networks with pulse-coupling.
Kielblock, Hinrich; Kirst, Christoph; Timme, Marc
2011-06-01
Symmetric networks of coupled dynamical units exhibit invariant subspaces with two or more units synchronized. In time-continuously coupled systems, these invariant sets constitute barriers for the dynamics. For networks of units with local dynamics defined on the real line, this implies that the units' ordering is preserved and that their winding number is identical. Here, we show that in permutation-symmetric networks with pulse-coupling, the order is often no longer preserved. We analytically study a class of pulse-coupled oscillators (characterizing for instance the dynamics of spiking neural networks) and derive quantitative conditions for the breakdown of order preservation. We find that in general pulse-coupling yields additional dimensions to the state space such that units may change their order by avoiding the invariant sets. We identify a system of two symmetrically pulse-coupled identical oscillators where, contrary to intuition, the oscillators' average frequencies and thus their winding numbers are different.
Development of an X-Band Coupled-Oscillator Transmit/Receive Phased Array
NASA Astrophysics Data System (ADS)
Venkatesan, J.; Pogorzelski, R.
2007-08-01
The development of an 8.4 GHz (X-band) coupled-oscillator phased array employing full-duplex transmit and receive capability is described. Attractive features of phased arrays for deep-space communication include enabling high-data-rate communication and providing low-mass electronic beam steering. The coupled-oscillator phased-array concept seeks to reduce the cost and power consumption incurred in a conventional phased array by simplifying the beam-steering mechanism of the array. In this article, the overall system-level architecture of a full-duplex transmit and receive coupled-oscillator array is described, and the progress made in designing various specific components of a linear 1 x 7 coupled-oscillator array is also detailed.
Bloch Oscillations in Optical and Zeeman Lattices in the Presence of Spin-Orbit Coupling
NASA Astrophysics Data System (ADS)
Kartashov, Yaroslav V.; Konotop, Vladimir V.; Zezyulin, Dmitry A.; Torner, Lluis
2016-11-01
We address Bloch oscillations of a spin-orbit coupled atom in periodic potentials of two types: optical and Zeeman lattices. We show that in optical lattices the spin-orbit coupling allows controlling the direction of atomic motion and may lead to complete suppression of the oscillations at specific values of the coupling strength. In Zeeman lattices the energy bands are found to cross each other at the boundaries of the Brillouin zone, resulting in period doubling of the oscillations. In all cases, the oscillations are accompanied by rotation of the pseudospin, with a dynamics that is determined by the strength of the spin-orbit coupling. The predicted effects are discussed also in terms of a Wannier-Stark ladder, which in optical lattices consist of two mutually shifted equidistant subladders.
NASA Astrophysics Data System (ADS)
Ferruzzo Correa, Diego Paolo; Wulff, Claudia; Piqueira, José Roberto Castilho
2015-05-01
In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence a part of the system might repeat itself, and properties of this subsystem are representative of the dynamics on the whole phase space. In this paper an analysis of the second order N-node time-delay fully connected network is presented which is based on previous work: synchronous states in time-delay coupled periodic oscillators: a stability criterion. Correa and Piqueira (2013), for a 2-node network. This study is carried out using symmetry groups. We show the existence of multiple eigenvalues forced by symmetry, as well as the existence of Hopf bifurcations. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. We determine a finite set of frequencies ω , that might correspond to Hopf bifurcations in each case for critical values of the delay. The Sn map is used to actually find Hopf bifurcations along with numerical calculations using the Lambert W function. Numerical simulations are used in order to confirm the analytical results. Although we restrict attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal.
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode.
Verhagen, E; Deléglise, S; Weis, S; Schliesser, A; Kippenberg, T J
2012-02-01
Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.
Self-feedback electrically coupled spin-Hall oscillator array for pattern-matching operation
NASA Astrophysics Data System (ADS)
Kudo, Kiwamu; Morie, Takashi
2017-04-01
An oscillator array has been proposed for associative memory, in which the synchronization of multiple oscillators is utilized for pattern-matching operations. An input pattern is represented by a set of frequency shifts of the oscillators and the matching result is attributed to the degree of synchronization. Here, we propose an electrically coupled spin-Hall oscillator (SHO) array in which multiple SHOs exhibit synchronization by interacting with each other through self-feedback spin torques. We numerically demonstrate the pattern matching functionality of the proposed SHO array.
NASA Astrophysics Data System (ADS)
Pecora, Louis
2001-03-01
We show here that it is possible to solve, once and for all, the stability problem of synchronizing any array of identical oscillators , whether chaotic or limit cycle. The scheme gives a master stability function. We apply this to a system of 8 coupled Rossler-like circuits. We further show that this approach allows an experimental probe of the stability of any array of any number of identical oscillators using only three oscillators. Finally, the synchronization of oscillators in smallworld systems is understandable using a master stability approach.
Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling.
Komarov, Maxim; Pikovsky, Arkady
2015-08-01
We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.
Experimental Observation of Multifrequency Patterns in Arrays of Coupled Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
in, Visarath; Kho, Andy; Neff, Joseph D.; Palacios, Antonio; Longhini, Patrick; Meadows, Brian K.
2003-12-01
Frequency-related oscillations in coupled oscillator systems, in which one or more oscillators oscillate at different frequencies than the other oscillators, have been studied using group theoretical methods by Armbruster and Chossat [
NASA Astrophysics Data System (ADS)
Matta, Vincenzo; Pierro, Vincenzo
2015-11-01
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first contribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i) the observed sequence of measurements (quantum tracks) corresponding to a single experiment converges to a limit point, and that (ii) the limit point is random over the ensemble of the experiments, being distributed as a zero-mean Gaussian random variable with a variance at most equal to the ground-state variance. As a second contribution, the richer scenario where the oscillator is coupled with a frozen (i.e., at the ground state) ensemble of independent quantum oscillators is considered. A sharply different behavior emerges: under the same measurement scheme, here we observe that the measurement sequences are essentially divergent. Such a rigorous statistical analysis of the sequential measurement process might be useful for characterizing the main quantities that are currently used for inference, manipulation, and monitoring of many quantum systems. Several interesting properties of the quantum tracks evolution, as well as of the associated (quantum) threshold crossing times, are discussed and the dependence upon the main system parameters (e.g., the choice of the measurement sampling time, the degree of interaction with the environment, the measurement device accuracy) is elucidated. At a more fundamental level, it is seen that, as an application of basic quantum mechanics principles, a sharp difference exists between the intrinsic randomness unavoidably present in any quantum system, and the extrinsic randomness arising from the environmental coupling, i.e., the randomness induced by an external source of disturbance.
An analytical and numerical study of the bifurcations in a system of linearly-coupled oscillators
NASA Astrophysics Data System (ADS)
Aronson, D. G.; Doedel, E. J.; Othmer, H. G.
1987-03-01
We study a two-parameter family of ordinary differential equations in R 4 that governs the dynamics of two coupled planar oscillators. Each oscillator has a unique periodic solution that is attracting and the uncoupled product system has a unique invariant torus that is attracting. The torus persists for weak coupling and contains two periodic solutions when the coupling is linear and conservative. One of these, in which the oscillators are synchronized, persists and is stable for all coupling strengths. The other, in which the oscillators are π radiant out of phase, disappears either in a Hopf bifurcation or when fixed points appear on the orbit at a critical ratio of the coupling strength to the frequency. The out-of-phase oscillation is unstable except on an open set in the frequency-coupling-strength plane which contains moderate values of both parameters. Furthermore, there are tori bifurcating from the out-of-phase solution, which means, according to the Arnol'd theory for Hopf bifurcations in maps, that there may be periodic solutions of arbitrarily large period and chaotic solutions as well. Numerous other bifurcations occur, and there are a number of higher codimension singularities. In a large region of the frequency-coupling parameter plane stable steady states coexist with stable periodic solutions.
The bistability phenomenon in single and coupled oscillators based on VO2 switches
NASA Astrophysics Data System (ADS)
Belyaev, M. A.; Putrolaynen, V. V.; Velichko, A. A.
2017-01-01
New operation regimes of single and coupled oscillators in circuits based on planar VO2 switches have been studied. The phenomenon of bistability is discovered, which consists in controlled switching of self-sustained oscillations by external pulses, which is a promising basis for the creation of oscillatory memory cells and implementation of pulse coupling regimes in artificial neural networks (ANNs). The duration of switch-on and switch-off pulses is no less that 20 μs and 30 ms, respectively. It is established that the region of threshold voltages for bistable switching in coupled oscillators is much wider than in a single oscillator and the hysteresis width in the former case can reach 2 V. A regime of initiation of switching packets has been observed that models the ANN packet activity.
Amplitude and phase effects on the synchronization of delay-coupled oscillators
D'Huys, O.; Vicente, R.; Danckaert, J.; Fischer, I.
2010-12-15
We consider the behavior of Stuart-Landau oscillators as generic limit-cycle oscillators when they are interacting with delay. We investigate the role of amplitude and phase instabilities in producing symmetry-breaking/restoring transitions. Using analytical and numerical methods we compare the dynamics of one oscillator with delayed feedback, two oscillators mutually coupled with delay, and two delay-coupled elements with self-feedback. Taking only the phase dynamics into account, no chaotic dynamics is observed, and the stability of the identical synchronization solution is the same in each of the three studied networks of delay-coupled elements. When allowing for a variable oscillation amplitude, the delay can induce amplitude instabilities. We provide analytical proof that, in case of two mutually coupled elements, the onset of an amplitude instability always results in antiphase oscillations, leading to a leader-laggard behavior in the chaotic regime. Adding self-feedback with the same strength and delay as the coupling stabilizes the system in the transverse direction and, thus, promotes the onset of identically synchronized behavior.
Synchronization in slowly switching networks of coupled oscillators
NASA Astrophysics Data System (ADS)
Zhou, Jie; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Boccaletti, S.
2016-10-01
Networks whose structure of connections evolves in time constitute a big challenge in the study of synchronization, in particular when the time scales for the evolution of the graph topology are comparable with (or even longer than) those pertinent to the units’ dynamics. We here focus on networks with a slow-switching structure, and show that the necessary conditions for synchronization, i.e. the conditions for which synchronization is locally stable, are determined by the time average of the largest Lyapunov exponents of transverse modes of the switching topologies. Comparison between fast- and slow-switching networks allows elucidating that slow-switching processes prompt synchronization in the cases where the Master Stability Function is concave, whereas fast-switching schemes facilitate synchronization for convex curves. Moreover, the condition of slow-switching enables the introduction of a control strategy for inducing synchronization in networks with arbitrary structure and coupling strength, which is of evident relevance for broad applications in real world systems.
Synchronization in slowly switching networks of coupled oscillators
Zhou, Jie; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Boccaletti, S.
2016-01-01
Networks whose structure of connections evolves in time constitute a big challenge in the study of synchronization, in particular when the time scales for the evolution of the graph topology are comparable with (or even longer than) those pertinent to the units’ dynamics. We here focus on networks with a slow-switching structure, and show that the necessary conditions for synchronization, i.e. the conditions for which synchronization is locally stable, are determined by the time average of the largest Lyapunov exponents of transverse modes of the switching topologies. Comparison between fast- and slow-switching networks allows elucidating that slow-switching processes prompt synchronization in the cases where the Master Stability Function is concave, whereas fast-switching schemes facilitate synchronization for convex curves. Moreover, the condition of slow-switching enables the introduction of a control strategy for inducing synchronization in networks with arbitrary structure and coupling strength, which is of evident relevance for broad applications in real world systems. PMID:27779253
Two pulse-coupled non-identical, frequency-different BZ oscillators with time delay.
Lavrova, Anastasia I; Vanag, Vladimir K
2014-04-14
Two non-identical, frequency-different pulse-coupled oscillators with time delay have been systematically studied using four-variable model of the Belousov-Zhabotinsky (BZ) reaction at mutual inhibitory, mutual excitatory, and mixed excitatory-inhibitory types of coupling. Different resonances like 1 : 2, 2 : 3, 1 : 3, etc., as well as complex rhythms and abrupt changes between them occur depending on the coupling strengths, time delay, and frequency ratio. Analogously to in-phase and anti-phase oscillations for 1 : 1 resonance, a similar phase locking exists for 1 : 2 resonance in the case of inhibitory coupling. For excitatory coupling, a bursting regime is found. The number of spikes in a single burst can be tuned by both the frequency ratio and time delay. For excitatory-inhibitory coupling, a region where one oscillator is suppressed (OS zone) has been found. Boundary of the OS zone depends on the frequency ratio. For weakly coupled oscillators, Farey sequence has been found for excitatory-inhibitory and mutual excitatory coupling.
Synchronization of coupled noisy oscillators: Coarse graining from continuous to discrete phases
NASA Astrophysics Data System (ADS)
Escaff, Daniel; Rosas, Alexandre; Toral, Raúl; Lindenberg, Katja
2016-11-01
The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that coupled discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators. In this work we explore conditions that justify this assumption by coarse graining continuous phase units. In particular, we determine the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators.
Synchronization of coupled noisy oscillators: Coarse graining from continuous to discrete phases.
Escaff, Daniel; Rosas, Alexandre; Toral, Raúl; Lindenberg, Katja
2016-11-01
The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that coupled discrete-state noisy Markov units can be used to model mathematically more complex coupled noisy continuous phase oscillators. In this work we explore conditions that justify this assumption by coarse graining continuous phase units. In particular, we determine the minimum number of states necessary to justify this correspondence for Kuramoto-like oscillators.
NASA Astrophysics Data System (ADS)
Pelinovsky, Dmitry; Penati, Tiziano; Paleari, Simone
2016-08-01
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrödinger type. We show how to justify this approximation by two methods, which have been very popular in the recent literature. The first method relies on a priori energy estimates and multi-scale decompositions. The second method is based on a resonant normal form theorem. We show that although the two methods are different in the implementation, they produce equivalent results as the end product. We also discuss the applications of the discrete nonlinear Schrödinger equation in the context of existence and stability of breathers of the Klein-Gordon lattice.
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Lepri, Stefano; Pikovsky, Arkady
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Apical oscillations in amnioserosa cells: basolateral coupling and mechanical autonomy.
Jayasinghe, Aroshan K; Crews, Sarah M; Mashburn, David N; Hutson, M Shane
2013-07-02
Holographic laser microsurgery is used to isolate single amnioserosa cells in vivo during early dorsal closure. During this stage of Drosophila embryogenesis, amnioserosa cells undergo oscillations in apical surface area. The postisolation behavior of individual cells depends on their preisolation phase in these contraction/expansion cycles: cells that were contracting tend to collapse quickly after isolation; cells that were expanding do not immediately collapse, but instead pause or even continue to expand for ∼40 s. In either case, the postisolation apical collapse can be prevented by prior anesthetization of the embryos with CO2. These results suggest that although the amnioserosa is under tension, its cells are subjected to only small elastic strains. Furthermore, their postisolation apical collapse is not a passive elastic relaxation, and both the contraction and expansion phases of their oscillations are driven by intracellular forces. All of the above require significant changes to existing computational models.
Apical Oscillations in Amnioserosa Cells: Basolateral Coupling and Mechanical Autonomy
Jayasinghe, Aroshan K.; Crews, Sarah M.; Mashburn, David N.; Hutson, M. Shane
2013-01-01
Holographic laser microsurgery is used to isolate single amnioserosa cells in vivo during early dorsal closure. During this stage of Drosophila embryogenesis, amnioserosa cells undergo oscillations in apical surface area. The postisolation behavior of individual cells depends on their preisolation phase in these contraction/expansion cycles: cells that were contracting tend to collapse quickly after isolation; cells that were expanding do not immediately collapse, but instead pause or even continue to expand for ∼40 s. In either case, the postisolation apical collapse can be prevented by prior anesthetization of the embryos with CO2. These results suggest that although the amnioserosa is under tension, its cells are subjected to only small elastic strains. Furthermore, their postisolation apical collapse is not a passive elastic relaxation, and both the contraction and expansion phases of their oscillations are driven by intracellular forces. All of the above require significant changes to existing computational models. PMID:23823245
How to induce multiple delays in coupled chaotic oscillators?
Bhowmick, Sourav K.; Ghosh, Dibakar; Roy, Prodyot K.; Kurths, Jürgen; Dana, Syamal K.
2013-12-15
Lag synchronization is a basic phenomenon in mismatched coupled systems, delay coupled systems, and time-delayed systems. It is characterized by a lag configuration that identifies a unique time shift between all pairs of similar state variables of the coupled systems. In this report, an attempt is made how to induce multiple lag configurations in coupled systems when different pairs of state variables attain different time shift. A design of coupling is presented to realize this multiple lag synchronization. Numerical illustration is given using examples of the Rössler system and the slow-fast Hindmarsh-Rose neuron model. The multiple lag scenario is physically realized in an electronic circuit of two Sprott systems.
Hwang, Myung-Joong; Choi, Mahn-Soo
2010-08-15
The nonclassical behavior of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solutions do not account accurately for nonclassical effects such as squeezing. We suggest a trial wave function and demonstrate that it has an excellent accuracy for the quantum correlation effects as well as for the energy.
Phase chaos in the dynamics of an ensemble of oscillators with time-modulated global coupling
NASA Astrophysics Data System (ADS)
Kuznetsov, S. P.; Sedova, Yu. V.
2013-01-01
The object of consideration is an ensemble of globally coupled self-sustained oscillating elements with a finite-width frequency distribution. The ensemble interacts with the field of a resonator, which is a linear oscillator with a frequency doubly exceeding the mean frequency of the oscillators in the ensemble. The global coupling is switched on and off alternately, so that the ensemble alternatively passes from synchrony to asynchrony (Kuramoto transition). At each stage of activity (synchronization), the field of the resonator causes the mean field of the ensemble to oscillate so that the phase doubles compared with the previous stage of excitation. Therefore, the mean field dynamics is chaotic and, as follows from numerical simulation data, can be associated with the Smale-Williams attractor. Systems of this type can be applied in electronics, specifically, in secure communication systems, noise location, etc.
Thoke, Henrik Seir; Tobiesen, Asger; Brewer, Jonathan; Hansen, Per Lyngs; Stock, Roberto P.; Olsen, Lars F.; Bagatolli, Luis A.
2015-01-01
We detected very strong coupling between the oscillating concentration of ATP and the dynamics of intracellular water during glycolysis in Saccharomyces cerevisiae. Our results indicate that: i) dipolar relaxation of intracellular water is heterogeneous within the cell and different from dilute conditions, ii) water dipolar relaxation oscillates with glycolysis and in phase with ATP concentration, iii) this phenomenon is scale-invariant from the subcellular to the ensemble of synchronized cells and, iv) the periodicity of both glycolytic oscillations and dipolar relaxation are equally affected by D2O in a dose-dependent manner. These results offer a new insight into the coupling of an emergent intensive physicochemical property of the cell, i.e. cell-wide water dipolar relaxation, and a central metabolite (ATP) produced by a robustly oscillating metabolic process. PMID:25705902
Correlated dynamics of a Rabi oscillation and a quantum tunneling in coupled quantum dots
NASA Astrophysics Data System (ADS)
Xie, Weidong; Chu, Bingxin; Duan, Suqing; Xie, Yan; Chu, Weidong; Yang, Ning; Zhao, Xian-Geng
2015-08-01
We couple the Rabi oscillation in a double quantum dot (DQD) with the quantum tunneling in another DQD by Coulomb interaction between the neighboring dots. Such a coupling leads to correlation of the Rabi oscillating electron and the quantum tunneling one, and gives a tendency of synchronizing them under appropriate Rabi frequency ΩR and tunneling rate Tc. The correlated oscillation is shown clearly in the tunneling current. As ΩR =Tc, the Rabi oscillation and the quantum tunneling reach their strongest correlation and the two electrons finish their complete transitions simultaneously. And then, a single optical signal accomplishes a gang control of two electrons. This result encourages superior design of two-qubit quantum gates based on correlated DQDs.
NASA Astrophysics Data System (ADS)
Nkomo, Simbarashe; Tinsley, Mark R.; Showalter, Kenneth
2016-09-01
Chimera and chimera-like states are characterized in populations of photochemically coupled Belousov-Zhabotinsky (BZ) oscillators. Simple chimeras and chimera states with multiple and traveling phase clusters, phase-slip behavior, and chimera-like states with phase waves are described. Simulations with a realistic model of the discrete BZ system of populations of homogeneous and heterogeneous oscillators are compared with each other and with experimental behavior.
Linear stability and the Braess paradox in coupled-oscillator networks and electric power grids.
Coletta, Tommaso; Jacquod, Philippe
2016-03-01
We investigate the influence that adding a new coupling has on the linear stability of the synchronous state in coupled-oscillator networks. Using a simple model, we show that, depending on its location, the new coupling can lead to enhanced or reduced stability. We extend these results to electric power grids where a new line can lead to four different scenarios corresponding to enhanced or reduced grid stability as well as increased or decreased power flows. Our analysis shows that the Braess paradox may occur in any complex coupled system, where the synchronous state may be weakened and sometimes even destroyed by additional couplings.
Signatures of the A2 term in ultrastrongly coupled oscillators
NASA Astrophysics Data System (ADS)
Tufarelli, Tommaso; McEnery, K. R.; Maier, S. A.; Kim, M. S.
2015-06-01
We study a bosonic matter excitation coupled to a single-mode cavity field via electric dipole. Counter-rotating and A2 terms are included in the interaction model, A being the vector potential of the cavity field. In the ultrastrong coupling regime the vacuum of the bare modes is no longer the ground state of the Hamiltonian and contains a nonzero population of polaritons, the true normal modes of the system. If the parameters of the model satisfy the Thomas-Reiche-Kuhn sum rule, we find that the two polaritons are always equally populated. We show how this prediction could be tested in a quenching experiment, by rapidly switching on the coupling and analyzing the radiation emitted by the cavity. A refinement of the model based on a microscopic minimal coupling Hamiltonian is also provided, and its consequences on our results are characterized analytically.
Average dynamics of a finite set of coupled phase oscillators
Dima, Germán C. Mindlin, Gabriel B.
2014-06-15
We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.
Yashin, Victor V.; Levitan, Steven P.; Balazs, Anna C.
2015-01-01
Lightweight, deformable materials that can sense and respond to human touch and motion can be the basis of future wearable computers, where the material itself will be capable of performing computations. To facilitate the creation of “materials that compute”, we draw from two emerging modalities for computation: chemical computing, which relies on reaction-diffusion mechanisms to perform operations, and oscillatory computing, which performs pattern recognition through synchronization of coupled oscillators. Chemical computing systems, however, suffer from the fact that the reacting species are coupled only locally; the coupling is limited by diffusion as the chemical waves propagate throughout the system. Additionally, oscillatory computing systems have not utilized a potentially wearable material. To address both these limitations, we develop the first model for coupling self-oscillating polymer gels to a piezoelectric (PZ) micro-electro-mechanical system (MEMS). The resulting transduction between chemo-mechanical and electrical energy creates signals that can be propagated quickly over long distances and thus, permits remote, non-diffusively coupled oscillators to communicate and synchronize. Moreover, the oscillators can be organized into arbitrary topologies because the electrical connections lift the limitations of diffusive coupling. Using our model, we predict the synchronization behavior that can be used for computational tasks, ultimately enabling “materials that compute”. PMID:26105979
Analysis and design of coupled-oscillator arrays for microwave systems
NASA Astrophysics Data System (ADS)
Moussounda, Renaud
The concept of synchronized nonlinear coupled oscillators is applied to microwave and antenna engineering for the analysis and design of wireless communication and sensing systems operating at the microwave and/or millimeter (mm)-wave frequencies. The significance of such approach is justified from the potential gain in efficiency, weight, cost and functionality although technical challenges stand in the way. Unlike typical phased array systems, which are currently used to construct such systems, coupled-oscillator systems present additional challenges that mainly arise from maintaining stability and synchronization as the the coupled nonlinear system is operated. Linear systems do not present such stability issues and are consequently faster since they do not rely on any gradual synchronization mechanism in order to function. However, at significantly higher frequencies in the quasi-optical domain, coupled-oscillator systems can make up for the speed difference and present significant efficiency advantages over typical phased array architectures. In addition, coupled nonlinear systems possess inherent analog properties that can be used for a multitude of functions. This dissertation advances the topic of coupled-oscillator arrays by 1) developing an alternative set of techniques for designing the oscillating unit cells called active integrated antennas (AIAs) at microwave or mm-wave frequencies, 2) developing a more accurate description of the dynamics of the array, 3) developing and implementing a new topology for a coupling network that is able to extend stability, 4) implementing a fully non-reciprocally coupled array able to produce large scan angle without loss of stability, 5) proposing an architecture based on a single phase-locked loop (PLL) and containing a self-calibration mechanism, and finally 6) implementing a phase-boosting mechanism using simple circuits to amplify the phase difference between adjacent radiating antennas in order to increase
Effect of parameter mismatch on the dynamics of strongly coupled self sustained oscillators
NASA Astrophysics Data System (ADS)
Chakrabarty, Nilaj; Jain, Aditya; Lal, Nijil; Das Gupta, Kantimay; Parmananda, Punit
2017-01-01
In this paper, we present an experimental setup and an associated mathematical model to study the synchronization of two self-sustained, strongly coupled, mechanical oscillators (metronomes). The effects of a small detuning in the internal parameters, namely, damping and frequency, have been studied. Our experimental system is a pair of spring wound mechanical metronomes; coupled by placing them on a common base, free to move along a horizontal direction. We designed a photodiode array based non-contact, non-magnetic position detection system driven by a microcontroller to record the instantaneous angular displacement of each oscillator and the small linear displacement of the base, coupling the two. In our system, the mass of the oscillating pendula forms a significant fraction of the total mass of the system, leading to strong coupling of the oscillators. We modified the internal mechanism of the spring-wound "clockwork" slightly, such that the natural frequency and the internal damping could be independently tuned. Stable synchronized and anti-synchronized states were observed as the difference in the parameters was varied in the experiments. The simulation results showed a rapid increase in the phase difference between the two oscillators beyond a certain threshold of parameter mismatch. Our simple model of the escapement mechanism did not reproduce a complete 180° out of phase state. However, the numerical simulations show that increased mismatch in parameters leads to a synchronized state with a large phase difference.
Chaotic dynamics of coupled transverse-longitudinal plasma oscillations in magnetized plasmas.
Teychenné, D; Bésuelle, E; Oloumi, A; Salomaa, R R
2000-12-25
The propagation of intense electromagnetic waves in cold magnetized plasma is tackled through a relativistic hydrodynamic approach. The analysis of coupled transverse-longitudinal plasma oscillations is performed for traveling plane waves. When these waves propagate perpendicularly to a static magnetic field, the model is describable in terms of a nonlinear dynamical system with 2 degrees of freedom. A constant of motion is obtained and the powerful classical mechanics methods can be used. A new class of solutions, i.e., the chaotic solutions, is discovered by the Poincaré surface of sections. As a result, coupled transverse-longitudinal plasma oscillations become aperiodically modulated.
Probabilistic convergence guarantees for type-II pulse-coupled oscillators
NASA Astrophysics Data System (ADS)
Nishimura, Joel; Friedman, Eric J.
2012-08-01
We show that a large class of pulse-coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic network analysis, and a classification scheme for type-II phase response curves to produce rigorous lower bounds for convergence probabilities based on network density. These results suggest methods for the analysis of pulse-coupled oscillators, and provide insights into the balance of excitation and inhibition in the operation of biological type-II phase response curves and also the design of decentralized and minimal clock synchronization schemes in sensor nets.
Frequency adjustment and synchrony in networks of delayed pulse-coupled oscillators
NASA Astrophysics Data System (ADS)
Nishimura, Joel
2015-01-01
We introduce a system of pulse-coupled oscillators that can change both their phases and frequencies and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on strongly connected graphs with time delays. The analysis involves decomposing the network into a forest of tree-like structures that capture causality. These results provide a robust method of sensor net synchronization as well as demonstrate a new avenue of possible pulse-coupled oscillator research.
NASA Astrophysics Data System (ADS)
Timms, L.; English, L. Q.
2014-03-01
We explore both analytically and numerically an ensemble of coupled phase oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time delay (due to finite signal-propagation speeds) and network plasticity (via dynamic coupling constants) inspired by the Hebbian learning rule in neuroscience. When time delay and learning effects combine, interesting synchronization phenomena are observed. We investigate the formation of spatiotemporal patterns in both one- and two-dimensional oscillator lattices with periodic boundary conditions and comment on the role of dimensionality.
Entrainment of a Synthetic Oscillator through Queueing Coupling
NASA Astrophysics Data System (ADS)
Hochendoner, Philip; Mather, William; Butzin, Nicholas; Ogle, Curtis
2014-03-01
Many biological systems naturally exhibit (often noisy) oscillatory patterns that are capable of being entrained by external stimuli, though the mechanism of entrainment is typically obscured by the complexity of native networks. A synthetic biology approach, where genetic programs are wired ``by hand,'' has proven useful in this regard. In the present study, we use a synthetic oscillator in Escherichia coli to demonstrate a novel and potentially widespread mechanism for biological entrainment: competition of proteins for degradation by common pathway, i.e. a entrainment by a bottleneck. To faithfully represent the discrete and stochastic nature of this bottleneck, we leverage results from a recent biological queueing theory, where in particular, the queueing theoretic concept of workload is discovered to simplify the analysis. NSF Award 1330180.
Wigner function and transition amplitude of three mutually coupled oscillators
NASA Astrophysics Data System (ADS)
Nassar, M. M.; Sebawe Abdalla, M.
2007-04-01
A full quantum mechanical treatment of three electromagnetic fields is considered. The proposed model consists of three different coupling parameters for which the rotating and counter-rotating terms are retained. An exact solution of the wave function in the Schrödinger picture is obtained and the connection with the coherent states wave function is given. The symmetrical ordered quasi-probability distribution function ( W-Wigner function) is calculated via the wave function in the coherent states representation. The squeezing phenomenon is also examined for both single mode and squared-amplitude, where the collapse and revival phenomena are observed. For the case in which λ3=0 and ω1=ω2=ω3 (exact resonances) we find that the late phenomenon is apparent but only after long period of the time considered. The transition amplitude between two different coherent states (a state in which all the coupling parameters are involved and a state when the coupling parameter λ3=0) is calculated. It is shown that the probability amplitude is sensitive to the variation of the mean photon numbers, and the coupling parameters as well as to the field frequencies.
NASA Astrophysics Data System (ADS)
Emenheiser, Jeffrey; Chapman, Airlie; Pósfai, Márton; Crutchfield, James P.; Mesbahi, Mehran; D'Souza, Raissa M.
2016-09-01
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.
Self-organized network of phase oscillators coupled by activity-dependent interactions.
Aoki, Takaaki; Aoyagi, Toshio
2011-12-01
We investigate a network of coupled phase oscillators whose interactions evolve dynamically depending on the relative phases between the oscillators. We found that this coevolving dynamical system robustly yields three basic states of collective behavior with their self-organized interactions. The first is the two-cluster state, in which the oscillators are organized into two synchronized groups. The second is the coherent state, in which the oscillators are arranged sequentially in time. The third is the chaotic state, in which the relative phases between oscillators and their coupling weights are chaotically shuffled. Furthermore, we demonstrate that self-assembled multiclusters can be designed by controlling the weight dynamics. Note that the phase patterns of the oscillators and the weighted network of interactions between them are simultaneously organized through this coevolving dynamics. We expect that these results will provide new insight into self-assembly mechanisms by which the collective behavior of a rhythmic system emerges as a result of the dynamics of adaptive interactions.
A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network
Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien
2017-01-01
With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices’ non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing. PMID:28322262
A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network.
Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien
2017-03-21
With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices' non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing.
A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network
NASA Astrophysics Data System (ADS)
Vodenicarevic, Damir; Locatelli, Nicolas; Abreu Araujo, Flavio; Grollier, Julie; Querlioz, Damien
2017-03-01
With conventional transistor technologies reaching their limits, alternative computing schemes based on novel technologies are currently gaining considerable interest. Notably, promising computing approaches have proposed to leverage the complex dynamics emerging in networks of coupled oscillators based on nanotechnologies. The physical implementation of such architectures remains a true challenge, however, as most proposed ideas are not robust to nanotechnology devices’ non-idealities. In this work, we propose and investigate the implementation of an oscillator-based architecture, which can be used to carry out pattern recognition tasks, and which is tailored to the specificities of nanotechnologies. This scheme relies on a weak coupling between oscillators, and does not require a fine tuning of the coupling values. After evaluating its reliability under the severe constraints associated to nanotechnologies, we explore the scalability of such an architecture, suggesting its potential to realize pattern recognition tasks using limited resources. We show that it is robust to issues like noise, variability and oscillator non-linearity. Defining network optimization design rules, we show that nano-oscillator networks could be used for efficient cognitive processing.
Collective Dipole Oscillations of a Spin-Orbit Coupled Bose-Einstein Condensate
NASA Astrophysics Data System (ADS)
Zhang, Jin-Yi; Ji, Si-Cong; Chen, Zhu; Zhang, Long; Du, Zhi-Dong; Yan, Bo; Pan, Ge-Sheng; Zhao, Bo; Deng, You-Jin; Zhai, Hui; Chen, Shuai; Pan, Jian-Wei
2012-09-01
In this Letter, we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. The dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region as a function of spin-orbit coupling parameters as well as the oscillation amplitude. The anharmonic properties beyond the effective-mass approximation are revealed, such as the amplitude-dependent frequency and finite oscillation frequency at a place with a divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of the spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility—a static physical quantity—can be measured via the dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates the magnetic nonzero-momentum condensate from the nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a benchmark for recently developed theoretical approaches.
Robustness of chimera states for coupled FitzHugh-Nagumo oscillators
NASA Astrophysics Data System (ADS)
Omelchenko, Iryna; Provata, Astero; Hizanidis, Johanne; Schöll, Eckehard; Hövel, Philipp
2015-02-01
Chimera states are complex spatio-temporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics. This counterintuitive phenomenon was first observed in systems of identical oscillators with symmetric coupling topology. Can one overcome these limitations? To address this question, we discuss the robustness of chimera states in networks of FitzHugh-Nagumo oscillators. Considering networks of inhomogeneous elements with regular coupling topology, and networks of identical elements with irregular coupling topologies, we demonstrate that chimera states are robust with respect to these perturbations and analyze their properties as the inhomogeneities increase. We find that modifications of coupling topologies cause qualitative changes of chimera states: additional random links induce a shift of the stability regions in the system parameter plane, gaps in the connectivity matrix result in a change of the multiplicity of incoherent regions of the chimera state, and hierarchical geometry in the connectivity matrix induces nested coherent and incoherent regions.
Permanent Rabi oscillations in coupled exciton-photon systems with PT-symmetry.
Chestnov, Igor Yu; Demirchyan, Sevak S; Alodjants, Alexander P; Rubo, Yuri G; Kavokin, Alexey V
2016-01-21
We propose a physical mechanism which enables permanent Rabi oscillations in driven-dissipative condensates of exciton-polaritons in semiconductor microcavities subjected to external magnetic fields. The method is based on stimulated scattering of excitons from the incoherent reservoir. We demonstrate that permanent non-decaying oscillations may appear due to the parity-time symmetry of the coupled exciton-photon system realized in a specific regime of pumping to the exciton state and depletion of the reservoir. At non-zero exciton-photon detuning, robust permanent Rabi oscillations occur with unequal amplitudes of exciton and photon components. Our predictions pave way to realization of integrated circuits based on exciton-polariton Rabi oscillators.
Permanent Rabi oscillations in coupled exciton-photon systems with PT -symmetry
Chestnov, Igor Yu.; Demirchyan, Sevak S.; Alodjants, Alexander P.; Rubo, Yuri G.; Kavokin, Alexey V.
2016-01-01
We propose a physical mechanism which enables permanent Rabi oscillations in driven-dissipative condensates of exciton-polaritons in semiconductor microcavities subjected to external magnetic fields. The method is based on stimulated scattering of excitons from the incoherent reservoir. We demonstrate that permanent non-decaying oscillations may appear due to the parity-time symmetry of the coupled exciton-photon system realized in a specific regime of pumping to the exciton state and depletion of the reservoir. At non-zero exciton-photon detuning, robust permanent Rabi oscillations occur with unequal amplitudes of exciton and photon components. Our predictions pave way to realization of integrated circuits based on exciton-polariton Rabi oscillators. PMID:26790534
Kudo, Kiwamu Suto, Hirofumi; Nagasawa, Tazumi; Mizushima, Koichi; Sato, Rie
2014-10-28
The fundamental function of any oscillator is to produce a waveform with a stable frequency. Here, we show a method of frequency stabilization for spin-torque nano-oscillators (STNOs) that relies on coupling with an adjacent nanomagnet through the magnetic dipole–dipole interaction. It is numerically demonstrated that highly stable oscillations occur as a result of mutual feedback between an STNO and a nanomagnet. The nanomagnet acts as a nonlinear resonator for the STNO. This method is based on the nonlinear behavior of the resonator and can be considered as a magnetic analogue of an optimization scheme in nanoelectromechanical systems. The oscillation frequency is most stabilized when the nanomagnet is driven at a special feedback point at which the feedback noise between the STNO and resonator is completely eliminated.
Globally attracting synchrony in a network of oscillators with all-to-all inhibitory pulse coupling
NASA Astrophysics Data System (ADS)
Canavier, Carmen C.; Tikidji-Hamburyan, Ruben A.
2017-03-01
The synchronization tendencies of networks of oscillators have been studied intensely. We assume a network of all-to-all pulse-coupled oscillators in which the effect of a pulse is independent of the number of oscillators that simultaneously emit a pulse and the normalized delay (the phase resetting) is a monotonically increasing function of oscillator phase with the slope everywhere less than 1 and a value greater than 2 φ -1 , where φ is the normalized phase. Order switching cannot occur; the only possible solutions are globally attracting synchrony and cluster solutions with a fixed firing order. For small conduction delays, we prove the former stable and all other possible attractors nonexistent due to the destabilizing discontinuity of the phase resetting at a phase of 0.
Gutierrez, Gabrielle J; O'Leary, Timothy; Marder, Eve
2013-03-06
Rhythmic oscillations are common features of nervous systems. One of the fundamental questions posed by these rhythms is how individual neurons or groups of neurons are recruited into different network oscillations. We modeled competing fast and slow oscillators connected to a hub neuron with electrical and inhibitory synapses. We explore the patterns of coordination shown in the network as a function of the electrical coupling and inhibitory synapse strengths with the help of a novel visualization method that we call the "parameterscape." The hub neuron can be switched between the fast and slow oscillators by multiple network mechanisms, indicating that a given change in network state can be achieved by degenerate cellular mechanisms. These results have importance for interpreting experiments employing optogenetic, genetic, and pharmacological manipulations to understand circuit dynamics.
NASA Astrophysics Data System (ADS)
Schmidt, Lennart; Krischer, Katharina
2015-06-01
We study an oscillatory medium with a nonlinear global coupling that gives rise to a harmonic mean-field oscillation with constant amplitude and frequency. Two types of cluster states are found, each undergoing a symmetry-breaking transition towards a related chimera state. We demonstrate that the diffusional coupling is non-essential for these complex dynamics. Furthermore, we investigate localized turbulence and discuss whether it can be categorized as a chimera state.
Correlations, fluctuations and stability of a finite-size network of coupled oscillators
NASA Astrophysics Data System (ADS)
Buice, Michael; Chow, Carson
2008-03-01
The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N -> infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model.
Spin Number Coherent States and the Problem of Two Coupled Oscillators
NASA Astrophysics Data System (ADS)
Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D.
2015-07-01
From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(2) generators and construct a new set of operators which also close the su(2) Lie algebra, being the Perelomov number coherent states the new basis for its unitary irreducible representation. We apply our results to obtain the energy spectrum, the eigenstates and the partition function of two coupled oscillators. We show that the eigenstates of two coupled oscillators are the SU(2) Perelomov number coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters. Supported by SNI-México, COFAA-IPN, EDD-IPN, EDI-IPN, SIP-IPN Project No. 20150935
NASA Astrophysics Data System (ADS)
Kagawa, Yuki; Takamatsu, Atsuko
2009-04-01
To reveal the relation between network structures found in two-dimensional biological systems, such as protoplasmic tube networks in the plasmodium of true slime mold, and spatiotemporal oscillation patterns emerged on the networks, we constructed coupled phase oscillators on weighted planar networks and investigated their dynamics. Results showed that the distribution of edge weights in the networks strongly affects (i) the propensity for global synchronization and (ii) emerging ratios of oscillation patterns, such as traveling and concentric waves, even if the total weight is fixed. In-phase locking, traveling wave, and concentric wave patterns were, respectively, observed most frequently in uniformly weighted, center weighted treelike, and periphery weighted ring-shaped networks. Controlling the global spatiotemporal patterns with the weight distribution given by the local weighting (coupling) rules might be useful in biological network systems including the plasmodial networks and neural networks in the brain.
Teaching the Physics of a String-Coupled Pendulum Oscillator: Not Just for Seniors Anymore
ERIC Educational Resources Information Center
Cho, Young-Ki
2012-01-01
Coupled oscillators are an example of resonant energy exchange that is an interesting topic for many students in various majors, such as physics, chemistry, and electrical and mechanical engineering. However, this subject matter is considered too advanced for freshmen and sophomores, usually because of the level of mathematics involved.…
ERIC Educational Resources Information Center
Marcotte, Ronald E.
2005-01-01
This physical chemistry lecture demonstration is designed to aid the understanding of intramolecular energy transfer processes as part of the presentation of the theory of unimolecular reaction rates. Coupled pendulums are used to show the rate of migration of energy between oscillators under resonant and nonresonant conditions with varying…
NASA Astrophysics Data System (ADS)
Amro, Rami M.; Neiman, Alexander B.
2014-11-01
Sensory hair cells of amphibians exhibit spontaneous activity in their hair bundles and membrane potentials, reflecting two distinct active amplification mechanisms employed in these peripheral mechanosensors. We use a two-compartment model of the bullfrog's saccular hair cell to study how the interaction between its mechanical and electrical compartments affects the emergence of distinct dynamical regimes, and the role of this interaction in shaping the response of the hair cell to weak mechanical stimuli. The model employs a Hodgkin-Huxley-type system for the basolateral electrical compartment and a nonlinear hair bundle oscillator for the mechanical compartment, which are coupled bidirectionally. In the model, forward coupling is provided by the mechanoelectrical transduction current, flowing from the hair bundle to the cell soma. Backward coupling is due to reverse electromechanical transduction, whereby variations of the membrane potential affect adaptation processes in the hair bundle. We isolate oscillation regions in the parameter space of the model and show that bidirectional coupling affects significantly the dynamics of the cell. In particular, self-sustained oscillations of the hair bundles and membrane potential can result from bidirectional coupling, and the coherence of spontaneous oscillations can be maximized by tuning the coupling strength. Consistent with previous experimental work, the model demonstrates that dynamical regimes of the hair bundle change in response to variations in the conductances of basolateral ion channels. We show that sensitivity of the hair cell to weak mechanical stimuli can be maximized by varying coupling strength, and that stochasticity of the hair bundle compartment is a limiting factor of the sensitivity.
Astakhov, Sergey; Gulai, Artem; Fujiwara, Naoya; Kurths, Jürgen
2016-02-01
A system of two asymmetrically coupled van der Pol oscillators has been studied. We show that the introduction of a small asymmetry in coupling leads to the appearance of a "wideband synchronization channel" in the bifurcational structure of the parameter space. An increase of asymmetry and transition to repulsive interaction leads to the formation of multistability. As the result, the tip of the Arnold's tongue widens due to the formation of folds defined by saddle-node bifurcation curves for the limit cycles on the torus.
NASA Astrophysics Data System (ADS)
Astakhov, Sergey; Gulai, Artem; Fujiwara, Naoya; Kurths, Jürgen
2016-02-01
A system of two asymmetrically coupled van der Pol oscillators has been studied. We show that the introduction of a small asymmetry in coupling leads to the appearance of a "wideband synchronization channel" in the bifurcational structure of the parameter space. An increase of asymmetry and transition to repulsive interaction leads to the formation of multistability. As the result, the tip of the Arnold's tongue widens due to the formation of folds defined by saddle-node bifurcation curves for the limit cycles on the torus.
Self-organized synchronous oscillations in a network of excitable cells coupled by gap junctions.
Lewis, T J; Rinzel, J
2000-11-01
Recent evidence suggests that electrical coupling plays a role in generating oscillatory behaviour in networks of neurons; however, the underlying mechanisms have not been identified. Using a cellular automata model proposed by Traub et al (Traub R D, Schmitz D, Jefferys J G and Draguhn A 1999 High-frequency population oscillations are predicted to occur in hippocampal pyramidal neural networks interconnected by axo-axonal gap junctions Neuroscience 92 407-26), we describe a novel mechanism for self-organized oscillations in networks that have strong, sparse random electrical coupling via gap junctions. The network activity is generated by random spontaneous activity that is moulded into regular population oscillations by the propagation of activity through the network. We explain how this activity gives rise to particular dependences of mean oscillation frequency on network connectivity parameters and on the rate of spontaneous activity, and we derive analytical expressions to approximate the mean frequency and variance of the oscillations. In doing so, we provide insight into possible mechanisms for frequency control and modulation in networks of neurons.
Occurrence and stability of chimera states in coupled externally excited oscillators
NASA Astrophysics Data System (ADS)
Dudkowski, Dawid; Maistrenko, Yuri; Kapitaniak, Tomasz
2016-11-01
We studied the phenomenon of chimera states in networks of non-locally coupled externally excited oscillators. Units of the considered networks are bi-stable, having two co-existing attractors of different types (chaotic and periodic). The occurrence of chimeras is discussed, and the influence of coupling radius and coupling strength on their co-existence is analyzed (including typical bifurcation scenarios). We present a statistical analysis and investigate sensitivity of the probability of observing chimeras to the initial conditions and parameter values. Due to the fact that each unit of the considered networks is individually excited, we study the influence of the excitation failure on stability of observed states. Typical transitions are shown, and changes in network's dynamics are discussed. We analyze systems of coupled van der Pol-Duffing oscillators and the Duffing ones. Described chimera states are robust as they are observed in the wide regions of parameter values, as well as in other networks of coupled forced oscillators.
Synchronization and plateau splitting of coupled oscillators with long-range power-law interactions
NASA Astrophysics Data System (ADS)
Kuo, Huan-Yu; Wu, Kuo-An
2015-12-01
We investigate synchronization and plateau splitting of coupled oscillators on a one-dimensional lattice with long-range interactions that decay over distance as a power law. We show that in the thermodynamic limit the dynamics of systems of coupled oscillators with power-law exponent α ≤1 is identical to that of the all-to-all coupling case. For α >1 , oscillatory behavior of the phase coherence appears as a result of single plateau splitting into multiple plateaus. A coarse-graining method is used to investigate the onset of plateau splitting. We analyze a simple oscillatory state formed by two plateaus in detail and propose a systematic approach to predict the onset of plateau splitting. The prediction of breaking points of plateau splitting is in quantitatively good agreement with numerical simulations.
NASA Astrophysics Data System (ADS)
Ramírez Ávila, G. M.; Kurths, J.; Guisset, J. L.; Deneubourg, J. L.
2014-12-01
We studied synchronization and clustering in two types of pulse-coupled oscillators, namely, integrate-and-fire and light-controlled oscillators. We considered for the analysis globally coupled oscillators, either by a mean-field type coupling or a distance-dependent one. Using statistically diverse measures such as the transient, probability of total synchronization, fraction of clustered oscillators, mean size, and mean number of clusters, we describe clustering and synchronous behavior for populations of nonidentical oscillators and perform a comparative analysis of the behavioral differences and similitudes among these types of oscillators. Considering a mean-field approach, we found high probability of total synchronization in all cases for integrate-and-fire oscillators; on the other hand, in a more realistic situation, for light-controlled oscillators, i.e., when oscillators do not fire instantaneously, the probability of total synchronization decreases drastically for small differences among the oscillators and subsequently, for larger differences, it slightly increases. When the coupling strength depends on the distance, the probability of total synchronization plummets dramatically with the number of oscillators especially in the case of integrate-and-fire oscillators. The latter constitutes an interesting result because it indicates that in realistic situations, the probability of total synchronization is not very high for a population of pulse-coupled oscillators; this entails that its utilization as a paradigmatic model of total synchronization does not suit well, especially when the coupling depends on the distance. This article is dedicated to our good friend and colleague Hilda Cerdeira as a tribute to the scientific work developed over her career.
Verification of the Model of Inductive Coupling between a Josephson Oscillator and a Stripline
NASA Astrophysics Data System (ADS)
Kudo, Keisuke; Yoshida, Keiji; Enpuku, Keiji; Yamafuji, Kaoru
1993-01-01
In order to realize an efficient coupling between a flux-flow-type Josephson oscillator (FFO) and a stripline, we have carried out experiments to verify the mathematical model of the inductive coupling scheme between FFO and a stripline resonator in the frequency range between 50 GHz and 350 GHz. It is shown that the simulation using the proposed equivalent circuit for the inductive coupling scheme well explains the experimental results. The experimentally obtained center frequency and the bandwidth of the matching circuit were as large as 120 GHz and 40 GHz, respectively, which are also in reasonable agreement with those obtained in the simulation.
Partial Synchronization in Pulse-Coupled Oscillator Networks I: Theory
NASA Astrophysics Data System (ADS)
Engelbrecht, Jan; Chen, Bolun; Mirollo, Renato
We study N identical integrate and fire model neurons coupled in an all to all network through α-function pulses, weighted by a parameter K. Studies of the dynamics of this system often focus on the stability of the fully synchronous and the fully asynchronous splay states, that naturally depend on the sign of K, i.e. excitation vs inhibition. We find that for finite N there is a rich set of other partially synchronized attractors, such as (N - 1 , 1) fixed states and partially synchronized splay states. Our framework exploits the neutrality of the dynamics for K = 0 which allows us to implement a dimensional reduction strategy that replaces the discrete pulses with a continuous flow, with the sign of K determining the flow direction. This framework naturally incorporates a hierarchy of partially synchronized subspaces in which the new states lie. For N = 2 , 3 , 4 , we completely describe the sequence of bifurcations and the stability of all fixed points and limit cycles. Work Supported by NSF DMS 1413020.
Chimera states in coupled Kuramoto oscillators with inertia
Olmi, Simona
2015-12-15
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.
Chimera states in coupled Kuramoto oscillators with inertia
NASA Astrophysics Data System (ADS)
Olmi, Simona
2015-12-01
The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.
Coherence-incoherence patterns in a ring of non-locally coupled phase oscillators
NASA Astrophysics Data System (ADS)
Omel'chenko, O. E.
2013-09-01
We consider a paradigmatic spatially extended model of non-locally coupled phase oscillators which are uniformly distributed within a one-dimensional interval and interact depending on the distance between their sites' modulo periodic boundary conditions. This model can display peculiar spatio-temporal patterns consisting of alternating patches with synchronized (coherent) or irregular (incoherent) oscillator dynamics, hence the name coherence-incoherence pattern, or chimera state. For such patterns we formulate a general bifurcation analysis scheme based on a hierarchy of continuum limit equations. This provides the possibility of classifying known coherence-incoherence patterns and of suggesting directions for the search for new ones.
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
NASA Astrophysics Data System (ADS)
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
Hippocampal strata theta oscillations change their frequency and coupling during spatial learning.
Hernández-Pérez, J Jesús; Gutiérrez-Guzmán, Blanca E; Olvera-Cortés, María E
2016-11-19
The theta rhythm is necessary for hippocampal-dependent spatial learning. It has been proposed that each hippocampal stratum can generate a current theta dipole. Therefore, considering that each hippocampal circuit (CA1, CA3, and Dentate Gyrus (DG)) contributes differently to distinct aspects of a spatial memory, the theta oscillations on each stratum and their couplings may exhibit oscillatory dynamics associated with different stages of learning. To test this hypothesis, the theta oscillations from five hippocampal strata were recorded in the rat during different stages of learning in a Morris maze. The peak power, the relative power (RP) and the coherence between hippocampal strata were analyzed. The early acquisition stage of the Morris task was characterized by the predominance of slow frequency theta activity and high coupling between specific hippocampal strata at slow frequencies. However, on the last training day, the theta oscillations were faster in all hippocampal strata, with tighter coupling at fast frequencies between the CA3 pyramidal stratum and other strata. Our results suggest that modifications to the theta frequency and its coupling can be a means by which the hippocampus differentially operates during acquisition and retrieval states.
NASA Astrophysics Data System (ADS)
Zhao, Jiaxin; Han, Song; Lin, Hai; Yang, Helin
2015-11-01
Metamaterials (MMs) can be tailored to support electromagnetic interference, which is the kernel for the material-based electromagnetically induced transparency (EIT) phenomena, alternatively transparency based on electric interference can be deemed as electrically resonant transparency (ERT). Here, we experimentally and theoretically demonstrate two kinds of bi-layered MMs. The C3-C6 hybrid MM exhibits triple-mode ERT with transmission peaks of 0.84 at 9.6 GHz, 0.92 at 10.4 GHz, and 0.93 at 11.5 GHz for the horizontally polarized wave, and dual-mode ERT with transmission peaks of 0.84 at 8.8 GHz and 0.91 at 10.2 GHz for the vertically polarized wave. However, the C4-C8 hybrid MM, with two stable transparent peaks of 0.92 and 0.88 at 10.46 GHz and 11.61 GHz, is proven to be polarization independent. The measured results show excellent agreement with numerical simulations. A coupled oscillator model is employed to theoretically study the near field interference between the induced dipoles on the transmission properties. The results presented here will find their application value for multi-mode slow light devices, filters and attenuators, and so on.
On the nonlinear electromagnetic coupling between a coil and an oscillating magnet
NASA Astrophysics Data System (ADS)
Sneller, Adam J.; Mann, Brian P.
2010-07-01
The electromagnetic induction of voltage across a coil due to the motion of a magnet is among the fundamental problems of physics, and it has a broad range of practical applications. While Maxwell's equations exactly describe this phenomenon, the physical complexity inherent in most realistic situations often prevents the generation of closed-form expressions for the electromagnetic coupling. This paper uses basic principles to develop an approximate analytical expression for the induced voltage in terms of a set of physical parameters, and experimental results demonstrate a high level of validity in the model over the parameter values tested. For oscillatory magnet motion about a point on a coil's axis, it is shown that the induced voltage is an infinite sum of harmonics at integer multiples of the oscillation frequency; the relative amplitudes of these harmonics vary as the magnet's equilibrium position migrates along the coil's axis, causing the odd and even harmonics to vanish, reappear and reach peak values at predictable locations. Several simplifications to the model are considered, and their validity is investigated analytically over a range of parameters.
Nicu, Valentin Paul
2016-08-03
Using two illustrative examples it is shown that the generalised coupled oscillator (GCO) mechanism implies that the stability of the VCD sign computed for a given normal mode is not reflected by the magnitude of the ratio ζ between the rotational strength and dipole strength of the respective mode, i.e., the VCD robustness criterium proposed by Góbi and Magyarfalvi. The performed VCD GCO analysis brings further insight into the GCO mechanism and also into the VCD robustness concept. First, it shows that the GCO mechanism can be interpreted as a VCD resonance enhancement mechanism, i.e. very large VCD signals can be observed when the interacting molecular fragments are in favourable orientation. Second, it shows that the uncertainties observed in the computed VCD signs are associated to uncertainties in the relative orientation of the coupled oscillator fragments and/or to uncertainties in the predicted nuclear displacement vectors, i.e. not uncertainties in the computed magnetic dipole transition moments as was originally assumed. Since it is able to identify such situations easily, the VCD GCO analysis can be used as a VCD robustness analysis.
NASA Astrophysics Data System (ADS)
Park, I. J.; Woo, S. I.
1993-09-01
Gas-phase coupling between two Pd(110) single crystals in a UHV CO oxidation reaction in a continuous stirred tank reactor (CSTR) has been simulated by solving gas-phase mass balance equations with kinetic rate equations. This work was motivated by the experimental results which show that the frequency of partial pressure change in carbon monoxide is the same as the frequency of the work function change in the oscillation region and that the coupling between the two crystals occurred entirely via CO partial pressure. The computer simulation described here gives qualitative agreement with the experimental results. The change in the oscillatory region originating from the coupling of chemical oscillators which are slightly different to each other is successfully demonstrated by this model. The coupling of two oscillators having a simple periodic oscillation to produce mixed-mode oscillation was also successfully simulated.
Assessing Aircraft Susceptibility to Nonlinear Aircraft-Pilot Coupling/Pilot-Induced Oscillations
NASA Technical Reports Server (NTRS)
Hess, R.A.; Stout, P. W.
1997-01-01
A unified approach for assessing aircraft susceptibility to aircraft-pilot coupling (or pilot-induced oscillations) which was previously reported in the literature and applied to linear systems is extended to nonlinear systems, with emphasis upon vehicles with actuator rate saturation. The linear methodology provided a tool for predicting: (1) handling qualities levels, (2) pilot-induced oscillation rating levels and (3) a frequency range in which pilot-induced oscillations are likely to occur. The extension to nonlinear systems provides a methodology for predicting the latter two quantities. Eight examples are presented to illustrate the use of the technique. The dearth of experimental flight-test data involving systematic variation and assessment of the effects of actuator rate limits presently prevents a more thorough evaluation of the methodology.
Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators
NASA Astrophysics Data System (ADS)
Wolfrum, Matthias; Omel'chenko, Oleh E.; Sieber, Jan
2015-05-01
We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.
Dynamical quorum-sensing in oscillators coupled through an external medium
NASA Astrophysics Data System (ADS)
Schwab, David J.; Baetica, Ania; Mehta, Pankaj
2012-11-01
Many biological and physical systems exhibit population-density-dependent transitions to synchronized oscillations in a process often termed “dynamical quorum sensing”. Synchronization frequently arises through chemical communication via signaling molecules distributed through an external medium. We study a simple theoretical model for dynamical quorum sensing: a heterogenous population of limit-cycle oscillators diffusively coupled through a common medium. We show that this model exhibits a rich phase diagram with four qualitatively distinct physical mechanisms that can lead to a loss of coherent population-level oscillations, including a novel mechanism arising from effective time-delays introduced by the external medium. We derive a single pair of analytic equations that allow us to calculate phase boundaries as a function of population density and show that the model reproduces many of the qualitative features of recent experiments on Belousov-Zhabotinsky catalytic particles as well as synthetically engineered bacteria.
Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators
Wolfrum, Matthias; Omel'chenko, Oleh E.; Sieber, Jan
2015-05-15
We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.
Lewis, M Anthony; Etienne-Cummings, Ralph; Hartmann, Mitra J; Xu, Zi Rong; Cohen, Avis H
2003-02-01
In biological systems, the task of computing a gait trajectory is shared between the biomechanical and nervous systems. We take the perspective that both of these seemingly different computations are examples of physical computation. Here we describe the progress that has been made toward building a minimal biped system that illustrates this idea. We embed a significant portion of the computation in physical devices, such as capacitors and transistors, to underline the potential power of emphasizing the understanding of physical computation. We describe results in the exploitation of physical computation by (1) using a passive knee to assist in dynamics computation, (2) using an oscillator to drive a monoped mechanism based on the passive knee, (3) using sensory entrainment to coordinate the mechanics with the neural oscillator, (4) coupling two such systems together mechanically at the hip and computationally via the resulting two oscillators to create a biped mechanism, and (5) demonstrating the resulting gait generation in the biped mechanism.
NASA Astrophysics Data System (ADS)
Miranda, Montserrat Ana; Burguete, Javier
2010-03-01
We report the first experimental evidence in hydrodynamics of a phase synchronization transition between 80 nonlocally coupled convective oscillators. The initial pattern corresponds to a spatiotemporal chaotic regime of irregular clusters which becomes unstable by increasing the vertical temperature difference. Further beyond, a robust pattern emerges with two large localized stationary clusters. We show that oscillators belonging to these stationary clusters have become synchronized through a supercritical bifurcation. The antiphase cross-correlations define surfaces of synchronized oscillators, we study how the interaction range between the initially nonlocally coupled oscillators increases as we cross quasi-statically the threshold of this bifurcation.
Antiresonant ring output-coupled continuous-wave optical parametric oscillator.
Devi, Kavita; Kumar, S Chaitanya; Esteban-Martin, A; Ebrahim-Zadeh, M
2012-08-13
We demonstrate the successful deployment of an antiresonant ring (ARR) interferometer for the attainment of optimum output coupling in a continuous-wave (cw) optical parametric oscillator (OPO). The cw OPO, configured as a singly-resonant oscillator (SRO), is based on a 50-mm-long MgO:PPLN crystal and pumped by cw Ytterbium-fiber laser at 1064 nm, with the ARR interferometer integrated into one arm of the standing-wave cavity. By fine adjustment of the ARR transmission, a continuously variable signal output coupling from 0.8% to 7.3% has been achieved, providing optimum output coupling for signal and optimum power extraction for the idler, at different input pumping levels. The experimental results are compared with theoretical calculations for conventional output-coupled cw SRO, and the study shows that by reducing the insertion loss of the ARR elements, the performance of the ARR-coupled cw SRO can be further enhanced. We also show that the use of the ARR does not lead to any degradation in the cw SRO output beam quality. The proof-of-principle demonstration confirms the effectiveness of the technique for continuous, in situ, and fine control of output coupling in cw OPOs to achieve maximum output power at any arbitrary pumping level above threshold.
Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion
Yang, Yuan; Solis-Escalante, Teodoro; van de Ruit, Mark; van der Helm, Frans C. T.; Schouten, Alfred C.
2016-01-01
Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis (ICA) and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e., the contralateral primary sensorimotor areas, supplementary motor area (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (EMG) is present with peaks in the beta band (15–35 Hz), while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4) and non-integer (2:3) harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (SMA, PFA) compared to the sensory association area (PPC); but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback. PMID:27999537
Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion.
Yang, Yuan; Solis-Escalante, Teodoro; van de Ruit, Mark; van der Helm, Frans C T; Schouten, Alfred C
2016-01-01
Coupling between cortical oscillations and muscle activity facilitates neuronal communication during motor control. The linear part of this coupling, known as corticomuscular coherence, has received substantial attention, even though neuronal communication underlying motor control has been demonstrated to be highly nonlinear. A full assessment of corticomuscular coupling, including the nonlinear part, is essential to understand the neuronal communication within the sensorimotor system. In this study, we applied the recently developed n:m coherence method to assess nonlinear corticomuscular coupling during isotonic wrist flexion. The n:m coherence is a generalized metric for quantifying nonlinear cross-frequency coupling as well as linear iso-frequency coupling. By using independent component analysis (ICA) and equivalent current dipole source localization, we identify four sensorimotor related brain areas based on the locations of the dipoles, i.e., the contralateral primary sensorimotor areas, supplementary motor area (SMA), prefrontal area (PFA) and posterior parietal cortex (PPC). For all these areas, linear coupling between electroencephalogram (EEG) and electromyogram (EMG) is present with peaks in the beta band (15-35 Hz), while nonlinear coupling is detected with both integer (1:2, 1:3, 1:4) and non-integer (2:3) harmonics. Significant differences between brain areas is shown in linear coupling with stronger coherence for the primary sensorimotor areas and motor association cortices (SMA, PFA) compared to the sensory association area (PPC); but not for the nonlinear coupling. Moreover, the detected nonlinear coupling is similar to previously reported nonlinear coupling of cortical activity to somatosensory stimuli. We suggest that the descending motor pathways mainly contribute to linear corticomuscular coupling, while nonlinear coupling likely originates from sensory feedback.
NASA Astrophysics Data System (ADS)
Xiaofang, Zhang; Lei, Wu; Qinsheng, Bi
2016-07-01
We explore the complicated bursting oscillations as well as the mechanism in a high-dimensional dynamical system. By introducing a periodically changed electrical power source in a coupled BVP oscillator, a fifth-order vector field with two scales in frequency domain is established when an order gap exists between the natural frequency and the exciting frequency. Upon the analysis of the generalized autonomous system, bifurcation sets are derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two typical cases are focused on as examples, in which different types of bursting oscillations such as subHopf/subHopf burster, subHopf/fold-cycle burster, and double-fold/fold burster can be observed. By employing the transformed phase portraits, the bifurcation mechanism of the bursting oscillations is presented, which reveals that different bifurcations occurring at the transition between the quiescent states (QSs) and the repetitive spiking states (SPs) may result in different forms of bursting oscillations. Furthermore, because of the inertia of the movement, delay may exist between the locations of the bifurcation points on the trajectory and the bifurcation points obtained theoretically. Project supported by the National Natural Science Foundation of China (Grant No. 21276115).
NASA Technical Reports Server (NTRS)
Edwards, John W.
1996-01-01
A viscous-inviscid interactive coupling method is used for the computation of unsteady transonic flows involving separation and reattachment. A lag-entrainment integral boundary layer method is used with the transonic small disturbance potential equation in the CAP-TSDV (Computational Aeroelasticity Program - Transonic Small Disturbance) code. Efficient and robust computations of steady and unsteady separated flows, including steady separation bubbles and self-excited shock-induced oscillations are presented. The buffet onset boundary for the NACA 0012 airfoil is accurately predicted and shown computationally to be a Hopf bifurcation. Shock-induced oscillations are also presented for the 18 percent circular arc airfoil. The oscillation onset boundaries and frequencies are accurately predicted, as is the experimentally observed hysteresis of the oscillations with Mach number. This latter stability boundary is identified as a jump phenomenon. Transonic wing flutter boundaries are also shown for a thin swept wing and for a typical business jet wing, illustrating viscous effects on flutter and the effect of separation onset on the wing response at flutter. Calculations for both wings show limit cycle oscillations at transonic speeds in the vicinity of minimum flutter speed indices.
Grouping synchronization in a pulse-coupled network of chaotic spiking oscillators.
Nakano, H; Saito, T
2004-09-01
This paper studies a pulse-coupled network consisting of simple chaotic spiking oscillators (CSOs). If a unit oscillator and its neighbor(s) have (almost) the same parameter values, they exhibit in-phase synchronization of chaos. As the parameter values differ, they exhibit asynchronous phenomena. Based on such behavior, some synchronous groups appear partially in the network. Typical phenomena are verified in the laboratory via a simple test circuit. These phenomena can be evaluated numerically by using an effective mapping procedure. We then apply the proposed network to image segmentation. Using a lattice pulse-coupled network via grouping synchronous phenomena, the input image data can be segmented into some sub-regions.
Mixed quantum-classical versus full quantum dynamics: Coupled quasiparticle-oscillator system
NASA Astrophysics Data System (ADS)
Schanz, Holger; Esser, Bernd
1997-05-01
The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered as a model for applying a stepwise quantization. Features of the nonlinear dynamics in the mixed description such as the presence of a separatrix structure or regular and chaotic motion are shown to be reflected in the evolu- tion of the quantum state vector of the fully quantized system. In particular, it is demonstrated how wave packets propagate along the separatrix structure of the mixed description, and that chaotic dynamics leads to a strongly entangled quantum state vector. Special emphasis is given to viewing the system from a dyn- amical Born-Oppenheimer approximation defining integrable reference oscillators, and elucidating the role of the nonadiabatic couplings which complement this approximation into a rigorous quantization scheme.
NASA Astrophysics Data System (ADS)
Guédra, Matthieu; Inserra, Claude; Mauger, Cyril; Gilles, Bruno
2016-11-01
We report observations of strong nonlinear interactions between the spherical, translational, and shape oscillations of micrometer-size bubbles. This is achieved through high-speed recordings of single bubble dynamics driven by amplitude-modulated ultrasound. The features of mode coupling are highlighted through (i) the exponential growth of the parametrically excited mode (n =3 ) triggered by the spherical oscillations followed by a saturation due to energy transfer towards the translation and even modes, (ii) the excitation of modes well below their parametric pressure threshold, and (iii) clear modification of the breathing mode R (t ) . These results are compared to recent theories accounting for nonlinear mode coupling, providing predictions in agreement with the observed bubble dynamics.
Multicluster and traveling chimera states in nonlocal phase-coupled oscillators.
Xie, Jianbo; Knobloch, Edgar; Kao, Hsien-Ching
2014-08-01
Chimera states consisting of domains of coherently and incoherently oscillating identical oscillators with nonlocal coupling are studied. These states usually coexist with the fully synchronized state and have a small basin of attraction. We propose a nonlocal phase-coupled model in which chimera states develop from random initial conditions. Several classes of chimera states have been found: (a) stationary multicluster states with evenly distributed coherent clusters, (b) stationary multicluster states with unevenly distributed clusters, and (c) a single cluster state traveling with a constant speed across the system. Traveling coherent states are also identified. A self-consistent continuum description of these states is provided and their stability properties analyzed through a combination of linear stability analysis and numerical simulation.
NASA Astrophysics Data System (ADS)
Teodorescu, Razvan
2009-10-01
Systems of oscillators coupled non-linearly (stochastically or not) are ubiquitous in nature and can explain many complex phenomena: coupled Josephson junction arrays, cardiac pacemaker cells, swarms or flocks of insects and birds, etc. They are know to have a non-trivial phase diagram, which includes chaotic, partially synchronized, and fully synchronized phases. A traditional model for this class of problems is the Kuramoto system of oscillators, which has been studied extensively for the last three decades. The model is a canonical example for non-equilibrium, dynamical phase transitions, so little understood in physics. From a stochastic analysis point of view, the transition is described by the large deviations principle, which offers little information on the scaling behavior near the critical point. I will discuss a special case of the model, which allows a rigorous analysis of the critical properties of the model, and reveals a new, anomalous scaling behavior in the vicinity of the critical point.
NASA Astrophysics Data System (ADS)
Wang, Peng-Fei; Ruan, Xiao-Dong; Xu, Zhong-Bin; Fu, Xin
2015-11-01
The Hong-Strogatz (HS) model of globally coupled phase oscillators with attractive and repulsive interactions reflects the fact that each individual (oscillator) has its own attitude (attractive or repulsive) to the same environment (mean field). Previous studies on HS model focused mainly on the stable states on Ott-Antonsen (OA) manifold. In this paper, the eigenvalues of the Jacobi matrix of each fixed point in HS model are explicitly derived, with the aim to understand the local dynamics around each fixed point. Phase transitions are described according to relative population and coupling strength. Besides, the dynamics off OA manifold is studied. Supported by the National Basic Research Program of China under Grant No. 2015CB057301, the Applied Research Project of Public Welfare Technology of Zhejiang Province under Grant No. 201SC31109 and China Postdoctoral Science Foundation under Grant No. 2014M560483
Strong effects of network architecture in the entrainment of coupled oscillator systems
NASA Astrophysics Data System (ADS)
Kori, Hiroshi; Mikhailov, Alexander S.
2006-12-01
Random networks of coupled phase oscillators, representing an approximation for systems of coupled limit-cycle oscillators, are considered. Entrainment of such networks by periodic external forcing applied to a subset of their elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window with a tongue shape becomes exponentially narrow for networks with higher hierarchical organization. However, the entrainment is significantly facilitated if the networks are directionally biased—i.e., closer to the feedforward networks. Furthermore, we show that the networks with high entrainment ability can be constructed by evolutionary optimization processes. The neural network structure of the master clock of the circadian rhythm in mammals is discussed from the viewpoint of our results.
Current driven spin–orbit torque oscillator: ferromagnetic and antiferromagnetic coupling
Johansen, Øyvind; Linder, Jacob
2016-01-01
We consider theoretically the impact of Rashba spin–orbit coupling on spin torque oscillators (STOs) in synthetic ferromagnets and antiferromagnets that have either a bulk multilayer or a thin film structure. The synthetic magnets consist of a fixed polarizing layer and two free magnetic layers that interact through the Ruderman-Kittel-Kasuya-Yosida interaction. We determine analytically which collinear states along the easy axis that are stable, and establish numerically the phase diagram for when the system is in the STO mode and when collinear configurations are stable, respectively. It is found that the Rashba spin–orbit coupling can induce anti-damping in the vicinity of the collinear states, which assists the spin transfer torque in generating self-sustained oscillations, and that it can substantially increase the STO part of the phase diagram. Moreover, we find that the STO phase can extend deep into the antiferromagnetic regime in the presence of spin–orbit torques. PMID:27653357
Borkowski, L; Perlikowski, P; Kapitaniak, T; Stefanski, A
2015-06-01
The subject of the experimental research supported with numerical simulations presented in this paper is an analog electrical circuit representing the ring of unidirectionally coupled single-well Duffing oscillators. The research is concentrated on the existence of the stable three-frequency quasiperiodic attractor in this system. It is shown that such solution can be robustly stable in a wide range of parameters of the system under consideration in spite of a parameter mismatch which is unavoidable during experiment.
NASA Astrophysics Data System (ADS)
Borkowski, L.; Perlikowski, P.; Kapitaniak, T.; Stefanski, A.
2015-06-01
The subject of the experimental research supported with numerical simulations presented in this paper is an analog electrical circuit representing the ring of unidirectionally coupled single-well Duffing oscillators. The research is concentrated on the existence of the stable three-frequency quasiperiodic attractor in this system. It is shown that such solution can be robustly stable in a wide range of parameters of the system under consideration in spite of a parameter mismatch which is unavoidable during experiment.
Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators
NASA Astrophysics Data System (ADS)
Semenova, N.; Zakharova, A.; Schöll, E.; Anishchenko, V.
2016-06-01
In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.
Coupled Oscillator Model of the Business Cycle withFluctuating Goods Markets
NASA Astrophysics Data System (ADS)
Ikeda, Y.; Aoyama, H.; Fujiwara, Y.; Iyetomi, H.; Ogimoto, K.; Souma, W.; Yoshikawa, H.
The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand, is a matter of interest in physics and economics. We consider an economic system made up of industry sectors and goods markets in order to analyze the sectoral synchronization observed for the Japanese business cycle. A coupled oscillator model that exhibits synchronization is developed based on the Kuramoto model with inertia by adding goods markets, and analytic solutions of the stationary state and the coupling strength are obtained. We simulate the effects on synchronization of a sectoral shock for systems with different price elasticities and the coupling strengths. Synchronization is reproduced as an equilibrium solution in a nearest neighbor graph. Analysis of the order parameters shows that the synchronization is stable for a finite elasticity, whereas the synchronization is broken and the oscillators behave like a giant oscillator with a certain frequency additional to the common frequency for zero elasticity.
Containment control for coupled harmonic oscillators with multiple leaders under directed topology
NASA Astrophysics Data System (ADS)
Xu, Chengjie; Zheng, Ying; Su, Housheng; Wang, Hua O.
2015-02-01
This paper investigates the problem of containment control for coupled harmonic oscillators with multiple leaders under directed topology. Using tools from matrix, graph and stability theories, necessary and sufficient conditions are obtained for coupled harmonic oscillators under continuous-time and sampled-data-based protocols, respectively. When the continuous-time protocol is used, it is proved that every follower will ultimately converge to the convex hull spanned by the leaders if and only if there exists at least one leader that has a directed path to that follower at any time. When the sampled-data-based protocol is used, it is shown that the containment can be achieved if and only if: (1) an appropriate sampling period is chosen and (2) for every follower, there exists at least one leader that has a directed path to that follower at any time. And we also give the containment conditions for coupled harmonic oscillators under undirected topology as a special case. Finally, numerical simulations are presented to illustrate the theoretical findings.
Robust synchronization of coupled circadian and cell cycle oscillators in single mammalian cells.
Bieler, Jonathan; Cannavo, Rosamaria; Gustafson, Kyle; Gobet, Cedric; Gatfield, David; Naef, Felix
2014-07-15
Circadian cycles and cell cycles are two fundamental periodic processes with a period in the range of 1 day. Consequently, coupling between such cycles can lead to synchronization. Here, we estimated the mutual interactions between the two oscillators by time-lapse imaging of single mammalian NIH3T3 fibroblasts during several days. The analysis of thousands of circadian cycles in dividing cells clearly indicated that both oscillators tick in a 1:1 mode-locked state, with cell divisions occurring tightly 5 h before the peak in circadian Rev-Erbα-YFP reporter expression. In principle, such synchrony may be caused by either unidirectional or bidirectional coupling. While gating of cell division by the circadian cycle has been most studied, our data combined with stochastic modeling unambiguously show that the reverse coupling is predominant in NIH3T3 cells. Moreover, temperature, genetic, and pharmacological perturbations showed that the two interacting cellular oscillators adopt a synchronized state that is highly robust over a wide range of parameters. These findings have implications for circadian function in proliferative tissues, including epidermis, immune cells, and cancer.
NASA Astrophysics Data System (ADS)
Ghoshal, Gourab; Muñuzuri, Alberto P.; Pérez-Mercader, Juan
2016-01-01
Oscillatory phenomena are ubiquitous in Nature. The ability of a large population of coupled oscillators to synchronize constitutes an important mechanism to express information and establish communication among members. To understand such phenomena, models and experimental realizations of globally coupled oscillators have proven to be invaluable in settings as varied as chemical, biological and physical systems. A variety of rich dynamical behavior has been uncovered, although usually in the context of a single state of synchronization or lack thereof. Through the experimental and numerical study of a large population of discrete chemical oscillators, here we report on the unexpected discovery of a new phenomenon revealing the existence of dynamically distinct synchronized states reflecting different degrees of communication. Specifically, we discover a novel large-amplitude super-synchronized state separated from the conventionally reported synchronized and quiescent states through an unusual sharp jump transition when sampling the strong coupling limit. Our results assume significance for further elucidating globally coherent phenomena, such as in neuropathologies, bacterial cell colonies, social systems and semiconductor lasers.
Ghoshal, Gourab; Muñuzuri, Alberto P.; Pérez-Mercader, Juan
2016-01-01
Oscillatory phenomena are ubiquitous in Nature. The ability of a large population of coupled oscillators to synchronize constitutes an important mechanism to express information and establish communication among members. To understand such phenomena, models and experimental realizations of globally coupled oscillators have proven to be invaluable in settings as varied as chemical, biological and physical systems. A variety of rich dynamical behavior has been uncovered, although usually in the context of a single state of synchronization or lack thereof. Through the experimental and numerical study of a large population of discrete chemical oscillators, here we report on the unexpected discovery of a new phenomenon revealing the existence of dynamically distinct synchronized states reflecting different degrees of communication. Specifically, we discover a novel large-amplitude super-synchronized state separated from the conventionally reported synchronized and quiescent states through an unusual sharp jump transition when sampling the strong coupling limit. Our results assume significance for further elucidating globally coherent phenomena, such as in neuropathologies, bacterial cell colonies, social systems and semiconductor lasers. PMID:26753772
Ghoshal, Gourab; Muñuzuri, Alberto P; Pérez-Mercader, Juan
2016-01-12
Oscillatory phenomena are ubiquitous in Nature. The ability of a large population of coupled oscillators to synchronize constitutes an important mechanism to express information and establish communication among members. To understand such phenomena, models and experimental realizations of globally coupled oscillators have proven to be invaluable in settings as varied as chemical, biological and physical systems. A variety of rich dynamical behavior has been uncovered, although usually in the context of a single state of synchronization or lack thereof. Through the experimental and numerical study of a large population of discrete chemical oscillators, here we report on the unexpected discovery of a new phenomenon revealing the existence of dynamically distinct synchronized states reflecting different degrees of communication. Specifically, we discover a novel large-amplitude super-synchronized state separated from the conventionally reported synchronized and quiescent states through an unusual sharp jump transition when sampling the strong coupling limit. Our results assume significance for further elucidating globally coherent phenomena, such as in neuropathologies, bacterial cell colonies, social systems and semiconductor lasers.
Coupled oscillator model of the dopaminergic neuron of the substantia nigra.
Wilson, C J; Callaway, J C
2000-05-01
membrane potential oscillations. The same currents much more accurately reproduced the calcium transients when distributed uniformly along a tapering cable in a multicompartment model. This model represented the dopaminergic neuron as a set of electrically coupled oscillators with different natural frequencies. Each frequency was determined by the surface area to volume ratio of the compartment. This model could account for additional features of the dopaminergic neurons seen in slices, such as slow adaptation of oscillation frequency and may produce irregular firing under different coupling conditions.
Non-Markovian dynamics of fully coupled fermionic and bosonic oscillators
NASA Astrophysics Data System (ADS)
Sargsyan, V. V.; Lacroix, D.; Adamian, G. G.; Antonenko, N. V.
2017-03-01
The non-Markovian Langevin approach is applied to study the dynamics of fermionic (bosonic) oscillator linearly coupled to a fermionic (bosonic) environment. The analytical expressions for occupation numbers in two different types of couplings (rotating-wave approximation and fully coupled) are compared and discussed. The weak-coupling and high- and low-temperature limits are considered as well. The conditions under which the environment imposes its thermal equilibrium on the collective subsystem are discussed. The sameness of the results, obtained with both the Langevin approach and the discretized environment method are shown. Short- and long-time nonequilibrium dynamics of fermionic and bosonic open quantum systems are analyzed both analytically and numerically.
NASA Astrophysics Data System (ADS)
Narahara, Koichi
2017-01-01
In this paper, we investigate the mutual synchronization of oscillating pulse edges developed in point-coupled transmission lines periodically loaded with tunnel diodes (TDs). When supplied with an appropriate voltage at the end of a TD line, a pulse edge exhibits a spatially extended limit-cycle oscillation on the line. In this study, the properties of this mutual synchronization of edge oscillation established in two coupled TD lines are discussed. We examine the mutual synchronization using phase sensitivity calculated by applying phase-reduction scheme to the transmission equation of a TD line. The phase difference between the synchronized edges and oscillation frequency is calculated depending on the coupling cell. We then validate the reduced model via time-domain calculations of edge oscillations.
El Nino-southern oscillation: A coupled response to the greenhouse effect?
Sun, De-Zheng
1997-11-01
The purpose of this article to elucidate the link between the El Nino-Southern Oscillation (ENSO) and radiative forcing (of which the greenhouse effect is a major part). A unified theory for the tropical Pacific climate is developed by considering the response of the coupled ocean-atmosphere to a changing radiative forcing. The hypothesis is that both the zonal surface sea temperature (SST) gradients and ENSO are a coupled response to the strong radiative heating or the tropical warmth. Owing to ocean-atmosphere interaction, the stronger the radiative heating, the larger the zonal SST gradients. When the SST gradients exceed a critical value, however, the ocean-atmosphere interaction in the cold-tongue region is too strong for the coupled system to hold steady. Consequently, the coupled system enters an oscillatory state. These coupled dynamics are examined in a simple mathematical model whose behavior is consistent with the hypothesis. With a linear temperature profile throughout the depth of subsurface ocean, the model predicts that both the magnitude and period of the oscillation increase with increases in radiative forcing or the greenhouse effect. The increase in the magnitude of the oscillation largely comes from an enhancement of the magnitude of the cold anomalies, while the increase in the period mostly comes from a prolonged duration of the warm events. With a profile in which the lapse rate decreases with depth, the sensitivity is more moderate. The simplicity of the model prevents a quantitative simulation of the sensitivity of ENSO to increases in the greenhouse effect, but qualitatively the model results support the empirical interpretation of the prolonged duration of the 1990-1995 ENSO event. 5 refs., 7 figs.
Memcapacitor model and its application in a chaotic oscillator
NASA Astrophysics Data System (ADS)
Guang-Yi, Wang; Bo-Zhen, Cai; Pei-Pei, Jin; Ti-Ling, Hu
2016-01-01
A memcapacitor is a new type of memory capacitor. Before the advent of practical memcapacitor, the prospective studies on its models and potential applications are of importance. For this purpose, we establish a mathematical memcapacitor model and a corresponding circuit model. As a potential application, based on the model, a memcapacitor oscillator is designed, with its basic dynamic characteristics analyzed theoretically and experimentally. Some circuit variables such as charge, flux, and integral of charge, which are difficult to measure, are observed and measured via simulations and experiments. Analysis results show that besides the typical period-doubling bifurcations and period-3 windows, sustained chaos with constant Lyapunov exponents occurs. Moreover, this oscillator also exhibits abrupt chaos and some novel bifurcations. In addition, based on the digital signal processing (DSP) technology, a scheme of digitally realizing this memcapacitor oscillator is provided. Then the statistical properties of the chaotic sequences generated from the oscillator are tested by using the test suit of the National Institute of Standards and Technology (NIST). The tested randomness definitely reaches the standards of NIST, and is better than that of the well-known Lorenz system. Project supported by the National Natural Science Foundation of China (Grant Nos. 61271064, 61401134, and 60971046), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LZ12F01001 and LQ14F010008), and the Program for Zhejiang Leading Team of S&T Innovation, China (Grant No. 2010R50010).
NASA Astrophysics Data System (ADS)
Goulet, Laurent; Duvel, Jean-Philippe
2000-08-01
This paper presents a method, the local mode analysis (LMA), that makes it possible to extract the most persistent oscillations present in the time evolution of an atmospheric field. This method is particularly suitable to analyze intermittent tropospheric oscillations related to dynamic or thermodynamic instabilities such as the intraseasonal oscillation (ISO). These intermittent oscillations generally exhibit various spatial structures that succeed one another in time and that are difficult to isolate in a simple and comprehensive manner using conventional approaches such as empirical orthogonal functions or composite analyses. The main objective of the LMA approach is to identify the different structures of a given oscillation in order to better understand its physical origin and to test the applicability of different theoretical hypotheses. The LMA also makes it possible to test the representativity of a mean structure in regard to actual modes that succeed one another in time.The LMA is applied to the National Oceanic and Atmosphere Administration-Advanced Very High Resolution Radiometer outgoing longwave radiation time series in order to study the variability of the convective perturbation at the intraseasonal timescale (30-60 days). The LMA depicts the most intense and persistent modes of the ISO very well and shows the strong variability of the spatial organization of the convective perturbation at this timescale. Results exhibit interannual and seasonal variations of the mean period and amplitude of the ISO with a tendency to have less persistent modes and smaller periods of the oscillation during El Niño years and during summer. The maximum perturbation of the convection by the ISO is not located on the equator but rather around 10°-15° in the summer hemisphere. Several persistent modes exhibit neither the phase opposition between the Indian and Pacific Oceans nor the eastward equatorial propagation that characterize the average mode of Northern
Himeoka, Yusuke; Kaneko, Kunihiko
2016-04-05
Cells generally convert nutrient resources to products via energy transduction. Accordingly, the thermodynamic efficiency of this conversion process is one of the most essential characteristics of living organisms. However, although these processes occur under conditions of dynamic metabolism, most studies of cellular thermodynamic efficiency have been restricted to examining steady states; thus, the relevance of dynamics to this efficiency has not yet been elucidated. Here, we develop a simple model of metabolic reactions with anabolism-catabolism coupling catalyzed by enzymes. Through application of external oscillation in the enzyme abundances, the thermodynamic efficiency of metabolism was found to be improved. This result is in strong contrast with that observed in the oscillatory input, in which the efficiency always decreased with oscillation. This improvement was effectively achieved by separating the anabolic and catabolic reactions, which tend to disequilibrate each other, and taking advantage of the temporal oscillations so that each of the antagonistic reactions could progress near equilibrium. In this case, anti-phase oscillation between the reaction flux and chemical affinity through oscillation of enzyme abundances is essential. This improvement was also confirmed in a model capable of generating autonomous oscillations in enzyme abundances. Finally, the possible relevance of the improvement in thermodynamic efficiency is discussed with respect to the potential for manipulation of metabolic oscillations in microorganisms.
NASA Astrophysics Data System (ADS)
Himeoka, Yusuke; Kaneko, Kunihiko
2016-04-01
Cells generally convert nutrient resources to products via energy transduction. Accordingly, the thermodynamic efficiency of this conversion process is one of the most essential characteristics of living organisms. However, although these processes occur under conditions of dynamic metabolism, most studies of cellular thermodynamic efficiency have been restricted to examining steady states; thus, the relevance of dynamics to this efficiency has not yet been elucidated. Here, we develop a simple model of metabolic reactions with anabolism-catabolism coupling catalyzed by enzymes. Through application of external oscillation in the enzyme abundances, the thermodynamic efficiency of metabolism was found to be improved. This result is in strong contrast with that observed in the oscillatory input, in which the efficiency always decreased with oscillation. This improvement was effectively achieved by separating the anabolic and catabolic reactions, which tend to disequilibrate each other, and taking advantage of the temporal oscillations so that each of the antagonistic reactions could progress near equilibrium. In this case, anti-phase oscillation between the reaction flux and chemical affinity through oscillation of enzyme abundances is essential. This improvement was also confirmed in a model capable of generating autonomous oscillations in enzyme abundances. Finally, the possible relevance of the improvement in thermodynamic efficiency is discussed with respect to the potential for manipulation of metabolic oscillations in microorganisms.
Quantum-coupled radial-breathing oscillations in double-walled carbon nanotubes.
Liu, Kaihui; Hong, Xiaoping; Wu, Muhong; Xiao, Fajun; Wang, Wenlong; Bai, Xuedong; Ager, Joel W; Aloni, Shaul; Zettl, Alex; Wang, Enge; Wang, Feng
2013-01-01
Van der Waals-coupled materials, ranging from multilayers of graphene and MoS(2) to superlattices of nanoparticles, exhibit rich emerging behaviour owing to quantum coupling between individual nanoscale constituents. Double-walled carbon nanotubes provide a model system for studying such quantum coupling mediated by van der Waals interactions, because each constituent single-walled nanotube can have distinctly different physical structures and electronic properties. Here we systematically investigate quantum-coupled radial-breathing mode oscillations in chirality-defined double-walled nanotubes by combining simultaneous structural, electronic and vibrational characterizations on the same individual nanotubes. We show that these radial-breathing oscillations are collective modes characterized by concerted inner- and outer-wall motions, and determine quantitatively the tube-dependent van der Waals potential governing their vibration frequencies. We also observe strong quantum interference between Raman scattering from the inner- and outer-wall excitation pathways, the relative phase of which reveals chirality-dependent excited-state potential energy surface displacement in different nanotubes.
Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
NASA Astrophysics Data System (ADS)
Salerno, Grazia; Ozawa, Tomoki; Price, Hannah M.; Carusotto, Iacopo
2016-02-01
We theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators, such as classical pendula or lumped-element electric circuits, whose oscillation frequency is modulated fast in time. Making use of Floquet theory in the high-frequency limit, we identify a regime in which the system is accurately described by a Harper-Hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency modulation of the different oscillators. We illustrate how the topologically protected chiral edge states, as well as the Hofstadter butterfly of bulk bands, can be observed in the driven-dissipative steady state under a monochromatic drive. In analogy with the integer quantum Hall effect, we show how the topological Chern numbers of the bands can be extracted from the mean transverse shift of the steady-state oscillation amplitude distribution. Finally, we discuss the regime where the analogy with the Harper-Hofstadter model breaks down.
Coupled slow and fast surface dynamics in an electrocatalytic oscillator: Model and simulations
Nascimento, Melke A.; Nagao, Raphael; Eiswirth, Markus; Varela, Hamilton
2014-12-21
The co-existence of disparate time scales is pervasive in many systems. In particular for surface reactions, it has been shown that the long-term evolution of the core oscillator is decisively influenced by slow surface changes, such as progressing deactivation. Here we present an in-depth numerical investigation of the coupled slow and fast surface dynamics in an electrocatalytic oscillator. The model consists of four nonlinear coupled ordinary differential equations, investigated over a wide parameter range. Besides the conventional bifurcation analysis, the system was studied by means of high-resolution period and Lyapunov diagrams. It was observed that the bifurcation diagram changes considerably as the irreversible surface poisoning evolves, and the oscillatory region shrinks. The qualitative dynamics changes accordingly and the chaotic oscillations are dramatically suppressed. Nevertheless, periodic cascades are preserved in a confined region of the resistance vs. voltage diagram. Numerical results are compared to experiments published earlier and the latter reinterpreted. Finally, the comprehensive description of the time-evolution in the period and Lyapunov diagrams suggests further experimental studies correlating the evolution of the system's dynamics with changes of the catalyst structure.
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
Freitas, Celso Macau, Elbert; Pikovsky, Arkady
2015-04-15
We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.
Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis
Tirabassi, Giulio; Sevilla-Escoboza, Ricardo; Buldú, Javier M.; Masoller, Cristina
2015-01-01
A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rössler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones. PMID:26042395
Lozano-Soldevilla, Diego; ter Huurne, Niels; Oostenveld, Robert
2016-01-01
Neuronal oscillations support cognitive processing. Modern views suggest that neuronal oscillations do not only reflect coordinated activity in spatially distributed networks, but also that there is interaction between the oscillations at different frequencies. For example, invasive recordings in animals and humans have found that the amplitude of fast oscillations (>40 Hz) occur non-uniformly within the phase of slower oscillations, forming the so-called cross-frequency coupling (CFC). However, the CFC patterns might be influenced by features in the signal that do not relate to underlying physiological interactions. For example, CFC estimates may be sensitive to spectral correlations due to non-sinusoidal properties of the alpha band wave morphology. To investigate this issue, we performed CFC analysis using experimental and synthetic data. The former consisted in a double-blind magnetoencephalography pharmacological study in which participants received either placebo, 0.5 or 1.5 mg of lorazepam (LZP; GABAergic enhancer) in different experimental sessions. By recording oscillatory brain activity with during rest and working memory (WM), we were able to demonstrate that posterior alpha (8–12 Hz) phase was coupled to beta-low gamma band (20–45 Hz) amplitude envelope during all sessions. Importantly, bicoherence values around the harmonics of the alpha frequency were similar both in magnitude and topographic distribution to the cross-frequency coherence (CFCoh) values observed in the alpha-phase to beta-low gamma coupling. In addition, despite the large CFCoh we found no significant cross-frequency directionality (CFD). Critically, simulations demonstrated that a sizable part of our empirical CFCoh between alpha and beta-low gamma coupling and the lack of CFD could be explained by two-three harmonics aligned in zero phase-lag produced by the physiologically characteristic alpha asymmetry in the amplitude of the peaks relative to the troughs. Furthermore, we
Differential Ring Oscillator Based Capacitance Sensor for Microfluidic Applications.
Mohammad, Kaveh; Thomson, Douglas J
2017-04-01
A simple high frequency capacitance sensor with 180 aF sensitivity is designed for a wide range of microfluidic applications. The sensor is implemented utilizing differential ring oscillators operating at [Formula: see text] MHz with a differential signal at [Formula: see text] MHz. The sensor occupies [Formula: see text] cm × 2 cm on a printed circuit board. The sensor is tuned using two precision variable capacitors and has a full scale range of [Formula: see text] pF. The sensor was able to detect less than 1% Isopropyl Alcohol in DI water and to detect 15 μm polystyrene spheres flowing over 25 μm lines and spaces coplanar electrodes in a microfluidic channel. The compact differential ring oscillator based architecture of the design makes it suitable to be integrated into microprocessor based systems for detection in Lab on Chip or Lab on Board applications.
Minati, Ludovico
2014-12-01
In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.
Minati, Ludovico E-mail: ludovico.minati@unitn.it
2014-12-01
In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.
Renewal Approach to the Analysis of the Asynchronous State for Coupled Noisy Oscillators
NASA Astrophysics Data System (ADS)
Farkhooi, Farzad; van Vreeswijk, Carl
2015-07-01
We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of the interevent density allows for a self-consistent calculation that determines the asynchronous state and its stability. This framework can readily be extended to the analysis of systems with more state variables and provides a population density treatment to evolve them in their thermodynamical limits. To demonstrate this we study a nonlinear pulse-coupled system, where couplings are dynamic and activity dependent. We investigate its stability and numerically study the nonequilibrium behavior of the system after the bifurcation. We show that this system undergoes a supercritical Hopf bifurcation to collective synchronization.
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
NASA Astrophysics Data System (ADS)
Kurt, Arzu; Eryigit, Resul
Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. Bolu, Turkey.
NASA Astrophysics Data System (ADS)
Traub, Roger D.; Pais, Isabel; Bibbig, Andrea; Lebeau, Fiona E. N.; Buhl, Eberhard H.; Hormuzdi, Sheriar G.; Monyer, Hannah; Whittington, Miles A.
2003-02-01
Electrical coupling between pyramidal cell axons, and between interneuron dendrites, have both been described in the hippocampus. What are the functional roles of the two types of coupling? Interneuron gap junctions enhance synchrony of oscillations (25-70 Hz) in isolated interneuron networks and also in networks containing both interneurons and principal cells, as shown in mice with a knockout of the neuronal (primarily interneuronal) connexin36. We have recently shown that pharmacological gap junction blockade abolishes kainate-induced oscillations in connexin36 knockout mice; without such gap junction blockade, oscillations do occur in the knockout mice, albeit at reduced power compared with wild-type mice. As interneuronal dendritic electrical coupling is almost absent in the knockout mice, these pharmacological data indicate a role of axonal electrical coupling in generating the oscillations. We construct a network model of an experimental oscillation, known to be regulated by both types of electrical coupling. In our model, axonal electrical coupling is required for the oscillation to occur at all; interneuron dendritic gap junctions exert a modulatory effect.
Goodfellow, Marc; Glendinning, Paul
2013-08-14
We investigate the dynamic mechanisms underlying intermittent state transitions in a recently proposed neural mass model of epilepsy. A low dimensional model is constructed, which preserves two key features of the neural mass model, namely (i) coupling between oscillators and (ii) heterogeneous proximity of these oscillators to a bifurcation between distinct limit cycles. We demonstrate that state transitions due to intermittency occur in the abstract model. This suggests that there is a general bifurcation mechanism responsible for this behaviour and that this is independent of the precise form of the evolution equations. Such abstractions of neural mass models allow a deeper insight into underlying dynamic and physiological mechanisms, and also allow the more efficient exploration of large scale brain dynamics in disease.
The universe dominated by oscillating scalar with non-minimal derivative coupling to gravity
Jinno, Ryusuke; Mukaida, Kyohei; Nakayama, Kazunori E-mail: mukaida@hep-th.phys.s.u-tokyo.ac.jp
2014-01-01
We study the expansion law of the universe dominated by the oscillating scalar field with non-minimal derivative coupling to gravity as G{sup μν}∂{sub μ}φ∂{sub ν}φ. In this system the Hubble parameter oscillates with a frequency of the effective mass of the scalar field, which formerly caused a difficulty in analyzing how the universe expands. We find an analytical solution for power law potentials and interpret the solution in an intuitive way by using a new invariant of the system. As a result, we find marginally accelerated expansion for the quadratic potential and no accelerated expansion for the potential with higher power.
Hatano, T; Kubo, T; Tokura, Y; Amaha, S; Teraoka, S; Tarucha, S
2011-02-18
Aharonov-Bohm (AB) oscillations are studied for a parallel-coupled vertical double quantum dot with a common source and drain electrode. We observe AB oscillations of current via a one-electron bonding state as the ground state and an antibonding state as the excited state. As the center gate voltage becomes more negative, the oscillation period is clearly halved for both the bonding and antibonding states, and the phase changes by half a period for the antibonding state. This result can be explained by a calculation that takes account of the indirect interdot coupling via the two electrodes.
NASA Astrophysics Data System (ADS)
Varney, R. H.; Wiltberger, M.; Zhang, B.; Lotko, W.; Lyon, J.
2016-10-01
We present the first simulations of magnetospheric sawtooth oscillations under steady solar wind conditions that are driven internally by heavy ion outflow from a physics-based model. The simulations presented use the multifluid Lyon-Fedder-Mobarry magnetohydrodynamics model two-way coupled to the ionosphere/polar wind model (IPWM). Depending on the type of wave-particle interactions utilized within IPWM, the coupled simulations exhibit either sawtooth oscillations or steady magnetospheric convection. Contrasting the simulations that do and do not develop sawtooth oscillations yields insights into the relationship between outflow and sawtooth oscillations. The total outflow rate is not an adequate predictor of the convection mode that will emerge. The simulations that develop sawtooth oscillations are characterized by intense outflow concentrated in the midnight auroral region. This outflow distribution mass loads the tail reconnection region without excessively mass loading the dayside reconnection region and leads to an imbalance between the dayside and nightside reconnection rates.
On cross-frequency phase-phase coupling between theta and gamma oscillations in the hippocampus
Scheffer-Teixeira, Robson; Tort, Adriano BL
2016-01-01
Phase-amplitude coupling between theta and multiple gamma sub-bands is a hallmark of hippocampal activity and believed to take part in information routing. More recently, theta and gamma oscillations were also reported to exhibit phase-phase coupling, or n:m phase-locking, suggesting an important mechanism of neuronal coding that has long received theoretical support. However, by analyzing simulated and actual LFPs, here we question the existence of theta-gamma phase-phase coupling in the rat hippocampus. We show that the quasi-linear phase shifts introduced by filtering lead to spurious coupling levels in both white noise and hippocampal LFPs, which highly depend on epoch length, and that significant coupling may be falsely detected when employing improper surrogate methods. We also show that waveform asymmetry and frequency harmonics may generate artifactual n:m phase-locking. Studies investigating phase-phase coupling should rely on appropriate statistical controls and be aware of confounding factors; otherwise, they could easily fall into analysis pitfalls. DOI: http://dx.doi.org/10.7554/eLife.20515.001 PMID:27925581
NASA Astrophysics Data System (ADS)
Luck, H.; Trepp, Ch.
Rott's (1969) theory of thermoacoustic oscillations is extended to allow its application to more complicated geometries. The modified theory permits determinations of frequencies, pressure amplitudes, power, and heat flow with only a moderate amount of computer calculations. The theory was experimentally verified using a thermoacoustic heat engine. Possible applications of thermoacoustic oscillations as heat engines and as refrigerators are discussed, and guidelines are presented for the correct design of cryogenic piping and of different dampers.
Inducing isolated-desynchronization states in complex network of coupled chaotic oscillators
NASA Astrophysics Data System (ADS)
Lin, Weijie; Li, Huiyan; Ying, Heping; Wang, Xingang
2016-12-01
In a recent study about chaos synchronization in complex networks [Nat. Commun. 5, 4079 (2014), 10.1038/ncomms5079], it is shown that a stable synchronous cluster may coexist with vast asynchronous nodes, resembling the phenomenon of a chimera state observed in a regular network of coupled periodic oscillators. Although of practical significance, this new type of state, namely, the isolated-desynchronization state, is hardly observed in practice due to its strict requirements on the network topology. Here, by the strategy of pinning coupling, we propose an effective method for inducing isolated-desynchronization states in symmetric networks of coupled chaotic oscillators. Theoretical analysis based on eigenvalue analysis shows that, by pinning a group of symmetric nodes in the network, there exists a critical pinning strength beyond which the group of pinned nodes can completely be synchronized while the unpinned nodes remain asynchronous. The feasibility and efficiency of the control method are verified by numerical simulations of both artificial and real-world complex networks with the numerical results in good agreement with the theoretical predictions.
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
A Kalman filtering approach to robust synchronization of coupled neural oscillators
NASA Astrophysics Data System (ADS)
Rigatos, Gerasimos G.; Rigatou, Efthymia G.
2013-10-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of the coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie Derivatives. For such a model it becomes possible to design a state feedback controller that assures synchronization for the state variables of the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and on computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
Incoherent chimera and glassy states in coupled oscillators with frustrated interactions
NASA Astrophysics Data System (ADS)
Choe, Chol-Ung; Ri, Ji-Song; Kim, Ryong-Son
2016-09-01
We suggest a site disorder model that describes the population of identical oscillators with quenched random interactions for both the coupling strength and coupling phase. We obtain the reduced equations for the suborder parameters, on the basis of Ott-Antonsen ansatz theory, and present a complete bifurcation analysis of the reduced system. New effects include the appearance of the incoherent chimera and glassy state, both of which are caused by heterogeneity of the coupling phases. In the incoherent chimera state, the system displays an exotic symmetry-breaking behavior in spite of the apparent structural symmetry where the oscillators for both of the two subpopulations are in a frustrated state, while the phase distribution for each subpopulation approaches a steady state that differs from each other. When the incoherent chimera undergoes Hopf bifurcation, the system displays a breathing incoherent chimera. The glassy state that occurs on a surface of three-dimensional parameter space exhibits a continuum of metastable states with zero value of the global order parameter. Explicit formulas are derived for the system's Hopf, saddle-node, and transcritical bifurcation curves, as well as the codimension-2 crossing points, including the Takens-Bogdanov point.
Quadratic coupling between a classical nanomechanical oscillator and a single spin
NASA Astrophysics Data System (ADS)
Dhingra, Shonali
Though the motions of macroscopic objects must ultimately be governed by quantum mechanics, the distinctive features of quantum mechanics can be hidden or washed out by thermal excitations and coupling to the environment. For the work of this thesis, we tried to develop a hybrid system consisting a classical and a quantum component, which can be used to probe the quantum nature of both these components. This hybrid system quadratically coupled a nanomechanical oscillator (NMO) with a single spin in presence of a uniform external magnetic field. The NMO was fabricated out of single-layer graphene, grown using Chemical Vapor Deposition (CVD) and patterned using various lithography and etching techniques. The NMO was driven electrically and detected optically. The NMO's resonant frequencies, and their stabilities were studied. The spin originated from a nitrogen vacancy (NV) center in a diamond nanocrystal which is positioned on the NMO. In presence of an external magnetic field, we show that the NV centers are excellen theta2 sensors. Their sensitivity is shown to increase much faster than linearly with the external magnetic field and diverges as the external field approaches an internally-defined limit. Both these components of the hybrid system get coupled by physical placement of NVcontaining diamond nanocrystals on top of NMO undergoing torsional mode of oscillation, in presence of an external magnetic field. The capability of the NV centers to detect the quadratic behavior of the oscillation angle of the NMO with excellent sensitivity, ensures quantum non-demolition (QND) measurement of both components of the hybrid system. This enables a bridge between the quantum and classical worlds for a simple readout of the NV center spin and observation of the discrete states of the NMO. This system could become the building block for a wide range of quantum nanomechanical devices.
Coexistence of Regular and Irregular Dynamics in Complex Networks of Pulse-Coupled Oscillators
NASA Astrophysics Data System (ADS)
Timme, Marc; Wolf, Fred; Geisel, Theo
2002-11-01
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is determined by a multitude of linear operators. We treat this multioperator problem exactly and show that for inhibitory interactions the synchronous state is stable, independent of the parameters and the network connectivity. In randomly connected networks with strong interactions this synchronous state, displaying regular dynamics, coexists with a balanced state exhibiting irregular dynamics. External signals may switch the network between qualitatively distinct states.
Robust autoassociative memory with coupled networks of Kuramoto-type oscillators
NASA Astrophysics Data System (ADS)
Heger, Daniel; Krischer, Katharina
2016-08-01
Uncertain recognition success, unfavorable scaling of connection complexity, or dependence on complex external input impair the usefulness of current oscillatory neural networks for pattern recognition or restrict technical realizations to small networks. We propose a network architecture of coupled oscillators for pattern recognition which shows none of the mentioned flaws. Furthermore we illustrate the recognition process with simulation results and analyze the dynamics analytically: Possible output patterns are isolated attractors of the system. Additionally, simple criteria for recognition success are derived from a lower bound on the basins of attraction.
Exact Nonlinear Fourth-order Equation for Two Coupled Oscillators: Metamorphoses of Resonance Curves
NASA Astrophysics Data System (ADS)
Kyzioł, J.; Okniński, A.
We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the Krylov-Bogoliubov-Mitropolsky approach - we compute the amplitude profiles, which from mathematical point of view are algebraic curves. In the present paper we investigate metamorphoses of amplitude profiles induced by changes of control parameters near singular points of these curves. It follows that dynamics changes qualitatively in the neighbourhood of a singular point.
Application of a Chaotic Oscillator in an Autonomous Mobile Robot
NASA Astrophysics Data System (ADS)
Tlelo-Cuautle, Esteban; Ramos-López, Hugo C.; Sánchez-Sánchez, Mauro; Pano-Azucena, Ana D.; Sánchez-Gaspariano, Luis A.; Núñez-Pérez, José C.; Camas-Anzueto, Jorge L.
2014-05-01
Terrain exploration robots can be of great usefulness in critical navigation circumstances. However, the challenge is how to guarantee a control for covering a full terrain area. That way, the application of a chaotic oscillator to control the wheels of an autonomous mobile robot, is introduced herein. Basically, we describe the realization of a random number generator (RNG) based on a double-scroll chaotic oscillator, which is used to guide the robot to cover a full terrain area. The resolution of the terrain exploration area is determined by both the number of bits provided by the RNG and the characteristics of step motors. Finally, the experimental results highlight the covered area by painting the trajectories that the robot explores.
Stability of two cluster solutions in pulse coupled networks of neural oscillators.
Chandrasekaran, Lakshmi; Achuthan, Srisairam; Canavier, Carmen C
2011-04-01
Phase response curves (PRCs) have been widely used to study synchronization in neural circuits comprised of pacemaking neurons. They describe how the timing of the next spike in a given spontaneously firing neuron is affected by the phase at which an input from another neuron is received. Here we study two reciprocally coupled clusters of pulse coupled oscillatory neurons. The neurons within each cluster are presumed to be identical and identically pulse coupled, but not necessarily identical to those in the other cluster. We investigate a two cluster solution in which all oscillators are synchronized within each cluster, but in which the two clusters are phase locked at nonzero phase with each other. Intuitively, one might expect this solution to be stable only when synchrony within each isolated cluster is stable, but this is not the case. We prove rigorously the stability of the two cluster solution and show how reciprocal coupling can stabilize synchrony within clusters that cannot synchronize in isolation. These stability results for the two cluster solution suggest a mechanism by which reciprocal coupling between brain regions can induce local synchronization via the network feedback loop.
Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillators
NASA Astrophysics Data System (ADS)
Wolfrum, M.; Gurevich, S. V.; Omel'chenko, O. E.
2016-02-01
In this paper we study the transition to synchrony in an one-dimensional array of oscillators with non-local coupling. For its description in the continuum limit of a large number of phase oscillators, we use a corresponding Ott-Antonsen equation, which is an integro-differential equation for the evolution of the macroscopic profiles of the local mean field. Recently, it was reported that in the spatially extended case at the synchronisation threshold there appear partially coherent plane waves with different wave numbers, which are organised in the well-known Eckhaus scenario. In this paper, we show that for Kuramoto-Sakaguchi phase oscillators the phase lag parameter in the interaction function can induce a Benjamin-Feir-type instability of the partially coherent plane waves. The emerging collective macroscopic chaos appears as an intermediate stage between complete incoherence and stable partially coherent plane waves. We give an analytic treatment of the Benjamin-Feir instability and its onset in a codimension-two bifurcation in the Ott-Antonsen equation as well as a numerical study of the transition from phase turbulence to amplitude turbulence inside the Benjamin-Feir unstable region.
Different coupled atmosphere-recharge oscillator Low Order Models for ENSO: a projection approach.
NASA Astrophysics Data System (ADS)
Bianucci, Marco; Mannella, Riccardo; Merlino, Silvia; Olivieri, Andrea
2016-04-01
El Ninõ-Southern Oscillation (ENSO) is a large scale geophysical phenomenon where, according to the celebrated recharge oscillator model (ROM), the Ocean slow variables given by the East Pacific Sea Surface Temperature (SST) and the average thermocline depth (h), interact with some fast "irrelevant" ones, representing mostly the atmosphere (the westerly wind burst and the Madden-Julian Oscillation). The fast variables are usually inserted in the model as an external stochastic forcing. In a recent work (M. Bianucci, "Analytical probability density function for the statistics of the ENSO phenomenon: asymmetry and power law tail" Geophysical Research Letters, under press) the author, using a projection approach applied to general deterministic coupled systems, gives a physically reasonable explanation for the use of stochastic models for mimicking the apparent random features of the ENSO phenomenon. Moreover, in the same paper, assuming that the interaction between the ROM and the fast atmosphere is of multiplicative type, i.e., it depends on the SST variable, an analytical expression for the equilibrium density function of the anomaly SST is obtained. This expression fits well the data from observations, reproducing the asymmetry and the power law tail of the histograms of the NINÕ3 index. Here, using the same theoretical approach, we consider and discuss different kind of interactions between the ROM and the other perturbing variables, and we take into account also non linear ROM as a low order model for ENSO. The theoretical and numerical results are then compared with data from observations.
Circadian organization of the rodent retina involves strongly coupled, layer-specific oscillators.
Jaeger, Catherine; Sandu, Cristina; Malan, André; Mellac, Katell; Hicks, David; Felder-Schmittbuhl, Marie-Paule
2015-04-01
Rhythmic physiology is central to retinal function and survival and adapts vision to daily light intensity changes. Mammalian retina rhythmically releases melatonin when cultured under constant conditions, and the occurrence of clock gene [e.g., Period (Per)] expression has been shown for most cellular layers. However, contribution of the distinct layers to genesis of circadian rhythms within the retina is still debated. To characterize their endogenous oscillatory capacity and their communication at the whole-tissue level, we used a vibratome-based method to isolate individual or paired retina cellular layers from the mPer2(Luc) mouse and Per1-luciferase (Per1-Luc) rat, and real-time recorded bioluminescence. We report that each layer of the mouse retina harbors a self-sustained oscillator whose period is significantly longer (∼ 26 hours) than in whole-retina explants (∼ 22.9 hours), indicating that the period is correlated with the degree of coupling. Accordingly, the maximal period (∼ 29 hours) is reached upon complete enzymatic dissociation of the retina. By using pharmacological approaches, we demonstrate that connection between retina oscillators involves gap junctions but only minor contribution from the main retina neurochemicals. Taken together with results from Per1-Luc rats, these data show that mammalian retina consists of a network of layer-specific oscillators whose period is determined by their connectivity.
State diagram of magnetostatic coupling phase-locked spin-torque oscillators
Zhang, Mengwei; Wang, Longze; Wei, Dan; Gao, Kai-Zhong
2015-05-07
The state diagram of magnetostatic coupling phase-locked spin torque oscillator (STO) with perpendicular reference layer and planar field generation layer (FGL) is studied by the macrospin model and the micromagnetic model. The state diagrams of current densities are calculated under various external fields. The simulation shows that there are two phase-lock current density regions. In the phase-locked STOs in low current region I, the spin configuration of FGL is uniform; in high current region II, the spin configuration of FGL is highly nonuniform. In addition, the results with different STOs separation L{sub s} are compared, and the coupling between two STOs is largely decreased when L{sub s} is increased from 40 nm to 60 nm.
Exploiting Vibrational Strong Coupling to Make an Optical Parametric Oscillator Out of a Raman Laser
NASA Astrophysics Data System (ADS)
del Pino, Javier; Garcia-Vidal, Francisco J.; Feist, Johannes
2016-12-01
When the collective coupling of the rovibrational states in organic molecules and confined electromagnetic modes is sufficiently strong, the system enters into vibrational strong coupling, leading to the formation of hybrid light-matter quasiparticles. In this Letter, we demonstrate theoretically how this hybridization in combination with stimulated Raman scattering can be utilized to widen the capabilities of Raman laser devices. We explore the conditions under which the lasing threshold can be diminished and the system can be transformed into an optical parametric oscillator. Finally, we show how the dramatic reduction of the many final molecular states into two collective excitations can be used to create an all-optical switch with output in the midinfrared.
Del Pino, Javier; Garcia-Vidal, Francisco J; Feist, Johannes
2016-12-30
When the collective coupling of the rovibrational states in organic molecules and confined electromagnetic modes is sufficiently strong, the system enters into vibrational strong coupling, leading to the formation of hybrid light-matter quasiparticles. In this Letter, we demonstrate theoretically how this hybridization in combination with stimulated Raman scattering can be utilized to widen the capabilities of Raman laser devices. We explore the conditions under which the lasing threshold can be diminished and the system can be transformed into an optical parametric oscillator. Finally, we show how the dramatic reduction of the many final molecular states into two collective excitations can be used to create an all-optical switch with output in the midinfrared.
NASA Astrophysics Data System (ADS)
Che, Yanqiu; Yang, Tingting; Li, Ruixue; Li, Huiyan; Han, Chunxiao; Wang, Jiang; Wei, Xile
2015-09-01
In this paper, we propose a dynamic delayed feedback control approach or desynchronization of chaotic-bursting synchronous activities in an ensemble of globally coupled neuronal oscillators. We demonstrate that the difference signal between an ensemble's mean field and its time delayed state, filtered and fed back to the ensemble, can suppress the self-synchronization in the ensemble. These individual units are decoupled and stabilized at the desired desynchronized states while the stimulation signal reduces to the noise level. The effectiveness of the method is illustrated by examples of two different populations of globally coupled chaotic-bursting neurons. The proposed method has potential for mild, effective and demand-controlled therapy of neurological diseases characterized by pathological synchronization.
Li, Jin-Liang; Li, Yu-Xian
2008-11-19
Using nonequilibrium Green's function techniques, we investigate Andreev reflection and Aharonov-Bohm oscillations through a parallel-coupled double quantum dot connected with a ferromagnetic lead and a superconductor lead. The possibility of controlling Andreev reflection and Aharonov-Bohm oscillations of the system is explored by tuning the interdot coupling, the gate voltage, the magnetic flux, and the intradot spin-flip scattering. When the spin-flip scattering increases, Fano resonant peaks resulting from the asymmetrical levels of the two quantum dots begin to split, and Aharonov-Bohm oscillations are suppressed. Due to the interdot coupling, one strongly and one weakly coupled state of the system can be formed. The magnetic flux can exchange the function of the two states, which leads to a swap effect.
Efficiency at maximum power of a quantum heat engine based on two coupled oscillators.
Wang, Jianhui; Ye, Zhuolin; Lai, Yiming; Li, Weisheng; He, Jizhou
2015-06-01
We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures T(h) and T(c)(
Radial oscillations of quark stars with strongly coupled QGP in the interior
NASA Astrophysics Data System (ADS)
Ramadas, Sineeba; Bannur, Vishnu. M.
2013-08-01
The radial oscillations of quark stars are analysed using the recently developed strongly coupled quark-gluon plasma (SCQGP) equation of state. This EOS describes the intermediate to strongly coupled phase of deconfined cold quark matter wherein the chiral symmetry has not yet been restored. By integrating the Chandrasekhar eigenequation governing the radial modes we obtain the periods for the fundamental and first overtone, which are plotted for different values of the confining parameter—the bag constant ( B)—pertaining to the equation of state. The eigenfunctions of some of the normal modes are also plotted and analysed. It is found that for lower mass quark stars the oscillation periods are typically of the order of one tenth of a millisecond and has negligible dependence on the bag parameter. For medium and higher mass stars a variation of pulsation period with change in the bag constant is seen—the period increases with increase in B. Comparing with strange stars composed of non-interacting quarks we see that the corresponding pulsation periods show considerable difference throughout the entire range of stellar masses with the difference increasing with decrease in B value (increasing stiffness) for the SCQGP equation of state. Finally we study the damping of small amplitude radial pulsations via non-equilibrium processes. We derive the corresponding neutrino emissivities in the SCQGP case and present the resulting temporal evolution of pulsation energies.
Efficiency at maximum power of a quantum heat engine based on two coupled oscillators
NASA Astrophysics Data System (ADS)
Wang, Jianhui; Ye, Zhuolin; Lai, Yiming; Li, Weisheng; He, Jizhou
2015-06-01
We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures Th and Tc(
Gaspers, Lawrence D; Bartlett, Paula J; Politi, Antonio; Burnett, Paul; Metzger, Walson; Johnston, Jane; Joseph, Suresh K; Höfer, Thomas; Thomas, Andrew P
2014-11-20
Receptor-mediated oscillations in cytosolic Ca(2+) concentration ([Ca(2+)]i) could originate either directly from an autonomous Ca(2+) feedback oscillator at the inositol 1,4,5-trisphosphate (IP3) receptor or as a secondary consequence of IP3 oscillations driven by Ca(2+) feedback on IP3 metabolism. It is challenging to discriminate these alternatives, because IP3 fluctuations could drive Ca(2+) oscillations or could just be a secondary response to the [Ca(2+)]i spikes. To investigate this problem, we constructed a recombinant IP3 buffer using type-I IP3 receptor ligand-binding domain fused to GFP (GFP-LBD), which buffers IP3 in the physiological range. This IP3 buffer slows hormone-induced [IP3] dynamics without changing steady-state [IP3]. GFP-LBD perturbed [Ca(2+)]i oscillations in a dose-dependent manner: it decreased both the rate of [Ca(2+)]i rise and the speed of Ca(2+) wave propagation and, at high levels, abolished [Ca(2+)]i oscillations completely. These data, together with computational modeling, demonstrate that IP3 dynamics play a fundamental role in generating [Ca(2+)]i oscillations and waves.
Kraus representation of a damped harmonic oscillator and its application
Liu Yuxi; Oezdemir, Sahin K.; Miranowicz, Adam; Imoto, Nobuyuki
2004-10-01
By definition, the Kraus representation of a harmonic oscillator suffering from the environment effect, modeled as the amplitude damping or the phase damping, is directly given by a simple operator algebra solution. As examples and applications, we first give a Kraus representation of a single qubit whose computational basis states are defined as bosonic vacuum and single particle number states. We further discuss the environment effect on qubits whose computational basis states are defined as the bosonic odd and even coherent states. The environment effects on entangled qubits defined by two different kinds of computational basis are compared with the use of fidelity.
Cluster synchronization in networks of identical oscillators with α -function pulse coupling
NASA Astrophysics Data System (ADS)
Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato
2017-02-01
We study a network of N identical leaky integrate-and-fire model neurons coupled by α -function pulses, weighted by a coupling parameter K . Studies of the dynamics of this system have mostly focused on the stability of the fully synchronized and the fully asynchronous splay states, which naturally depends on the sign of K , i.e., excitation vs inhibition. We find that there is also a rich set of attractors consisting of clusters of fully synchronized oscillators, such as fixed (N -1 ,1 ) states, which have synchronized clusters of sizes N -1 and 1, as well as splay states of clusters with equal sizes greater than 1. Additionally, we find limit cycles that clarify the stability of previously observed quasiperiodic behavior. Our framework exploits the neutrality of the dynamics for K =0 which allows us to implement a dimensional reduction strategy that simplifies the dynamics to a continuous flow on a codimension 3 subspace with the sign of K determining the flow direction. This reduction framework naturally incorporates a hierarchy of partially synchronized subspaces in which the new attracting states lie. Using high-precision numerical simulations, we describe completely the sequence of bifurcations and the stability of all fixed points and limit cycles for N =2 -4 . The set of possible attracting states can be used to distinguish different classes of neuron models. For instance from our previous work [Chaos 24, 013114 (2014), 10.1063/1.4858458] we know that of the types of partially synchronized states discussed here, only the (N -1 ,1 ) states can be stable in systems of identical coupled sinusoidal (i.e., Kuramoto type) oscillators, such as θ -neuron models. Upon introducing a small variation in individual neuron parameters, the attracting fixed points we discuss here generalize to equivalent fixed points in which neurons need not fire coincidently.
2013-07-01
Madden- Julian Oscillation Simulated by the Coupled Ocean-Atmosphere Mesoscale Prediction System 0601153N 73-4347-22-5 Toshiaki Shinoda, Tommy G...unlimited. Simulation of surface wind and upper-ocean variability associated with the Madden - Julian oscillation (MJO) by a regional coupled model, the...based on the comparison with the spatial variation of surface forcing fields. Indian Ocean, diurnal effects, Madden- Julian oscillation, coupled
NASA Astrophysics Data System (ADS)
Nori, Franco; Ashhab, Sahel
2011-03-01
We consider a system composed of a two-level system (i.e. a qubit) and a harmonic oscillator in the ultrastrong-coupling regime, where the coupling strength is comparable to the qubit and oscillator energy scales. We explore the possibility of preparing nonclassical states in this system, especially in the ground state of the combined system. The nonclassical states that we consider include squeezed states, Schrodinger-cat states and entangled states. We also analyze the nature of the change in the ground state as the coupling strength is increased, going from a separable ground state in the absence of coupling to a highly entangled ground state in the case of very strong coupling. Reference: S. Ashhab and F. Nori, Phys. Rev. A 81, 042311 (2010). We thank support from DARPA, AFOSR, NSA, LPS, ARO, NSF, MEXT, JSPS, FIRST, and JST.
NASA Astrophysics Data System (ADS)
Kriener, Birgit
2012-09-01
Under which conditions can a network of pulse-coupled oscillators sustain stable collective activity states? Previously, it was shown that stability of the simplest pattern conceivable, i.e., global synchrony, in networks of symmetrically pulse-coupled oscillators can be decided in a rigorous mathematical fashion, if interactions either all advance or all retard oscillation phases ("mono-interaction network"). Yet, many real-world networks—for example neuronal circuits—are asymmetric and moreover crucially feature both types of interactions. Here, we study complex networks of excitatory (phase-advancing) and inhibitory (phase-retarding) leaky integrate-and-fire (LIF) oscillators. We show that for small coupling strength, previous results for mono-interaction networks also apply here: pulse time perturbations eventually decay if they are smaller than a transmission delay and if all eigenvalues of the linear stability operator have absolute value smaller or equal to one. In this case, the level of inhibition must typically be significantly stronger than that of excitation to ensure local stability of synchrony. For stronger coupling, however, network synchrony eventually becomes unstable to any finite perturbation, even if inhibition is strong and all eigenvalues of the stability operator are at most unity. This new type of instability occurs when any oscillator, inspite of receiving inhibitory input from the network on average, can by chance receive sufficient excitatory input to fire a pulse before all other pulses in the system are delivered, thus breaking the near-synchronous perturbation pattern.
Magnetic nanoparticles for applications in oscillating magnetic field
Peeraphatdit, Chorthip
2009-01-01
Enzymatic and thermochemical catalysis are both important industrial processes. However, the thermal requirements for each process often render them mutually exclusive: thermochemical catalysis requires high temperature that denatures enzymes. One of the long-term goals of this project is to design a thermocatalytic system that could be used with enzymatic systems in situ to catalyze reaction sequences in one pot; this system would be useful for numerous applications e.g. conversion of biomass to biofuel and other commodity products. The desired thermocatalytic system would need to supply enough thermal energy to catalyze thermochemical reactions, while keeping the enzymes from high temperature denaturation. Magnetic nanoparticles are known to generate heat in an oscillating magnetic field through mechanisms including hysteresis and relaxational losses. We envisioned using these magnetic nanoparticles as the local heat source embedded in sub-micron size mesoporous support to spatially separate the particles from the enzymes. In this study, we set out to find the magnetic materials and instrumental conditions that are sufficient for this purpose. Magnetite was chosen as the first model magnetic material in this study because of its high magnetization values, synthetic control over particle size, shape, functionalization and proven biocompatibility. Our experimental designs were guided by a series of theoretical calculations, which provided clues to the effects of particle size, size distribution, magnetic field, frequency and reaction medium. Materials of theoretically optimal size were synthesized, functionalized, and their effects in the oscillating magnetic field were subsequently investigated. Under our conditions, the materials that clustered e.g. silica-coated and PNIPAM-coated iron oxides exhibited the highest heat generation, while iron oxides embedded in MSNs and mesoporous iron oxides exhibited the least bulk heating. It is worth noting that the specific
Rouse, Andrew A.; Cook, Peter F.; Large, Edward W.; Reichmuth, Colleen
2016-01-01
Human capacity for entraining movement to external rhythms—i.e., beat keeping—is ubiquitous, but its evolutionary history and neural underpinnings remain a mystery. Recent findings of entrainment to simple and complex rhythms in non-human animals pave the way for a novel comparative approach to assess the origins and mechanisms of rhythmic behavior. The most reliable non-human beat keeper to date is a California sea lion, Ronan, who was trained to match head movements to isochronous repeating stimuli and showed spontaneous generalization of this ability to novel tempos and to the complex rhythms of music. Does Ronan's performance rely on the same neural mechanisms as human rhythmic behavior? In the current study, we presented Ronan with simple rhythmic stimuli at novel tempos. On some trials, we introduced “perturbations,” altering either tempo or phase in the middle of a presentation. Ronan quickly adjusted her behavior following all perturbations, recovering her consistent phase and tempo relationships to the stimulus within a few beats. Ronan's performance was consistent with predictions of mathematical models describing coupled oscillation: a model relying solely on phase coupling strongly matched her behavior, and the model was further improved with the addition of period coupling. These findings are the clearest evidence yet for parity in human and non-human beat keeping and support the view that the human ability to perceive and move in time to rhythm may be rooted in broadly conserved neural mechanisms. PMID:27375418
Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime
NASA Astrophysics Data System (ADS)
Yoshihara, Fumiki; Fuse, Tomoko; Ashhab, Sahel; Kakuyanagi, Kosuke; Saito, Shiro; Semba, Kouichi
2017-01-01
The interaction between an atom and the electromagnetic field inside a cavity has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies, including lasers and many quantum computing architectures. Superconducting qubits have allowed the realization of strong and ultrastrong coupling between artificial atoms and cavities. If the coupling strength g becomes as large as the atomic and cavity frequencies (Δ and ωo, respectively), the energy eigenstates including the ground state are predicted to be highly entangled. There has been an ongoing debate over whether it is fundamentally possible to realize this regime in realistic physical systems. By inductively coupling a flux qubit and an LC oscillator via Josephson junctions, we have realized circuits with g/ωo ranging from 0.72 to 1.34 and g/Δ >> 1. Using spectroscopy measurements, we have observed unconventional transition spectra that are characteristic of this new regime. Our results provide a basis for ground-state-based entangled pair generation and open a new direction of research on strongly correlated light-matter states in circuit quantum electrodynamics.
Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure
NASA Astrophysics Data System (ADS)
Jiang, Hai-Bo; Zhang, Li-Ping; Yu, Jian-Jiang
2015-02-01
Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincaré map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincaré map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations. Project supported by the National Natural Science Foundation of China (Grant Nos. 11402224, 11202180, 61273106, and 11171290), the Qing Lan Project of the Jiangsu Higher Educational Institutions of China, and the Jiangsu Overseas Research and Training Program for University Prominent Young and Middle-aged Teachers and Presidents.
Independent Noise Can Synchronize Interacting Networks of Pulse-Coupled Oscillators
NASA Astrophysics Data System (ADS)
Riecke, Hermann; Meng, John
Structured networks comprised of subnetwork modules are ubiquitous. Motivated by the observation of rhythms and their interaction in different brain areas, we study a network consisting of two subnetworks of pulse-coupled integrate-fire neurons. Through mutual inhibition the neurons in the individual subnetworks can become synchronized and each subnetwork can exhibit coherent oscillatory dynamics, e.g. an ING-rhythm. In the absence of coupling between the networks the rhythms will in general have different frequencies. We investigate the interaction between these different rhythms. Strikingly, we find that increasing the noise level in the input to the individual neurons can synchronize the rhythms of the two networks, even though the inputs to different neurons are uncorrelated, sharing no common component. A heuristic phase model for the coupled networks shows that this synchronization hinges on the fact that only a fraction of the neurons may spike in a given cycle. Thus, the synchronization of the network rhythms differs qualitatively from that of individual oscillators. Supported by NSF-CMMI 1435358.
Evolution of quantum correlations in the open quantum systems consisting of two coupled oscillators
NASA Astrophysics Data System (ADS)
Abbasnezhad, Farkhondeh; Mehrabankar, Somayeh; Afshar, Davood; Jafarpour, Mojtaba
2017-04-01
The open quantum systems consisting of coupled and uncoupled asymmetric oscillators are considered with an initial quantum-dot trapped-ion coherent state. The quantum correlations between spatial modes of this trapped ion are examined to find their dependence on the temperature, asymmetric parameter, dissipation coefficient and the magnetic field. It is observed that the discord of the initial state is an increasing function of the asymmetric parameter and the magnetic field. Moreover, in the case of two uncoupled modes, entanglement and discord are decreasing functions of temperature and the dissipation coefficient. However, as the temperature and dissipation coefficient increase, the discord fades out faster. In the case of two coupled modes, as the temperature and dissipation coefficient increase, the sudden death of the entanglement and fade out of the discord happen sooner; moreover, as the magnetic field increases, the entanglement sudden death and the discord fade out time occur sooner. Also, with the increase in the asymmetric parameter, the entanglement sudden death is postponed. In addition, in the asymmetric system, appreciable discord can be created in the temperature range 0-10 K, while appreciable entanglement can be created in the temperature range 0-5 mK. Finally, it is observed that non-monotonic evolution of quantum correlations is due to coupling of modes.
Collective dynamics of identical phase oscillators with high-order coupling
Xu, Can; Xiang, Hairong; Gao, Jian; Zheng, Zhigang
2016-01-01
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various regions of parameter space are analyzed. Furthermore, a detailed linear stability analysis proves that the stationary symmetric distribution is only neutrally stable in the marginal regime which stems from the generalized time-reversal symmetry. Moreover, the critical parameters of the transition among various regimes are determined analytically by both the Ott-Antonsen method and linear stability analysis, the transient dynamics are further revealed in terms of the characteristic curves method. Finally, for the more general initial condition the symmetric dynamics could be reduced to a rigorous three-dimensional manifold which shows that the neutrally stable chaos could also occur in this model for particular parameters. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the dynamical properties in general systems with higher-order harmonics couplings. PMID:27491401
Rouse, Andrew A; Cook, Peter F; Large, Edward W; Reichmuth, Colleen
2016-01-01
Human capacity for entraining movement to external rhythms-i.e., beat keeping-is ubiquitous, but its evolutionary history and neural underpinnings remain a mystery. Recent findings of entrainment to simple and complex rhythms in non-human animals pave the way for a novel comparative approach to assess the origins and mechanisms of rhythmic behavior. The most reliable non-human beat keeper to date is a California sea lion, Ronan, who was trained to match head movements to isochronous repeating stimuli and showed spontaneous generalization of this ability to novel tempos and to the complex rhythms of music. Does Ronan's performance rely on the same neural mechanisms as human rhythmic behavior? In the current study, we presented Ronan with simple rhythmic stimuli at novel tempos. On some trials, we introduced "perturbations," altering either tempo or phase in the middle of a presentation. Ronan quickly adjusted her behavior following all perturbations, recovering her consistent phase and tempo relationships to the stimulus within a few beats. Ronan's performance was consistent with predictions of mathematical models describing coupled oscillation: a model relying solely on phase coupling strongly matched her behavior, and the model was further improved with the addition of period coupling. These findings are the clearest evidence yet for parity in human and non-human beat keeping and support the view that the human ability to perceive and move in time to rhythm may be rooted in broadly conserved neural mechanisms.
Collective dynamics of identical phase oscillators with high-order coupling
NASA Astrophysics Data System (ADS)
Xu, Can; Xiang, Hairong; Gao, Jian; Zheng, Zhigang
2016-08-01
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various regions of parameter space are analyzed. Furthermore, a detailed linear stability analysis proves that the stationary symmetric distribution is only neutrally stable in the marginal regime which stems from the generalized time-reversal symmetry. Moreover, the critical parameters of the transition among various regimes are determined analytically by both the Ott-Antonsen method and linear stability analysis, the transient dynamics are further revealed in terms of the characteristic curves method. Finally, for the more general initial condition the symmetric dynamics could be reduced to a rigorous three-dimensional manifold which shows that the neutrally stable chaos could also occur in this model for particular parameters. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the dynamical properties in general systems with higher-order harmonics couplings.
Multi-Scale Entrainment of Coupled Neuronal Oscillations in Primary Auditory Cortex
O’Connell, M. N.; Barczak, A.; Ross, D.; McGinnis, T.; Schroeder, C. E.; Lakatos, P.
2015-01-01
Earlier studies demonstrate that when the frequency of rhythmic tone sequences or streams is task relevant, ongoing excitability fluctuations (oscillations) of neuronal ensembles in primary auditory cortex (A1) entrain to stimulation in a frequency dependent way that sharpens frequency tuning. The phase distribution across A1 neuronal ensembles at time points when attended stimuli are predicted to occur reflects the focus of attention along the spectral attribute of auditory stimuli. This study examined how neuronal activity is modulated if only the temporal features of rhythmic stimulus streams are relevant. We presented macaques with auditory clicks arranged in 33 Hz (gamma timescale) quintets, repeated at a 1.6 Hz (delta timescale) rate. Such multi-scale, hierarchically organized temporal structure is characteristic of vocalizations and other natural stimuli. Monkeys were required to detect and respond to deviations in the temporal pattern of gamma quintets. As expected, engagement in the auditory task resulted in the multi-scale entrainment of delta- and gamma-band neuronal oscillations across all of A1. Surprisingly, however, the phase-alignment, and thus, the physiological impact of entrainment differed across the tonotopic map in A1. In the region of 11–16 kHz representation, entrainment most often aligned high excitability oscillatory phases with task-relevant events in the input stream and thus resulted in response enhancement. In the remainder of the A1 sites, entrainment generally resulted in response suppression. Our data indicate that the suppressive effects were due to low excitability phase delta oscillatory entrainment and the phase amplitude coupling of delta and gamma oscillations. Regardless of the phase or frequency, entrainment appeared stronger in left A1, indicative of the hemispheric lateralization of auditory function. PMID:26696866
Coupled Dirac fermions and neutrino-like oscillations in twisted bilayer graphene.
Xian, Lede; Wang, Z F; Chou, M Y
2013-11-13
The low-energy quasiparticles in graphene can be described by a Dirac-Weyl Hamiltonian for massless fermions, hence graphene has been proposed to be an effective medium to study exotic phenomena originally predicted for relativistic particle physics, such as Klein tunneling and Zitterbewegung. In this work, we show that another important particle-physics phenomenon, the neutrino oscillation, can be studied and observed in a particular graphene system, namely, twisted bilayer graphene. It has been found that graphene layers grown epitaxially on SiC or by the chemical vapor deposition method on metal substrates display a stacking pattern with adjacent layers rotated by an angle with respect to each other. The quasiparticle states in two distinct graphene layers act as neutrinos with two flavors, and the interlayer interaction between them induces an appreciable coupling between these two "flavors" of massless fermions, leading to neutrino-like oscillations. In addition, our calculation shows that anisotropic transport properties manifest in a specific energy window, which is accessible experimentally in twisted bilayer graphene. Combining two graphene layers enables us to probe the rich physics involving multiple interacting Dirac fermions.
Phase-shift inversion in oscillator systems with periodically switching couplings.
Lee, Sang Hoon; Lee, Sungmin; Son, Seung-Woo; Holme, Petter
2012-02-01
A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such a temporal response. The Kuramoto model under periodically switching interactions has the same type of phase transition as the original mean-field model. Furthermore, we see that the signature of the synchronization transition appears in the relative delay of the order parameter with respect to the phase of oscillating interactions as well. Specifically, the phase shift becomes significantly larger as the system gets closer to the phase transition, so that the order parameter at the minimum interaction density can even be larger than that at the maximum interaction density, counterintuitively. We argue that this phase-shift inversion is caused by the diverging relaxation time, in a similar way to the resonance near the critical point in the kinetic Ising model. Our result, based on exhaustive simulations on globally coupled systems as well as scale-free networks, shows that an oscillator system's phase transition can be manifested in the temporal response to the topological dynamics of the underlying connection structure.
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.
2016-06-01
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.
Rodriguez-Gallardo, M.; Arias, J. M.; Gomez-Camacho, J.; Moro, A. M.; Johnson, R. C.; Tostevin, J. A.; Thompson, I. J.
2008-06-15
The scattering of a weakly bound three-body system by a target is discussed. A transformed harmonic oscillator basis is used to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum of the projectile. The continuum-discretized coupled-channels framework is used for the scattering calculations. The formalism is applied to different reactions, {sup 6}He+{sup 12}C at 229.8 MeV, {sup 6}He+{sup 64}Zn at 10 and 13.6 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV, induced by the Borromean nucleus {sup 6}He. Both the Coulomb and nuclear interactions with a target are taken into account.
Moro, A. M.; Arias, J. M.; Gomez-Camacho, J.; Perez-Bernal, F.
2009-11-15
A new method for continuum discretization in continuum-discretized coupled-channels calculations is proposed. The method is based on an analytic local-scale transformation of the harmonic-oscillator wave functions proposed for other purposes in a recent work [Karatagladis et al., Phys. Rev. C 71, 064601 (2005)]. The new approach is compared with the standard method of continuum discretization in terms of energy bins for the reactions d+{sup 58}Ni at 80 MeV, {sup 6}Li+{sup 40}Ca at 156 MeV, and {sup 6}He+{sup 208}Pb at 22 MeV and 240 MeV/nucleon. In all cases very good agreement between both approaches is found.
Coupling of Thalamocortical Sleep Oscillations Are Important for Memory Consolidation in Humans
Niknazar, Mohammad; Krishnan, Giri P.; Bazhenov, Maxim; Mednick, Sara C.
2015-01-01
Sleep, specifically non-rapid eye movement (NREM) sleep, is thought to play a critical role in the consolidation of recent memories. Two main oscillatory activities observed during NREM, cortical slow oscillations (SO, 0.5–1.0Hz) and thalamic spindles (12–15Hz), have been shown to independently correlate with memory improvement. Yet, it is not known how these thalamocortical events interact, or the significance of this interaction, during the consolidation process. Here, we found that systemic administration of the GABAergic drug (zolpidem) increased both the phase-amplitude coupling between SO and spindles, and verbal memory improvement in humans. These results suggest that thalamic spindles that occur during transitions to the cortical SO Up state are optimal for memory consolidation. Our study predicts that the timely interactions between cortical and thalamic events during consolidation, contribute to memory improvement and is mediated by the level of inhibitory neurotransmission. PMID:26671283
Entanglement in a continuously measured two-level system coupled to a harmonic oscillator
Hernandez-Concepcion, E.; Alonso, D.; Brouard, S.
2009-05-15
The dynamics of a two-level system (TLS) coupled to a harmonic oscillator (HO) is studied under the combined effect of a thermal bath acting on the HO and of a detector continuously measuring one of the components of the spinlike TLS. The analysis focuses on the dynamics of the 'relative entropy of entanglement' (REE) in the one-energy-excitation manifold of the reduced TLS+HO system. For this model system, a stationary state is shown to be reached for which the relative entropy of entanglement is in general nonzero, even though, under certain approximations, the separate effects of bath and detector would be to remove any trace of this resource from the system. Analytical as well as numerical results are obtained for the REE as a function of the different parameters involved in the model definition.
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.
2016-02-27
Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.
Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins
NASA Astrophysics Data System (ADS)
Ujjwal, Sangeeta Rani; Punetha, Nirmal; Ramaswamy, Ram; Agrawal, Manish; Prasad, Awadhesh
2016-06-01
We study the multistability that results when a chaotic response system that has an invariant symmetry is driven by another chaotic oscillator. We observe that there is a transition from a desynchronized state to a situation of multistability. In the case considered, there are three coexisting attractors, two of which are synchronized and one is desynchronized. For large coupling, the asynchronous attractor disappears, leaving the system bistable. We study the basins of attraction of the system in the regime of multistability. The three attractor basins are interwoven in a complex manner, with extensive riddling within a sizeable region of (but not the entire) phase space. A quantitative characterization of the riddling behavior is made via the so-called uncertainty exponent, as well as by evaluating the scaling behavior of tongue-like structures emanating from the synchronization manifold.
Anti-resonance in a one-dimensional chain of driven coupled oscillators
NASA Astrophysics Data System (ADS)
Belbasi, Somayyeh; Ebrahim Foulaadvand, M.; Joe, Yong S.
2014-01-01
We investigate a driven system of N one-dimensional coupled oscillators with identical masses. The first mass is connected to a sinusoidal driving force of frequency ω. In the steady state, when all the masses perform simple harmonic motion, we analytically obtain the dependence of their amplitudes on ω and show that there are resonance and anti-resonance frequencies. At an anti-resonance frequency, the amplitude of one of the masses becomes exactly zero. The mass directly connected to the driving force has the largest number of anti-resonance frequencies, N - 1. The phase of each mass's motion is either 0 or π with respect to the driving force. The case where damping forces are present is also considered, and the amplitude dependence on driving frequency is analytically obtained. In the presence of damping, there is no anti-resonance.
Statistical properties of multiphoton time-dependent three-boson coupled oscillators
Abdalla, M. Sebawe; Perina, Jan; Krepelka, Jaromir
2006-06-15
We investigate the quantum statistics of three time-dependent coupled oscillators in the presence of multiphoton processes. The system is connected with the two-atom multiphoton Tavis-Cummings model. The solution of the Heisenberg equations of the motion is obtained in a compact form. We assume that the modes are initially prepared in coherent states, and we discuss nonclassical phenomena (squeezing and sub-Poissonian behavior). Further, we examine the joint quasi-distribution functions as well as photon-number distribution and its factorial moments. The system has shown that the nonclassical effect is apparent in compound modes (1,3) and (2,3). Moreover, the superstructure phenomenon is observed when the photon transition is increased.
Radwan, Basma; Dvorak, Dino; Fenton, André A
2016-04-01
Fragile X syndrome (FXS) patients do not make the fragile X mental retardation protein (FMRP). The absence of FMRP causes dysregulated translation, abnormal synaptic plasticity and the most common form of inherited intellectual disability. But FMRP loss has minimal effects on memory itself, making it difficult to understand why the absence of FMRP impairs memory discrimination and increases risk of autistic symptoms in patients, such as exaggerated responses to environmental changes. While Fmr1 knockout (KO) and wild-type (WT) mice perform cognitive discrimination tasks, we find abnormal patterns of coupling between theta and gamma oscillations in perisomatic and dendritic hippocampal CA1 local field potentials of the KO. Perisomatic CA1 theta-gamma phase-amplitude coupling (PAC) decreases with familiarity in both the WT and KO, but activating an invisible shock zone, subsequently changing its location, or turning it off, changes the pattern of oscillatory events in the LFPs recorded along the somato-dendritic axis of CA1. The cognition-dependent changes of this pattern of neural activity are relatively constrained in WT mice compared to KO mice, which exhibit abnormally weak changes during the cognitive challenge caused by changing the location of the shock zone and exaggerated patterns of change when the shock zone is turned off. Such pathophysiology might explain how dysregulated translation leads to intellectual disability in FXS. These findings demonstrate major functional abnormalities after the loss of FMRP in the dynamics of neural oscillations and that these impairments would be difficult to detect by steady-state measurements with the subject at rest or in steady conditions.
Coronal loop seismology using damping of standing kink oscillations by mode coupling
NASA Astrophysics Data System (ADS)
Pascoe, D. J.; Goddard, C. R.; Nisticò, G.; Anfinogentov, S.; Nakariakov, V. M.
2016-05-01
Context. Kink oscillations of solar coronal loops are frequently observed to be strongly damped. The damping can be explained by mode coupling on the condition that loops have a finite inhomogeneous layer between the higher density core and lower density background. The damping rate depends on the loop density contrast ratio and inhomogeneous layer width. Aims: The theoretical description for mode coupling of kink waves has been extended to include the initial Gaussian damping regime in addition to the exponential asymptotic state. Observation of these damping regimes would provide information about the structuring of the coronal loop and so provide a seismological tool. Methods: We consider three examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) for which the general damping profile (Gaussian and exponential regimes) can be fitted. Determining the Gaussian and exponential damping times allows us to perform seismological inversions for the loop density contrast ratio and the inhomogeneous layer width normalised to the loop radius. The layer width and loop minor radius are found separately by comparing the observed loop intensity profile with forward modelling based on our seismological results. Results: The seismological method which allows the density contrast ratio and inhomogeneous layer width to be simultaneously determined from the kink mode damping profile has been applied to observational data for the first time. This allows the internal and external Alfvén speeds to be calculated, and estimates for the magnetic field strength can be dramatically improved using the given plasma density. Conclusions: The kink mode damping rate can be used as a powerful diagnostic tool to determine the coronal loop density profile. This information can be used for further calculations such as the magnetic field strength or phase mixing rate.
NASA Technical Reports Server (NTRS)
Stein, S. R.
1980-01-01
The potential applications of superconductivity in space are examined. It is shown that superconducting oscillators have achieved better frequency stability that any other device for averaging times of 10 s to 1000 s. Such a high stability results from the use of solid niobium resonators having Q factors greater that 10 to the 10th. Oscillators of this type have direct applications as clocks and spectrally pure sources. In addition, they may also be used for accurate measurements of many physical quantities and to perform a variety of experiments on fundamental constants, relativity, and gravity waves.
NASA Astrophysics Data System (ADS)
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2016-07-01
We investigate the emergence of different kinds of imperfectly synchronized states and chimera states in two interacting populations of nonlocally coupled Stuart-Landau oscillators. We find that the complete synchronization in population I and existence of solitary oscillators which escape from the synchronized group in population II lead to imperfectly synchronized states for sufficiently small values of nonisochronicity parameter. Interestingly, upon increasing the strength of this parameter further there occurs an onset of mixed imperfectly synchronized states where the solitary oscillators occur from both the populations. Synchronized oscillators from both the populations are locked to a common average frequency. In both cases of imperfectly synchronized states, synchronized oscillators exhibit periodic motion while the solitary oscillators are quasiperiodic in nature. In this region, for spatially prepared initial conditions, we can observe the mixed chimera states where the coexistence of synchronized and desynchronized oscillations occur from both the populations. On the other hand, imperfectly synchronized states are not always stable, and they can drift aperiodically due to instability caused by an increase of nonisochronicity parameter. We observe that these states are robust to the introduction of frequency mismatch between the two populations.
The Acoustic Simple Harmonic Oscillator: Experimental Verification and Applications
NASA Astrophysics Data System (ADS)
Matteson, Sam
2009-04-01
In his famous volume, The Sensations of Tone, published in 1877, Hermann Helmholtz introduced a resonator that was central to his investigations of acoustics. This talk revisits the device that Helmholtz described and examines it as a manifestation of an acoustic simple harmonic oscillator (SHO). The presentation demonstrates that an enclosed volume which communicates with the outside world via a narrow tube exhibits a single strong frequency response in analogy to a mechanical SHO, along with weaker resonances of the air in the short pipe that comprises the ``neck.'' The investigations, furthermore, report results of a straightforward experiment that confirms the SHO model (with damping) and that is very accessible to undergraduate students using inexpensive equipment and internet-obtainable freeware. The current work also extends the analysis to include applications of the Helmholtz Resonator to several folk instruments, namely, the ocarina, whistling, and the ``bottle band.''
Barnes, George L.; Kellman, Michael E.
2013-12-07
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is “designed” by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of “classicalizing” behavior in the approach to thermal equilibrium are briefly considered.
NASA Astrophysics Data System (ADS)
Barnes, George L.; Kellman, Michael E.
2013-12-01
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.
Barnes, George L; Kellman, Michael E
2013-12-07
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level pattern to have a thermodynamic temperature. A random coupling causes the system and environment to become entangled in the course of time evolution. The approach to a Boltzmann distribution is observed, and effective fitted temperatures close to the designed temperature are obtained. All initial pure states of the system are driven to equilibrium at very similar rates, with quick loss of memory of the initial state. The time evolution of the von Neumann entropy is calculated as a measure of equilibration and of quantum coherence. It is pointed out using spatial density distribution plots that quantum interference is eliminated only with maximal entropy, which corresponds thermally to infinite temperature. Implications of our results for the notion of "classicalizing" behavior in the approach to thermal equilibrium are briefly considered.
Stability switches and multistability coexistence in a delay-coupled neural oscillators system.
Song, Zigen; Xu, Jian
2012-11-21
In this paper, we present a neural network system composed of two delay-coupled neural oscillators, where each of these can be regarded as the dynamical system describing the average activity of neural population. Analyzing the corresponding characteristic equation, the local stability of rest state is studied. The system exhibits the switch phenomenon between the rest state and periodic activity. Furthermore, the Hopf bifurcation is analyzed and the bifurcation curve is given in the parameters plane. The stability of the bifurcating periodic solutions and direction of the Hopf bifurcation are exhibited. Regarding time delay and coupled weight as the bifurcation parameters, the Fold-Hopf bifurcation is investigated in detail in terms of the central manifold reduction and normal form method. The neural system demonstrates the coexistence of the rest states and periodic activities in the different parameter regions. Employing the normal form of the original system, the coexistence regions are illustrated approximately near the Fold-Hopf singularity point. Finally, numerical simulations are performed to display more complex dynamics. The results illustrate that system may exhibit the rich coexistence of the different neuro-computational properties, such as the rest states, periodic activities, and quasi-periodic behavior. In particular, some periodic activities can evolve into the bursting-type behaviors with the varying time delay. It implies that the coexistence of the quasi-periodic activity and bursting-type behavior can be obtained if the suitable value of system parameter is chosen.
El Nino-southern oscillation simulated in an MRI atmosphere-ocean coupled general circulation model
Nagai, T.; Tokioka, T.; Endoh, M.; Kitamura, Y. )
1992-11-01
A coupled atmosphere-ocean general circulation model (GCM) was time integrated for 30 years to study interannual variability in the tropics. The atmospheric component is a global GCM with 5 levels in the vertical and 4[degrees]latitude X 5[degrees] longitude grids in the horizontal including standard physical processes (e.g., interactive clouds). The oceanic component is a GCM for the Pacific with 19 levels in the vertical and 1[degrees]x 2.5[degrees] grids in the horizontal including seasonal varying solar radiation as forcing. The model succeeded in reproducing interannual variations that resemble the El Nino-Southern Oscillation (ENSO) with realistic seasonal variations in the atmospheric and oceanic fields. The model ENSO cycle has a time scale of approximately 5 years and the model El Nino (warm) events are locked roughly in phase to the seasonal cycle. The cold events, however, are less evident in comparison with the El Nino events. The time scale of the model ENSO cycle is determined by propagation time of signals from the central-eastern Pacific to the western Pacific and back to the eastern Pacific. Seasonal timing is also important in the ENSO time scale: wind anomalies in the central-eastern Pacific occur in summer and the atmosphere ocean coupling in the western Pacific operates efficiently in the first half of the year.
Feillet, Celine; van der Horst, Gijsbertus T J; Levi, Francis; Rand, David A; Delaunay, Franck
2015-01-01
Uncontrolled cell proliferation is one of the key features leading to cancer. Seminal works in chronobiology have revealed that disruption of the circadian timing system in mice, either by surgical, genetic, or environmental manipulation, increased tumor development. In humans, shift work is a risk factor for cancer. Based on these observations, the link between the circadian clock and cell cycle has become intuitive. But despite identification of molecular connections between the two processes, the influence of the clock on the dynamics of the cell cycle has never been formally observed. Recently, two studies combining single live cell imaging with computational methods have shed light on robust coupling between clock and cell cycle oscillators. We recapitulate here these novel findings and integrate them with earlier results in both healthy and cancerous cells. Moreover, we propose that the cell cycle may be synchronized or slowed down through coupling with the circadian clock, which results in reduced tumor growth. More than ever, systems biology has become instrumental to understand the dynamic interaction between the circadian clock and cell cycle, which is critical in cellular coordination and for diseases such as cancer.
Marine biogeochemical responses to the North Atlantic Oscillation in a coupled climate model
NASA Astrophysics Data System (ADS)
Patara, Lavinia; Visbeck, Martin; Masina, Simona; Krahmann, Gerd; Vichi, Marcello
2011-07-01
In this study a coupled ocean-atmosphere model containing interactive marine biogeochemistry is used to analyze interannual, lagged, and decadal marine biogeochemical responses to the North Atlantic Oscillation (NAO), the dominant mode of North Atlantic atmospheric variability. The coupled model adequately reproduces present-day climatologies and NAO atmospheric variability. It is shown that marine biogeochemical responses to the NAO are governed by different mechanisms according to the time scale considered. On interannual time scales, local changes in vertical mixing, caused by modifications in air-sea heat, freshwater, and momentum fluxes, are most relevant in influencing phytoplankton growth through light and nutrient limitation mechanisms. At subpolar latitudes, deeper mixing occurring during positive NAO winters causes a slight decrease in late winter chlorophyll concentration due to light limitation and a 10%-20% increase in spring chlorophyll concentration due to higher nutrient availability. The lagged response of physical and biogeochemical properties to a high NAO winter shows some memory in the following 2 years. In particular, subsurface nutrient anomalies generated by local changes in mixing near the American coast are advected along the North Atlantic Current, where they are suggested to affect downstream chlorophyll concentration with 1 year lag. On decadal time scales, local and remote mechanisms act contemporaneously in shaping the decadal biogeochemical response to the NAO. The slow circulation adjustment, in response to NAO wind stress curl anomalies, causes a basin redistribution of heat, freshwater, and biogeochemical properties which, in turn, modifies the spatial structure of the subpolar chlorophyll bloom.
NASA Astrophysics Data System (ADS)
Tero, A.; Kobayashi, R.; Nakagaki, T.
2005-06-01
Experiments on the fusion and partial separation of plasmodia of the true slime mold Physarum polycephalum are described, concentrating on the spatio-temporal phase patterns of rhythmic amoeboid movement. On the basis of these experimental results we introduce a new model of coupled oscillators with one conserved quantity. Simulations using the model equations reproduce the experimental results well.
The Lever oscillator for use in high resistance resonator applications
Wessendorf, K.O.
1993-07-01
The Lever oscillator has been specifically designed for use with quartz resonator sensors. The use of quartz resonators as sensors is of particular interest and depending on the sensing environment, e.g., liquid, the oscillator design is both critical and difficult due to the wide dynamic range of resonator resistance possible due to damping of the resonator. Standard oscillator designs do not work well as sensor oscillators. An oscillator design will be presented that allows both frequency and loss (R{sub m}) of the resonator to be determined over a wide dynamic range of resonator loss. The Lever oscillator uses negative feedback in a differential amplifier configuration to actively and variably divide (or leverage) the resonator impedance such that the oscillator can maintain the phase and gain of the loop over a wide range of resonator resistance.
Park, Hyojin; Ince, Robin A A; Schyns, Philippe G; Thut, Gregor; Gross, Joachim
2015-06-15
Humans show a remarkable ability to understand continuous speech even under adverse listening conditions. This ability critically relies on dynamically updated predictions of incoming sensory information, but exactly how top-down predictions improve speech processing is still unclear. Brain oscillations are a likely mechanism for these top-down predictions [1, 2]. Quasi-rhythmic components in speech are known to entrain low-frequency oscillations in auditory areas [3, 4], and this entrainment increases with intelligibility [5]. We hypothesize that top-down signals from frontal brain areas causally modulate the phase of brain oscillations in auditory cortex. We use magnetoencephalography (MEG) to monitor brain oscillations in 22 participants during continuous speech perception. We characterize prominent spectral components of speech-brain coupling in auditory cortex and use causal connectivity analysis (transfer entropy) to identify the top-down signals driving this coupling more strongly during intelligible speech than during unintelligible speech. We report three main findings. First, frontal and motor cortices significantly modulate the phase of speech-coupled low-frequency oscillations in auditory cortex, and this effect depends on intelligibility of speech. Second, top-down signals are significantly stronger for left auditory cortex than for right auditory cortex. Third, speech-auditory cortex coupling is enhanced as a function of stronger top-down signals. Together, our results suggest that low-frequency brain oscillations play a role in implementing predictive top-down control during continuous speech perception and that top-down control is largely directed at left auditory cortex. This suggests a close relationship between (left-lateralized) speech production areas and the implementation of top-down control in continuous speech perception.
NASA Astrophysics Data System (ADS)
Mokhov, I. I.; Smirnov, D. A.
2015-09-01
On the basis of monthly mean data obtained over a period of 1870-2013, relations between the Atlantic Multidecadal Oscillation (AMO) and the El Niño/Southern Oscillation (ENSO) have been studied using the Granger causality analysis and estimates of long-Term effects. A bidirectional relationship has been revealed in the dynamics of these processes; moreover, over the entire period as a whole, the ENSO influence on the AMO was significantly stronger than the AMO influence on the ENSO. However, a more detailed analysis has revealed the variable character of this relationship: the ENSO influence on the AMO was stronger at the beginning of the period under study, while, in recent years, the reverse influence and its increase have become more significant against the background of a decrease in the ENSO influence on the AMO.
El-Nino Southern Oscillation simulated and predicted in SNU coupled GCMs
NASA Astrophysics Data System (ADS)
Ham, Yoo-Geun; Kang, In-Sik; Kim, Daehyun; Kug, Jong-Seong
2012-06-01
The characteristics of the El-Nino Southern Oscillation (ENSO) simulated in free integrations using two versions of the Seoul National University (SNU) ocean-atmosphere coupled global climate model (CGCM) are examined. A revised version of the SNU CGCM is developed by incorporating a reduced air-sea coupling interval (from 1 day to 2 h), a parameterization for cumulus momentum transport, a minimum entrainment rate threshold for convective plumes, and a shortened auto-conversion time scale of cloud water to raindrops. With the revised physical processes, lower tropospheric zonal wind anomalies associated with the ENSO-related sea surface temperature anomalies (SSTA) are represented with more realism than those in the original version. From too weak, the standard deviation of SST over the eastern Pacific becomes too strong in the revised version due to the enhanced air-sea coupling strength and intraseasonal variability associated with ENSO. From the oceanic side, the stronger stratification and the shallower-than-observed thermocline over the eastern Pacific also contribute to the excessive ENSO. The impacts of the revised physical processes on the seasonal predictability are investigated in two sets of the hindcast experiment performed using the two versions of CGCMs. The prediction skill measured by anomaly correlation coefficients of monthly-mean SSTA shows that the new version has a higher skill over the tropical Pacific regions compared to the old version. The better atmospheric responses to the ENSO-related SSTA in the revised version lead to the basin-wide SSTA maintained and developed in a manner that is closer to observations. The symptom of an excessively strong ENSO of the new version in the free integration is not prominent in the hindcast experiment because the thermocline depth over the eastern Pacific is maintained as initialized over the arc of time of the hindcast (7 months).
The North-South asymmetry of solar activity: A signature of two coupled chaotic oscillators?
NASA Astrophysics Data System (ADS)
Donner, Reik V.
2010-05-01
The phase-coherent oscillatory dynamics on the 11-year frequency band (Schwabe cycle) is a common feature in all characteristic observables of solar activity. In this work, a wavelet-based framework [1,2] is applied for studying the mutual phase synchronicity of these oscillations. As a problem of specific scientific interest, the variability recorded on both solar hemispheres is systematically studied. It is demonstrated that time-varying phase shifts between the activity on Northern and Southern hemispheres provides a major contribution to the so-called North-South asymmetry (NSA). The presented results indicate that the NSA observations are consistent with the assumption of a different long-term phase diffusion of two weekly chaotic coupled oscillators, which evolve coherently in time. The obtained quantitative results on the variability of interhemispheric phase shifts are critically compared with the outcome of other studies using complementary methods of time series analysis [3]. The statistical reliability and implications of the derived long-term phase shift variability result are discussed. By using sophisticated methods for time series continuation and extrapolation [4], the recently hypothesised relationship between strong phase asynchrony of hemispheric variability and the occurrence of great minima of solar activity [5] is critically reexamined. References: [1] R. Donner, M. Thiel, A&A 475, L33-L36 (2007) [2] R. Donner, in: Nonlinear Time Series Analysis in the Geosciences (ed. by R.V. Donner and S.M. Barbosa), Springer, Berlin, 2008, pp. 355-386 [3] N.V. Zolotova, D.I. Ponyavin, N. Marwan, J. Kurths, A&A 503, 197-201 (2009) [4] C. Komalapriya, M. Thiel, M.C. Romano, N. Marwan, U. Schwarz, J. Kurths, Phys. Rev. E 78, 066217 (2008) [5] N.V. Zolotova, D.I. Ponyavin, A&A 470, L17-L20 (2007)
The Madden-Julian oscillation in ECHAM4 coupled and uncoupled general circulation models
Sperber, Kenneth R.; Gualdi, Silvio; Legutke, Stephanie; ...
2005-06-29
The Madden-Julian oscillation (MJO) dominates tropical variability on timescales of 30–70 days. During the boreal winter/spring, it is manifested as an eastward propagating disturbance, with a strong convective signature over the eastern hemisphere. The space–time structure of the MJO is analyzed using simulations with the ECHAM4 atmospheric general circulation model run with observed monthly mean sea-surface temperatures (SSTs), and coupled to three different ocean models. The coherence of the eastward propagation of MJO convection is sensitive to the ocean model to which ECHAM4 is coupled. For ECHAM4/OPYC and ECHO-G, models for which ~100 years of daily data is available, Montemore » Carlo sampling indicates that their metrics of eastward propagation are different at the 1% significance level. The flux-adjusted coupled simulations, ECHAM4/OPYC and ECHO-G, maintain a more realistic mean-state, and have a more realistic MJO simulation than the nonadjusted scale interaction experiment (SINTEX) coupled runs. The SINTEX model exhibits a cold bias in Indian Ocean and tropical West Pacific Ocean sea-surface temperature of ~0.5°C. This cold bias affects the distribution of time-mean convection over the tropical eastern hemisphere. Furthermore, the eastward propagation of MJO convection in this model is not as coherent as in the two models that used flux adjustment or when compared to an integration of ECHAM4 with prescribed observed SST. This result suggests that simulating a realistic basic state is at least as important as air–sea interaction for organizing the MJO. While all of the coupled models simulate the warm (cold) SST anomalies that precede (succeed) the MJO convection, the interaction of the components of the net surface heat flux that lead to these anomalies are different over the Indian Ocean. The ECHAM4/OPYC model in which the atmospheric model is run at a horizontal resolution of T42, has eastward propagating zonal wind anomalies and latent heat
The Madden-Julian Oscillation in ECHAM4 Coupled and Uncoupled GCMs
Sperber, K R; Gualdi, S; Legutke, S; Gayler, V
2004-10-13
The Madden-Julian Oscillation (MJO) dominates tropical variability on timescales of 30-70 days. During the boreal winter/spring it is manifested as an eastward propagating disturbance, with a strong convective signature over the eastern hemisphere. The space-time structure of the MJO is analyzed using simulations with the ECHAM4 atmospheric general circulation model run with observed monthly mean sea-surface temperatures, and coupled to three different ocean models. The coherence of the eastward propagation of MJO convection is sensitive to the ocean model to which ECHAM4 is coupled. For ECHAM4/OPYC and ECHO-G, models for which {approx}100 years of daily data is available, Monte Carlo sampling indicates that their metrics of eastward propagation are different at the 1% significance level. The flux-adjusted coupled simulations, ECHAM4/OPYC and ECHO-G, maintain a more realistic mean-state, and have a more realistic MJO simulation than the non-adjusted SINTEX coupled runs. The SINTEX model exhibits a cold bias in Indian Ocean and tropical West Pacific Ocean sea-surface temperature of {approx}0.5 C. This cold bias affects the distribution of time-mean convection over the tropical Eastern Hemisphere. Furthermore, the eastward propagation of MJO convection in this model is not as coherent as in the two models that used flux adjustment or compared to an integration of ECHAM4 with prescribed observed SST. This result suggests that simulating a realistic basic state is at least as important as air-sea interaction for organizing the MJO. While all of the coupled models simulate the warm (cold) SST anomalies that precede (succeed) the MJO convection, the interaction of the components of the net surface heat flux that lead to these anomalies are different over the Indian Ocean. The ECHAM4/OPYC model, in which the atmospheric model is run at a horizontal resolution of T42, has eastward propagating zonal wind anomalies and latent heat flux anomalies. However, the integrations
NASA Astrophysics Data System (ADS)
Stankovski, Tomislav; Petkoski, Spase; Raeder, Johan; Smith, Andrew F.; McClintock, Peter V. E.; Stefanovska, Aneta
2016-05-01
The precise mechanisms underlying general anaesthesia pose important and still open questions. To address them, we have studied anaesthesia induced by the widely used (intravenous) propofol and (inhalational) sevoflurane anaesthetics, computing cross-frequency coupling functions between neuronal, cardiac and respiratory oscillations in order to determine their mutual interactions. The phase domain coupling function reveals the form of the function defining the mechanism of an interaction, as well as its coupling strength. Using a method based on dynamical Bayesian inference, we have thus identified and analysed the coupling functions for six relationships. By quantitative assessment of the forms and strengths of the couplings, we have revealed how these relationships are altered by anaesthesia, also showing that some of them are differently affected by propofol and sevoflurane. These findings, together with the novel coupling function analysis, offer a new direction in the assessment of general anaesthesia and neurophysiological interactions, in general.
Petkoski, Spase; Raeder, Johan; Smith, Andrew F.; McClintock, Peter V. E.; Stefanovska, Aneta
2016-01-01
The precise mechanisms underlying general anaesthesia pose important and still open questions. To address them, we have studied anaesthesia induced by the widely used (intravenous) propofol and (inhalational) sevoflurane anaesthetics, computing cross-frequency coupling functions between neuronal, cardiac and respiratory oscillations in order to determine their mutual interactions. The phase domain coupling function reveals the form of the function defining the mechanism of an interaction, as well as its coupling strength. Using a method based on dynamical Bayesian inference, we have thus identified and analysed the coupling functions for six relationships. By quantitative assessment of the forms and strengths of the couplings, we have revealed how these relationships are altered by anaesthesia, also showing that some of them are differently affected by propofol and sevoflurane. These findings, together with the novel coupling function analysis, offer a new direction in the assessment of general anaesthesia and neurophysiological interactions, in general. PMID:27045000
A 10 GHz Y-Ba-Cu-O/GaAs hybrid oscillator proximity coupled to a circular microstrip patch antenna
NASA Technical Reports Server (NTRS)
Rohrer, Norman J.; Richard, M. A.; Valco, George J.; Bhasin, Kul B.
1993-01-01
A 10 GHz hybrid Y-Ba-Cu-O / GaAs microwave oscillator proximity coupled to a circular microstrip antenna was designed, fabricated and characterized. The oscillator was a reflection mode type using a GaAs MESFET as the active element. The feedline, transmission lines, RF chokes, and bias lines were all fabricated from YBa2Cu3O(7-x) superconducting thin films on a 1 cm x 1 cm lanthanum aluminate substrate. The output feedline of the oscillator was wire bonded to a superconducting feedline on a second 1 cm x 1 cm lanthanum aluminate substrate, which was in turn proximity coupled to a circular microstrip patch antenna. Antenna patterns from this active patch antenna and the performance of the oscillator measured at 77 K are reported. The oscillator had a maximum output power of 11.5 dBm at 77 K, which corresponded to an efficiency of 10 percent. In addition, the efficiency of the microstrip patch antenna together with its high temperature superconducting feedline was measured from 85 K to 30 K and was found to be 71 percent at 77 4 increasing to a maximum of 87.4 percent at 30 K.
NASA Astrophysics Data System (ADS)
Chakrabarti, R.; Jenisha, B. Virgin
2015-10-01
We study the evolution of bipartite entangled quasi-Bell states in a strongly coupled qubit-oscillator system in the presence of a static bias, and extend it to the ultra-strong coupling regime. Using the adiabatic approximation the reduced density matrix of the qubit is obtained for the strong coupling domain in closed form that involves linear combinations of the Jacobi theta functions. The reduced density matrix of the oscillator yields the phase space Husimi Q-distribution. In the strong coupling regime the Q-function evolves to uniformly separated macroscopically distinct Gaussian peaks representing 'kitten' states at certain specified times that depend on multiple time scales present in the interacting system. For the ultra-strong coupling realm the delocalization in the phase space of the oscillator is studied by using the Wehrl entropy and the complexity of the quantum state. For a small phase space amplitude the entangled quasi-Bell state develops, during its time evolution, squeezing property and nonclassicality of the photon statistics which are measured by the quadrature variance and the Mandel parameter, respectively.
Generation of mechanical oscillation applicable to vibratory rate gyroscopes
NASA Technical Reports Server (NTRS)
Lemkin, Mark A. (Inventor); Juneau, Thor N. (Inventor); Clark, William A. (Inventor); Roessig, Allen W. (Inventor)
2001-01-01
To achieve a drive-axis oscillation with improved frequency and amplitude stability, additional feedback loops are used to adjust force-feedback loop parameters. An amplitude-control loop measures oscillation amplitude, compares this value to the desired level, and adjusts damping of the mechanical sense-element to grow or shrink oscillation amplitude as appropriate. A frequency-tuning loop measures the oscillation frequency, compares this value with a highly stable reference, and adjusts the gain in the force-feedback loop to keep the drive-axis oscillation frequency at the reference value. The combined topology simultaneously controls both amplitude and frequency. Advantages of the combined topology include improved stability, fast oscillation start-up, low power consumption, and excellent shock rejection.
Memcapacitor model and its application in chaotic oscillator with memristor
NASA Astrophysics Data System (ADS)
Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching
2017-01-01
Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.
Memcapacitor model and its application in chaotic oscillator with memristor.
Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching
2017-01-01
Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.
Finger, Holger; König, Peter
2013-01-01
Synchronization has been suggested as a mechanism of binding distributed feature representations facilitating segmentation of visual stimuli. Here we investigate this concept based on unsupervised learning using natural visual stimuli. We simulate dual-variable neural oscillators with separate activation and phase variables. The binding of a set of neurons is coded by synchronized phase variables. The network of tangential synchronizing connections learned from the induced activations exhibits small-world properties and allows binding even over larger distances. We evaluate the resulting dynamic phase maps using segmentation masks labeled by human experts. Our simulation results show a continuously increasing phase synchrony between neurons within the labeled segmentation masks. The evaluation of the network dynamics shows that the synchrony between network nodes establishes a relational coding of the natural image inputs. This demonstrates that the concept of binding by synchrony is applicable in the context of unsupervised learning using natural visual stimuli.
Finger, Holger; König, Peter
2014-01-01
Synchronization has been suggested as a mechanism of binding distributed feature representations facilitating segmentation of visual stimuli. Here we investigate this concept based on unsupervised learning using natural visual stimuli. We simulate dual-variable neural oscillators with separate activation and phase variables. The binding of a set of neurons is coded by synchronized phase variables. The network of tangential synchronizing connections learned from the induced activations exhibits small-world properties and allows binding even over larger distances. We evaluate the resulting dynamic phase maps using segmentation masks labeled by human experts. Our simulation results show a continuously increasing phase synchrony between neurons within the labeled segmentation masks. The evaluation of the network dynamics shows that the synchrony between network nodes establishes a relational coding of the natural image inputs. This demonstrates that the concept of binding by synchrony is applicable in the context of unsupervised learning using natural visual stimuli. PMID:24478685
Traub, Roger D; Middleton, Steven J; Knöpfel, Thomas; Whittington, Miles A
2009-01-01
Very fast oscillations (VFO, >75 Hz) occur transiently in vivo, in the cerebellum of mice genetically modified to model Angelman syndrome, and in a mouse model of fetal alcohol syndrome. We recently reported VFO in slices of mouse cerebellar cortex (Crus I and II of ansiform and paramedian lobules), either in association with gamma oscillations (~40 Hz, evoked by nicotine), or in isolation (evoked by nicotine in combination with GABAA receptor blockade). The experimental data suggest a role for electrical coupling between Purkinje cells (blockade of VFO by drugs reducing gap junction conductance, and spikelets in some Purkinje cells); and the data suggest the specific involvement of Purkinje cell axons (because of field oscillation maxima in the granular layer). We show here that a detailed network model (1,000 multicompartment Purkinje cells) replicates the experimental data, when gap junctions are located on the proximal axons of Purkinje cells, provided sufficient spontaneous firing is present. Unlike other VFO models, most somatic spikelets do not correspond to axonal spikes in the parent axon, but reflect spikes in electrically coupled axons. The model predicts gating of VFO frequency by gNa inactivation, and experiments prolonging this inactivation time constant, with β-pompilidotoxin, are consistent with this prediction. The model also predicts that cerebellar VFO can be explained as an electrically coupled system of axons which are not intrinsic oscillators: the electrically uncoupled cells do not individually oscillate (in the model), and axonal firing rates are much lower in the uncoupled state than in the coupled state. PMID:18973579
Field Studies of Raindrop Oscillations with Applications to Radar Meteorology.
NASA Astrophysics Data System (ADS)
Tokay, Ali
1993-01-01
The characteristics and causes of raindrop oscillations were studied from two field experiments in Hawaiian and Illinois showers. The former experiment (HaRP) focused on the onset of raindrop oscillations as well as oscillations frequencies of small raindrops, whereas the latter experiment (ISWS) had a broader purpose to investigate the oscillation characteristics of moderate-to-large size raindrops including amplitudes as well as frequencies, and oscillation causes. Raindrop oscillations were found to start at a diameter of d = 1.0 to 1.1 mm in both HaRP and ISWS experiments, consistent with 1991 laboratory observations of Beard, Kubesh and Ochs and with the expected onset of eddy shedding. Most of the oscillation frequencies (>95%) were near the fundamental harmonic (f_2) with only a few observed near the first harmonic (f _3) in both experiments. The oscillation frequencies around the fundamental harmonic showed a size dependency that crossed the theoretical value for f _2 at about d = 1.5 to 1.6 mm. The oscillation amplitude measurements determined from the vertical extent of the dash streaks showed good agreement with the 1988 data of Sterlyadkin, whereas the oscillation amplitudes estimated from the distortion indicated somewhat larger values for d > 2mm. Eddy shedding was found to be the most likely cause of small raindrop oscillations because of the onset oscillations near 1.0 mm and weak forcing by drop collisions, turbulence, and wind shear. The influence of raindrop oscillations on dual -polarization radar parameters was investigated for the observed and theoretical size distributions using axis ratios based on four different sets of calculations and measurements. Differential reflectivity (Z_ {rm DR}) decreased by as much as 0.74 dB from its value for non-oscillating raindrops. Similar change caused by raindrop oscillations were also found for the other dual-polarization parameters, such as the circular and linear depolarization ratios (CDR, LDR
NASA Astrophysics Data System (ADS)
Mizrahi, A.; Locatelli, N.; Grollier, J.; Querlioz, D.
2016-08-01
Superparamagnetic tunnel junctions are nanostructures that auto-oscillate stochastically under the effect of thermal noise. Recent works showed that despite their stochasticity, such junctions possess a capability to synchronize to subthreshold voltage drives, in a way that can be enhanced or controlled by adding noise. In this work, we investigate a system composed of two electrically coupled junctions, connected in series to a periodic voltage source. We make use of numerical simulations and of an analytical model to demonstrate that both junctions can be phase locked to the drive, in phase or in antiphase. This synchronization phenomenon can be controlled by both thermal and electrical noises, although the two types of noises induce qualitatively different behaviors. Namely, thermal noise can stabilize a regime where one junction is phase locked to the drive voltage while the other is blocked in one state; on the contrary, electrical noise causes the junctions to have highly correlated behaviors and thus cannot induce the latter. These results open the way for the design of superparamagnetic tunnel junctions that can perform computation through synchronization, and which harvest the largest part of their energy consumption from thermal noise.
NASA Technical Reports Server (NTRS)
Smith, John W.; Montgomery, Terry
1996-01-01
During rapid rolling maneuvers, the F-16 XL aircraft exhibits a 2.5 Hz lightly damped roll oscillation, perceived and described as 'roll ratcheting.' This phenomenon is common with fly-by-wire control systems, particularly when primary control is derived through a pedestal-mounted side-arm controller. Analytical studies have been conducted to model the nature of the integrated control characteristics. The analytical results complement the flight observations. A three-degree-of-freedom linearized set of aerodynamic matrices was assembled to simulate the aircraft plant. The lateral-directional control system was modeled as a linear system. A combination of two second-order transfer functions was derived to couple the lateral acceleration feed through effect of the operator's arm and controller to the roll stick force input. From the combined systems, open-loop frequency responses and a time history were derived, describing and predicting an analogous in-flight situation. This report describes the primary control, aircraft angular rate, and position time responses of the F-16 XL-2 aircraft during subsonic and high-dynamic-pressure rolling maneuvers. The analytical description of the pilot's arm and controller can be applied to other aircraft or simulations to assess roll ratcheting susceptibility.
NASA Astrophysics Data System (ADS)
Zhang, Kaichun; Wu, Zhenhua; Liu, Shenggang
2009-04-01
An extended interaction oscillator (EIO) generating Terahertz (THz) wave is presented by theoretical study and simulation study in this paper. A rectangular reentrant coupled-cavity is proposed as its slow-wave structure (SWS). The equivalent circuit method (ECM) is adopted to calculate the dispersion relation and circuit parameters of the SWS. The beam-wave interaction of the EIO is theoretically studied in detail, including the beam loading conductance, the conversion efficiency and the optimal gap number. The dependence is investigated of the beam loading conductance and the conversion efficiency on the gap number and the beam velocity. Some properties of the cold circuit are simulated by CST software, including the dispersion relation and the filed distribution. These simulation results agree well with those of ECM. The operating mode of EIO is chosen very close to the β L = 2π point with corresponding frequency about 0.225 THz, when the beam voltage is 13 kV, the current 105 mA, the cavity was designed with the period 0.3 mm, 14-gap, the height 1.6 mm and the width 0.76 mm . Simulation results of beam-wave interaction with PIC codes show that the excited frequency is 0.225 THz and peak output power 44 W.
Synchronization in Dynamical Networks of Locally Coupled Self-Propelled Oscillators
NASA Astrophysics Data System (ADS)
Levis, Demian; Pagonabarraga, Ignacio; Díaz-Guilera, Albert
2017-01-01
The emergent cooperative behavior of mobile physical entities exchanging information with their neighborhood has become an important problem across disciplines, thus requiring a general framework to describe such a variety of situations. We introduce a generic model to tackle this problem by considering the synchronization in time-evolving networks generated by the stochastic motion of self-propelled physical interacting units. This framework generalizes previous approaches and brings a unified picture to understand the role played by the network topology, the motion of the agents, and their mutual interaction. This allows us to identify different dynamic regimes where synchronization can be understood from theoretical considerations. While for noninteracting particles, self-propulsion accelerates synchronization, the presence of excluded volume interactions gives rise to a richer scenario, where self-propulsion has a nonmonotonic impact on synchronization. We show that the synchronization of locally coupled mobile oscillators generically proceeds through coarsening, verifying the dynamic scaling hypothesis, with the same scaling laws as the 2D X Y model following a quench. Our results shed light into the generic nature of synchronization in time-dependent networks, providing an efficient way to understand more specific situations involving interacting mobile agents.
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; ...
2016-02-27
Artificial perceptions of light called phosphenes were motivated by earlier studies. We analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolutionmore » and stability of planar fronts. Moreover, our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.« less
Tunable Coupling to a Mechanical Oscillator Circuit Using a Coherent Feedback Network
NASA Astrophysics Data System (ADS)
Kerckhoff, Joseph; Andrews, Reed W.; Ku, H. S.; Kindel, William F.; Cicak, Katarina; Simmonds, Raymond W.; Lehnert, K. W.
2013-04-01
We demonstrate a fully cryogenic microwave feedback network composed of modular superconducting devices connected by transmission lines and designed to control a mechanical oscillator that is coupled to one of the devices. The network features an electromechanical device and a tunable controller that coherently receives, processes, and feeds back continuous microwave signals that modify the dynamics and readout of the mechanical state. While previous electromechanical systems represent some compromise between efficient control and efficient readout of the mechanical state, as set by the electromagnetic decay rate, the tunable controller produces a closed-loop network that can be dynamically and continuously tuned between both extremes much faster than the mechanical response time. We demonstrate that the microwave decay rate may be modulated by at least a factor of 10 at a rate greater than 104 times the mechanical response rate. The system is easy to build and suggests that some useful functions may arise most naturally at the network level of modular, quantum electromagnetic devices.
Garcia-Morales, Vladimir Pellicer, Julio; Manzanares, Jose A.
2008-08-15
We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization.
Lyo, Sungkwun Kenneth; Pan, Wei; Reno, John Louis; Wendt, Joel Robert; Barton, Daniel Lee
2008-09-01
We have investigated the physics of Bloch oscillations (BO) of electrons, engineered in high mobility quantum wells patterned into lateral periodic arrays of nanostructures, i.e. two-dimensional (2D) quantum dot superlattices (QDSLs). A BO occurs when an electron moves out of the Brillouin zone (BZ) in response to a DC electric field, passing back into the BZ on the opposite side. This results in quantum oscillations of the electron--i.e., a high frequency AC current in response to a DC voltage. Thus, engineering a BO will yield continuously electrically tunable high-frequency sources (and detectors) for sensor applications, and be a physics tour-de-force. More than a decade ago, Bloch oscillation (BO) was observed in a quantum well superlattice (QWSL) in short-pulse optical experiments. However, its potential as electrically biased high frequency source and detector so far has not been realized. This is partially due to fast damping of BO in QWSLs. In this project, we have investigated the possibility of improving the stability of BO by fabricating lateral superlattices of periodic coupled nanostructures, such as metal grid, quantum (anti)dots arrays, in high quality GaAs/Al{sub x}Ga{sub 1-x}As heterostructures. In these nanostructures, the lateral quantum confinement has been shown theoretically to suppress the optical-phonon scattering, believed to be the main mechanism for fast damping of BO in QWSLs. Over the last three years, we have made great progress toward demonstrating Bloch oscillations in QDSLs. In the first two years of this project, we studied the negative differential conductance and the Bloch radiation induced edge-magnetoplasmon resonance. Recently, in collaboration with Prof. Kono's group at Rice University, we investigated the time-domain THz magneto-spectroscopy measurements in QDSLs and two-dimensional electron systems. A surprising DC electrical field induced THz phase flip was observed. More measurements are planned to investigate this
Ih Tunes Theta/Gamma Oscillations and Cross-Frequency Coupling In an In Silico CA3 Model
Neymotin, Samuel A.; Hilscher, Markus M.; Moulin, Thiago C.; Skolnick, Yosef; Lazarewicz, Maciej T.; Lytton, William W.
2013-01-01
channels are uniquely positioned to act as neuromodulatory control points for tuning hippocampal theta (4–12 Hz) and gamma (25 Hz) oscillations, oscillations which are thought to have importance for organization of information flow. contributes to neuronal membrane resonance and resting membrane potential, and is modulated by second messengers. We investigated oscillatory control using a multiscale computer model of hippocampal CA3, where each cell class (pyramidal, basket, and oriens-lacunosum moleculare cells), contained type-appropriate isoforms of . Our model demonstrated that modulation of pyramidal and basket allows tuning theta and gamma oscillation frequency and amplitude. Pyramidal also controlled cross-frequency coupling (CFC) and allowed shifting gamma generation towards particular phases of the theta cycle, effected via 's ability to set pyramidal excitability. Our model predicts that in vivo neuromodulatory control of allows flexibly controlling CFC and the timing of gamma discharges at particular theta phases. PMID:24204609
Ih tunes theta/gamma oscillations and cross-frequency coupling in an in silico CA3 model.
Neymotin, Samuel A; Hilscher, Markus M; Moulin, Thiago C; Skolnick, Yosef; Lazarewicz, Maciej T; Lytton, William W
2013-01-01
Ih channels are uniquely positioned to act as neuromodulatory control points for tuning hippocampal theta (4-12 Hz) and gamma (25 Hz) oscillations, oscillations which are thought to have importance for organization of information flow. contributes to neuronal membrane resonance and resting membrane potential, and is modulated by second messengers. We investigated oscillatory control using a multiscale computer model of hippocampal CA3, where each cell class (pyramidal, basket, and oriens-lacunosum moleculare cells), contained type-appropriate isoforms of . Our model demonstrated that modulation of pyramidal and basket allows tuning theta and gamma oscillation frequency and amplitude. Pyramidal also controlled cross-frequency coupling (CFC) and allowed shifting gamma generation towards particular phases of the theta cycle, effected via 's ability to set pyramidal excitability. Our model predicts that in vivo neuromodulatory control of allows flexibly controlling CFC and the timing of gamma discharges at particular theta phases.
Chen, Tao; Jiang, Peipei; Yang, Dingzhong; Hu, Chengzhi; Wu, Bo; Shen, Yonghang
2013-09-01
We have experimentally demonstrated a periodically poled magnesium-oxide-doped lithium niobate (PPMgLN)-based, fiber-laser-pumped optical parametric oscillator (OPO) generating idler wavelength of 3.82 μm. The pump fiber laser was constructed with a linearly polarized, semi-fiber-coupled acousto-optic Q-switched fiber oscillator and a polarization-maintaining fiber amplifier with pulse duration of 190 ns at the highest output power. The OPO was specifically configured in single-pass, singly resonant linear cavity structure to avoid the damage risk of the pump fiber laser, which is always a serious issue in the fiber-laser-pumped, double-pass, singly oscillating structured OPOs. Under the highest pump power of 25 W, an idler average output power of 3.27 W with one-hour peak-to-peak instability of 5.2% was obtained. The measured M2 factors were 1.98 and 1.44 for horizontal and vertical axis, respectively. The high power stability and good beam quality demonstrated the suitability of such technology for practical application.
NASA Astrophysics Data System (ADS)
Pascoe, D. J.; Anfinogentov, S.; Nisticò, G.; Goddard, C. R.; Nakariakov, V. M.
2017-04-01
Context. The strong damping of kink oscillations of coronal loops can be explained by mode coupling. The damping envelope depends on the transverse density profile of the loop. Observational measurements of the damping envelope have been used to determine the transverse loop structure which is important for understanding other physical processes such as heating. Aims: The general damping envelope describing the mode coupling of kink waves consists of a Gaussian damping regime followed by an exponential damping regime. Recent observational detection of these damping regimes has been employed as a seismological tool. We extend the description of the damping behaviour to account for additional physical effects, namely a time-dependent period of oscillation, the presence of additional longitudinal harmonics, and the decayless regime of standing kink oscillations. Methods: We examine four examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We use forward modelling of the loop position and investigate the dependence on the model parameters using Bayesian inference and Markov chain Monte Carlo (MCMC) sampling. Results: Our improvements to the physical model combined with the use of Bayesian inference and MCMC produce improved estimates of model parameters and their uncertainties. Calculation of the Bayes factor also allows us to compare the suitability of different physical models. We also use a new method based on spline interpolation of the zeroes of the oscillation to accurately describe the background trend of the oscillating loop. Conclusions: This powerful and robust method allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects.
Wulff, Peer; Ponomarenko, Alexey A; Bartos, Marlene; Korotkova, Tatiana M; Fuchs, Elke C; Bähner, Florian; Both, Martin; Tort, Adriano B L; Kopell, Nancy J; Wisden, William; Monyer, Hannah
2009-03-03
Hippocampal theta (5-10 Hz) and gamma (35-85 Hz) oscillations depend on an inhibitory network of GABAergic interneurons. However, the lack of methods for direct and cell-type-specific interference with inhibition has prevented better insights that help link synaptic and cellular properties with network function. Here, we generated genetically modified mice (PV-Deltagamma(2)) in which synaptic inhibition was ablated in parvalbumin-positive (PV+) interneurons. Hippocampal local field potential and unit recordings in the CA1 area of freely behaving mice revealed that theta rhythm was strongly reduced in these mice. The characteristic coupling of theta and gamma oscillations was strongly altered in PV-Deltagamma(2) mice more than could be accounted for by the reduction in theta rhythm only. Surprisingly, gamma oscillations were not altered. These data indicate that synaptic inhibition onto PV+ interneurons is indispensable for theta- and its coupling to gamma oscillations but not for rhythmic gamma-activity in the hippocampus. Similar alterations in rhythmic activity were obtained in a computational hippocampal network model mimicking the genetic modification, suggesting that intrahippocampal networks might contribute to these effects.
Hameed, S.; Meinster, A. ); Sperber, K.R. )
1993-03-01
The Oregon State University coupled upper ocean-atmosphere GCM has been shown to qualitatively simulate the Southern Oscillation. A composite analysis of the warm and cold events simulated in this 23-year integration has been performed. During the low phase of the Southern Oscillation, when warm anomalies occur in the eastern Pacific, the model simulates for the Atlantic region during March-May (1) a deficit of precipitation over the tropical South American continent, (2) Caribbean and Gulf of Mexico sea level pressure and sea surface temperature are in phase with the eastern Pacific anomalies, while those east of the Nordeste region are out of phase, and (3) northeast trade winds are anomalously weak and southwest trade winds are anomalously strong (as inferred from surface current anomalies). The anomalies in the oceanic processes are induced by perturbations in the atmospheric circulation over the Atlantic and are coupled to changes in the Walker circulation. During the high phase of the simulated Southern Oscillation, conditions in the atmosphere and ocean are essentially the reverse of the low phase. The model produces a response in the South American region during the opposing phases of the Southern Oscillation that is in general agreement with observations. The interannual variation of Nordeste rainfall is shown to be dominated by a few band-limited frequencies. These frequencies are found in the SST series of those regions of the Atlantic and Pacific oceans where strong correlations with Nordeste precipitation exist.
Fukunaga, Tomohiro; Imasaka, Tomoaki; Ito, Akira; Sugitani, Yoshiki; Konishi, Keiji; Hara, Naoyuki
2016-02-01
This paper investigates dynamics of a management system for controlling a pair of energy storages. The system involves the following two characteristics: each storage behaves in a manner that reduces the number of charge noncharge cycles and begins to be charged when the price of power is lower than a particular price threshold. The price is proportional to the past total power flow from a power grid to all storages. A peak of the total power flow occurs when these storages are charged simultaneously. From the viewpoint of nonlinear dynamics, the energy storages can be considered as relaxation oscillators coupled by a delay connection. Our analytical results suggest that the peak can be reduced by inducing an antiphase synchronization in coupled oscillators. We confirm these analytical results through numerical simulations. In addition, we numerically investigate the dynamical behavior in 10 storages and find that time delay in the connection is important in reducing the peak.
Modulation of the Convectively Coupled Kelvin Waves by the Madden-Julian Oscillation
NASA Astrophysics Data System (ADS)
Guo, Y.; Jiang, X.; Waliser, D. E.
2013-12-01
As one of the major tropical wave modes, the convectively-coupled equatorial Kelvin wave (CCKW) plays a critical role in tropical climate / weather variability. CCKW activity exhibits strong variation on both seasonal and intraseasonal time scales. In this study, evidence of the strong modulation of the CCKW activity by the Madden-Julian Oscillation (MJO) will be presented, with a particular focus over South America and tropical Atlantic region. The primary modulation of CCKWs over this region, as noted in anomalous fields of rainfall as well as vertical profiles of wind, moisture and temperature, is found to be a modulation of wave activity - namely amplitude, with secondary effects on vertical structure, and very little impact on wavenumber. CCKW activity is enhanced during MJO phases 8, 1, and 2, and damped during MJO phases 4, 5, and 6. Further analyses reveal that the strong modulation of the MJO on the CCKW activity could be largely through two factors, namely, the vertical zonal wind shear and the lower-middle troposphere specific humidity. The CCKW activity tends to be enhanced during MJO phases when the westward vertical wind shear and positive lower to mid-troposphere moisture anomalies are evident, and vice versa. These two physical processes associated with the MJO are found to have positively (negatively) reinforcing influences in the CCKW activity in phase 1 (4, and 5), while counteracting influences in phases 2, 3, 6, 7, and 8, leading to the observed MJO cycle of the CCKW activity anomalies in the study region. The results presented in this study may have important implications for extended-range prediction of tropical wave activity, and possibly initiation of the MJO further downstream in the Indian Ocean.
Parsons, Sean P; Huizinga, Jan D
2016-01-01
Pacemaker activities generated by networks of interstitial cells of Cajal (ICC), in conjunction with the enteric nervous system, orchestrate most motor patterns in the gastrointestinal tract. It was our objective to understand the role of network features of ICC associated with the myenteric plexus (ICC-MP) in the shaping of motor patterns of the small intestine. To that end, a model of weakly coupled oscillators (oscillators influence each other's phase but not amplitude) was created with most parameters derived from experimental data. The ICC network is a uniform two dimensional network coupled by gap junctions. All ICC generate pacemaker (slow wave) activity with a frequency gradient in mice from 50/min at the proximal end of the intestine to 40/min at the distal end. Key features of motor patterns, directly related to the underlying pacemaker activity, are frequency steps and dislocations. These were accurately mimicked by reduction of coupling strength at a point in the chain of oscillators. When coupling strength was expressed as a product of gap junction density and conductance, and gap junction density was varied randomly along the chain (i.e., spatial noise) with a long-tailed distribution, plateau steps occurred at pointsof low density. As gap junction conductance was decreased, the number of plateaus increased, mimicking the effect of the gap junction inhibitor carbenoxolone. When spatial noise was added to the natural interval gradient, as gap junction conductance decreased, the number of plateaus increased as before but in addition the phase waves frequently changed direction of apparent propagation, again mimicking the effect of carbenoxolone. In summary, key features of the motor patterns that are governed by pacemaker activity may be a direct consequence of biological noise, specifically spatial noise in gap junction coupling and pacemaker frequency.
Parsons, Sean P; Huizinga, Jan D
2015-02-15
Waves of contraction in the small intestine correlate with slow waves generated by the myenteric network of interstitial cells of Cajal. Coupled oscillator theory has been used to explain steplike gradients in the frequency (frequency plateaux) of contraction waves along the length of the small intestine. Inhibition of gap junction coupling between oscillators should lead to predictable effects on these plateaux and the wave dislocation (wave drop) phenomena associated with their boundaries. It is these predictions that we wished to test. We used a novel multicamera diameter-mapping system to measure contraction along 25- to 30-cm lengths of murine small intestine. There were typically two to three plateaux per length of intestine. Dislocations could be limited to the wavefronts immediately about the terminated wave, giving the appearance of a three-pronged fork, i.e., a fork dislocation; additionally, localized decreases in velocity developed across a number of wavefronts, ending with the terminated wave, which could appear as a fork, i.e., slip dislocations. The gap junction inhibitor carbenoxolone increased the number of plateaux and dislocations and decreased contraction wave velocity. In some cases, the usual frequency gradient was reversed, with a plateau at a higher frequency than its proximal neighbor; thus fork dislocations were inverted, and the direction of propagation was reversed. Heptanol had no effect on the frequency or velocity of contractions but did reduce their amplitude. To understand intestinal motor patterns, the pacemaker network of the interstitial cells of Cajal is best evaluated as a system of coupled oscillators.
Dang, Christian K; Schindler, Markus; Chauvet, Eric; Gessner, Mark O
2009-01-01
Diel temperature oscillations are a nearly ubiquitous phenomenon, with amplitudes predicted to change along with mean temperatures under global-warming scenarios. Impact assessments of global warming have largely disregarded diel temperature oscillations, even though key processes in ecosystems, such as decomposition, may be affected. We tested the effect of a 5 degrees C temperature increase with and without diel oscillations on litter decomposition by fungal communities in stream microcosms. Five temperature regimes with identical thermal sums (degree days) were applied: constant 3 degrees and 8 degrees C; diel temperature oscillations of 5 degrees C around each mean; and oscillations of 9 degrees C around 8 degrees C. Temperature oscillations around 8 degrees C (warming scenario), but not 3 degrees C (ambient scenario), accelerated decomposition by 18% (5 degrees C oscillations) and 31% (9 degrees C oscillations), respectively, compared to the constant temperature regime at 8 degrees C. Community structure was not affected by oscillating temperatures, although the rise in mean temperature from 3 degrees to 8 degrees C consistently shifted the relative abundance of species. A simple model using temperature-growth responses of the dominant fungal decomposers accurately described the experimentally observed pattern, indicating that the effect of temperature oscillations on decomposition in our warming scenario was caused by strong curvilinear responses of species to warming at low temperature, particularly of the species becoming most abundant at 8 degrees C (Tetracladium marchalianum). These findings underscore the need to consider species-specific temperature characteristics in concert with changes in communities when assessing consequences of global warming on ecosystem processes.
NASA Astrophysics Data System (ADS)
Dong, Chunhua; Htay Oo, Thein; Fiore, Victor; Wang, Hailin
2013-03-01
Tensile stressed SiN nanostrings can feature a picogram effective mass and a mechanical Q-factor exceeding a million. These remarkable nanomechanical oscillators can be dispersively-coupled to an ultra-high finesse optical microresonator via its evanescent field. This composite optomechanical system can potentially lead to a cooperativity that far exceeds that of monolithic optomechanical resonators. Here, we report an experimental study coupling a SiN nanostring to evanescent fields of a whispering gallery mode (WGM) in a silica microsphere. The slight deformation of the microsphere enables us to use free-space optical excitation to probe the optomechanical coupling. The dispersive coupling between a nanostring and the evanescent field of a WGM is generally expected to lead to a red shift in the resonance frequency of the WGM. Our experiments, however, reveal a blue frequency shift of the WGM. Detailed experimental studies and possible physical mechanisms for the blue shift will be presented.
Multi-kW cw fiber oscillator pumped by wavelength stabilized fiber coupled diode lasers
NASA Astrophysics Data System (ADS)
Becker, Frank; Neumann, Benjamin; Winkelmann, Lutz; Belke, Steffen; Ruppik, Stefan; Hefter, Ulrich; Köhler, Bernd; Wolf, Paul; Biesenbach, Jens
2013-02-01
High power Yb doped fiber laser sources are beside CO2- and disk lasers one of the working horses of industrial laser applications. Due to their inherently given robustness, scalability and high efficiency, fiber laser sources are best suited to fulfill the requirements of modern industrial laser applications in terms of power and beam quality. Pumping Yb doped single-mode fiber lasers at 976nm is very efficient. Thus, high power levels can be realized avoiding limiting nonlinear effects like SRS. However the absorption band of Yb doped glass around 976nm is very narrow. Therefore, one has to consider the wavelength shift of the diode lasers used for pumping. The output spectrum of passively cooled diode lasers is mainly defined by the applied current and by the heat sink temperature. Furthermore the overall emission line width of a high power pump source is dominated by the large number of needed diode laser emitters, each producing an individual spectrum. Even though it is possible to operate multi-kW cw single-mode fiber lasers with free running diode laser pumps, wavelength stabilizing techniques for diode lasers (e.g. volume holographic gratings, VHG) can be utilized in future fiber laser sources to increase the output power level while keeping the energy consumption constant. To clarify the benefits of wavelength stabilized diode lasers with integrated VHG for wavelength locking the performance of a dual side pumped fiber oscillator is discussed in this article. For comparison, different pumping configurations consisting of stabilized and free-running diode lasers are presented.
Oscillation spectrum of a magnetized strongly coupled one-component plasma.
Ott, T; Kählert, H; Reynolds, A; Bonitz, M
2012-06-22
A first-principles study of the collective oscillation spectrum of a strongly correlated one-component plasma in a strong magnetic field is presented. The spectrum consists of six fundamental modes that are found to be in good agreement with results from the quasilocalized charge approximation. At high frequencies, additional modes are observed that include Bernstein-type oscillations and their transverse counterparts, which are of importance for the high-frequency optical and transport properties of these plasmas.
Application of Fibonacci oscillators in the Debye model
NASA Astrophysics Data System (ADS)
Marinho, André A. A.; Brito, F. A.; Chesman, C.
2014-12-01
In this paper we study the thermodynamics of a crystalline solid by applying q-deformed algebra of Fibonacci oscillators through the generalized Fibonacci sequence of two real and independent deformation parameters q1 and q2. We find a (q1, q2)-deformed Hamiltonian and consequently the q-deformed thermodynamic quantities. The results led us to interpret the deformation parameters acting as disturbance or impurities factors modifying the characteristics of a crystal structure. More specifically, we found the possibility of adjusting the Fibonacci oscillators to describe the change of thermal conductivity of a given element as one inserts impurites.
Witte, Herbert; Putsche, Peter; Hemmelmann, Claudia; Schelenz, Christoph; Leistritz, Lutz
2008-08-01
Low-frequency (0.5-2.5 Hz) and individually defined high-frequency (7-11 or 8-12 Hz; 11-15 or 14-18 Hz) oscillatory components of the electroencephalogram (EEG) burst activity derived from thiopental-induced burst-suppression patterns (BSP) were investigated in seven sedated patients (17-26 years old) with severe head injury. The predominant high-frequency burst oscillations (>7 Hz) were detected for each patient by means of time-variant amplitude spectrum analysis. Thereafter, the instantaneous envelope (IE) and the instantaneous frequency (IF) were computed for these low- and high-frequency bands to quantify amplitude-frequency dependencies (envelope-envelope, envelope-frequency, and frequency-frequency correlations). Time-variant phase-locking, phase synchronization, and quadratic phase couplings are associated with the observed amplitude-frequency characteristics. Additionally, these time-variant analyses were carried out for modeled burst patterns. Coupled Duffing oscillators were adapted to each EEG burst and by means of these models data-based burst simulations were generated. Results are: (1) strong envelope-envelope correlations (IE courses) can be demonstrated; (2) it can be shown that a rise of the IE is associated with an increase of the IF (only for the frequency bands 0.5-2.5 and 7-11 or 8-12 Hz); (3) the rise characteristics of all individually averaged envelope-frequency courses (IE-IF) are strongly correlated; (4) for the 7-11 or 8-12 Hz oscillation these associations are weaker and the variation between the time courses of the patients is higher; (5) for both frequency ranges a quantitative amplitude-frequency dependency can be shown because higher IE peak maxima are accompanied by stronger IF changes; (6) the time range of significant phase-locking within the 7-11 or 8-12 Hz frequency bands and of the strongest quadratic phase couplings (between 0.5-2.5 and 7-11 or 8-12 Hz) is between 0 and 1,000 ms; (7) all phase coupling characteristics of the
Krishnakumar, S; Gaudana, Sandeep B; Vinh, Nguyen X; Viswanathan, Ganesh A; Chetty, Madhu; Wangikar, Pramod P
2015-01-01
Unicellular diazotrophic cyanobacteria such as Cyanothece sp. ATCC 51142 (henceforth Cyanothece), temporally separate the oxygen sensitive nitrogen fixation from oxygen evolving photosynthesis not only under diurnal cycles (LD) but also in continuous light (LL). However, recent reports demonstrate that the oscillations in LL occur with a shorter cycle time of ~11 h. We find that indeed, majority of the genes oscillate in LL with this cycle time. Genes that are upregulated at a particular time of day under diurnal cycle also get upregulated at an equivalent metabolic phase under LL suggesting tight coupling of various cellular events with each other and with the cell's metabolic status. A number of metabolic processes get upregulated in a coordinated fashion during the respiratory phase under LL including glycogen degradation, glycolysis, oxidative pentose phosphate pathway, and tricarboxylic acid cycle. These precede nitrogen fixation apparently to ensure sufficient energy and anoxic environment needed for the nitrogenase enzyme. Photosynthetic phase sees upregulation of photosystem II, carbonate transport, carbon concentrating mechanism, RuBisCO, glycogen synthesis and light harvesting antenna pigment biosynthesis. In Synechococcus elongates PCC 7942, a non-nitrogen fixing cyanobacteria, expression of a relatively smaller fraction of genes oscillates under LL condition with the major periodicity being 24 h. In contrast, the entire cellular machinery of Cyanothece orchestrates coordinated oscillation in anticipation of the ensuing metabolic phase in both LD and LL. These results may have important implications in understanding the timing of various cellular events and in engineering cyanobacteria for biofuel production.
NASA Astrophysics Data System (ADS)
Ratas, Irmantas; Pyragas, Kestutis
2016-09-01
We analyze the dynamics of a large network of coupled quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rate and the mean membrane potential, which are exact in the infinite-size limit. The bifurcation analysis of the reduced equations reveals a rich scenario of asymptotic behavior, the most interesting of which is the macroscopic limit-cycle oscillations. It is shown that the finite width of synaptic pulses is a necessary condition for the existence of such oscillations. The robustness of the oscillations against aging damage, which transforms spiking neurons into nonspiking neurons, is analyzed. The validity of the reduced equations is confirmed by comparing their solutions with the solutions of microscopic equations for the finite-size networks.
Das, Saptarshi; Maharatna, Koushik
2013-12-01
In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators, which are coupled by time delays and gains. In this paper, we suitably modify the three state equations corresponding to the nonlinear cross-product of states, time delay coupling of the two oscillators and low-pass filtering, using the concept of fractional derivatives. Our results show that a wide variety of ECG like waveforms can be simulated from the proposed generalized models, characterizing heart conditions under different physiological conditions. Such generalization of the modelling of ECG waveforms may be useful to understand the physiological process behind ECG signal generation in normal and abnormal heart conditions. Along with the proposed FO models, an optimization based approach is also presented to estimate the VdP oscillator parameters for representing a realistic ECG like signal.
Ratas, Irmantas; Pyragas, Kestutis
2016-09-01
We analyze the dynamics of a large network of coupled quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rate and the mean membrane potential, which are exact in the infinite-size limit. The bifurcation analysis of the reduced equations reveals a rich scenario of asymptotic behavior, the most interesting of which is the macroscopic limit-cycle oscillations. It is shown that the finite width of synaptic pulses is a necessary condition for the existence of such oscillations. The robustness of the oscillations against aging damage, which transforms spiking neurons into nonspiking neurons, is analyzed. The validity of the reduced equations is confirmed by comparing their solutions with the solutions of microscopic equations for the finite-size networks.
NASA Astrophysics Data System (ADS)
Chicoli, Amanda; Paley, Derek A.
2016-11-01
Individuals in a group may obtain information from other group members about the environment, including the location of a food source or the presence of a predator. Here, we model how information spreads in a group using a susceptible-infected-removed epidemic model. We apply this model to a simulated shoal of fish using the motion dynamics of a coupled oscillator model, in order to test the biological hypothesis that polarized or aligned shoaling leads to faster and more accurate escape responses. The contributions of this study are the (i) application of a probabilistic model of epidemics to the study of collective animal behavior; (ii) testing the biological hypothesis that group cohesion improves predator escape; (iii) quantification of the effect of social cues on startle propagation; and (iv) investigation of the variation in response based on network connectivity. We find that when perfectly aligned individuals in a group are startled, there is a rapid escape by individuals that directly detect the threat, as well as by individuals responding to their neighbors. However, individuals that are not startled do not head away from the threat. In startled groups that are randomly oriented, there is a rapid, accurate response by individuals that directly detect the threat, followed by less accurate responses by individuals responding to neighbor cues. Over the simulation duration, however, even unstartled individuals head away from the threat. This study illustrates a potential speed-accuracy trade-off in the startle response of animal groups, in agreement with several previous experimental studies. Additionally, the model can be applied to a variety of group decision-making processes, including those involving higher-dimensional motion.
NASA Astrophysics Data System (ADS)
Jenkins, Alejandro
2013-04-01
Physicists are very familiar with forced and parametric resonance, but usually not with self-oscillation, a property of certain dynamical systems that gives rise to a great variety of vibrations, both useful and destructive. In a self-oscillator, the driving force is controlled by the oscillation itself so that it acts in phase with the velocity, causing a negative damping that feeds energy into the vibration: no external rate needs to be adjusted to the resonant frequency. The famous collapse of the Tacoma Narrows bridge in 1940, often attributed by introductory physics texts to forced resonance, was actually a self-oscillation, as was the swaying of the London Millennium Footbridge in 2000. Clocks are self-oscillators, as are bowed and wind musical instruments. The heart is a “relaxation oscillator”, i.e., a non-sinusoidal self-oscillator whose period is determined by sudden, nonlinear switching at thresholds. We review the general criterion that determines whether a linear system can self-oscillate. We then describe the limiting cycles of the simplest nonlinear self-oscillators, as well as the ability of two or more coupled self-oscillators to become spontaneously synchronized (“entrained”). We characterize the operation of motors as self-oscillation and prove a theorem about their limit efficiency, of which Carnot’s theorem for heat engines appears as a special case. We briefly discuss how self-oscillation applies to servomechanisms, Cepheid variable stars, lasers, and the macroeconomic business cycle, among other applications. Our emphasis throughout is on the energetics of self-oscillation, often neglected by the literature on nonlinear dynamical systems.
Ku, Wai Lim; Girvan, Michelle; Ott, Edward
2015-12-15
In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is “extensive” in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.
NASA Astrophysics Data System (ADS)
English, L. Q.; Mertens, David; Abdoulkary, Saidou; Fritz, C. B.; Skowronski, K.; Kevrekidis, P. G.
2016-12-01
We derive the Kuramoto-Sakaguchi model from the basic circuit equations governing two coupled Wien-bridge oscillators. A Wien-bridge oscillator is a particular realization of a tunable autonomous oscillator that makes use of frequency filtering (via an R C bandpass filter) and positive feedback (via an operational amplifier). In the past few years, such oscillators have started to be utilized in synchronization studies. We first show that the Wien-bridge circuit equations can be cast in the form of a coupled pair of van der Pol equations. Subsequently, by applying the method of multiple time scales, we derive the differential equations that govern the slow evolution of the oscillator phases and amplitudes. These equations are directly reminiscent of the Kuramoto-Sakaguchi-type models for the study of synchronization. We analyze the resulting system in terms of the existence and stability of various coupled oscillator solutions and explain on that basis how their synchronization emerges. The phase-amplitude equations are also compared numerically to the original circuit equations and good agreement is found. Finally, we report on experimental measurements of two coupled Wien-bridge oscillators and relate the results to the theoretical predictions.
Quantum noise and squeezing in optical parametric oscillator with arbitrary output coupling
NASA Technical Reports Server (NTRS)
Prasad, Sudhakar
1993-01-01
The redistribution of intrinsic quantum noise in the quadratures of the field generated in a sub-threshold degenerate optical parametric oscillator exhibits interesting dependences on the individual output mirror transmittances, when they are included exactly. We present a physical picture of this problem, based on mirror boundary conditions, which is valid for arbitrary transmittances. Hence, our picture applies uniformly to all values of the cavity Q factor representing, in the opposite extremes, both perfect oscillator and amplifier configurations. Beginning with a classical second-harmonic pump, we shall generalize our analysis to the finite amplitude and phase fluctuations of the pump.
A defence-like reaction: an emergent property of a system of coupled non-linear oscillators.
Gebber, G L
2001-01-01
1. The present paper deals with the central mechanisms responsible for the defence-like differential pattern of spinal sympathetic outflow elicited by electrical activation of the midbrain periaqueductal grey (PAG) in urethane-anaesthetized, baroreceptor-denervated cats. The pattern is characterized by increases in the 10 Hz discharges of the inferior cardiac (CN) and renal (RN) sympathetic nerves and a decrease in 10 Hz activity of the vertebral sympathetic nerve (VN) that supplies vasoconstrictor outflow to the forelimb. 2. The model used to explain this pattern is based on the self-organizing properties of a system of coupled brainstem oscillators rather than the activation of point-to-point hard-wired connections leading to increases in sympathetic outflow to some targets and decreases to others. 3. The fact that VN 10 Hz activity was inhibited by PAG stimulus frequencies equal to or just above, but not just below, that of the free-running (control) rhythm argues against a 'hard-wired' model. 4. The evidence supporting the hypothesis that the defence-like pattern is an emergent property of a system of coupled oscillators includes changes in the phase lag of VN 10 Hz activity relative to that in the CN, temporal correlation of the changes in phase angle and 10 Hz powers and the direct relationship between the magnitude of the change in phase angle and the degree to which PAG stimulation reciprocally affected the 10 Hz discharges of the CN and VN. 5. It is proposed that changes in phase angle reflect the reorganization of the coupling of 10 Hz oscillators and that such changes in state lead to differential patterns of spinal sympathetic outflow.
Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications
NASA Astrophysics Data System (ADS)
Li, Jibin; Feng, Zhaosheng
We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.
NASA Technical Reports Server (NTRS)
Pogorzelski, Ronald J.
2004-01-01
When electronic oscillators are coupled to nearest neighbors to form an array on a hexagonal lattice, the planar phase distributions desired for excitation of a phased array antenna are not steady state solutions of the governing non-linear equations describing the system. Thus the steady state phase distribution deviates from planar. It is shown to be possible to obtain an exact solution for the steady state phase distribution and thus determine the deviation from the desired planar distribution as a function of beam steering angle.
NASA Astrophysics Data System (ADS)
Laukhin, Vladimir N.; Audouard, Alain; Fortin, Jean-Yves; Vignolles, David; Prokhorova, Tatyana G.; Yagubskii, Eduard B.; Canadell, Enric
2017-01-01
Band structure calculations relevant to bis-ethylenedithio-tetrathiafulvalene-based charge transfer salts containing tris(oxalato)metallate anions, with generic formula (BEDT-TTF)4A[M(C2O4)3].Solv, where A is a monovalent anion, M is a trivalent cation and Solv is a solvent, suggest that their Fermi surface is liable to achieve networks of compensated orbits coupled by magnetic breakdown. Even though this picture accounts for quantum oscillations spectra of a number of these compounds, puzzling results can be noticed in several cases, pointing to the possibility of Fermi surface reconstruction at low temperature.
NASA Astrophysics Data System (ADS)
Watanabe, Shingo; Takahashi, Masaaki
2005-09-01
Equatorial Kelvin waves and ozone Kelvin waves were simulated by a T63L250 chemistry-coupled general circulation model with a high vertical resolution (300 m). The model produces a realistic quasi-biennial oscillation (QBO) and a semiannual oscillation (SAO) in the equatorial stratosphere. The QBO has a period slightly longer than 2 years, and the SAO shows rapid reversals from westerly to easterly regimes and gradual descents of westerlies. Results for the zonal wave number 1 slow and fast Kelvin waves are discussed. Structure of the waves and phase relationships between temperature and ozone perturbations coincide well with satellite observations made by LIMS, CLAES, and MLS. They are generally in phase (antiphase) in the lower (upper) stratosphere as theoretically expected. The fast Kelvin waves in the temperature and ozone are dominant in the upper stratosphere because the slow Kelvin waves are effectively filtered by the QBO westerly. In this simulation, the fast Kelvin waves encounter their critical levels in the upper stratosphere when zonal asymmetry of the SAO westerly is enhanced by an intrusion of the extratropical planetary waves. In addition to the critical level filtering effect, modulations of wave properties by background winds are evident near easterly and westerly shears associated with the QBO and SAO. Enhancement of wave amplitude in the QBO westerly shear is well coincident with radiosonde observations. Increase/decrease of vertical wavelength in the QBO easterly/westerly is obvious in this simulation, which is consistent with the linear wave theory. Shortening of wave period due to the descending QBO westerly shear zone is demonstrated for the first time. Moreover, dominant periods during the QBO westerly phase are longer than those during the QBO easterly phase for both the slow and fast Kelvin waves.
Dynamical regimes of a pH-oscillator operated in two mass-coupled flow-through reactors.
Pešek, Oldřich; Schreiberová, Lenka; Schreiber, Igor
2011-05-28
We present results of experiments focused on emergent and cooperative dynamics in a system of two coupled flow-through stirred reaction cells with diffusion-like mass exchange and a strongly nonlinear chemical reaction between hydrogen peroxide and thiosulphate catalysed by cupric ions in diluted solution of sulphuric acid. Due to complex mechanism, in which a crucial role is played by hydrogen and/or hydroxide ions, dynamics in a single cell entail multiple stationary states, excitability and oscillations conveniently indicated by measuring pH. When coupled, the system shows a plethora of dynamical regimes depending on the coupling strength and flow rate. Under certain conditions both cells display dynamics close to that in the absence of coupling, but majority of the regimes are emergent and cannot be deduced from dynamics of decoupled reactors. The most prominent is a stationary state maintaining highly acidic values of pH in one of the reactors and weakly acidic in the other. When each cell is set to display excitability and the coupled system is externally perturbed, the cells may cooperate and transmit excitations elicited by pulsed perturbations in one cell to the other. Periodic pulses induce firing patterns marked by a various degree of propagated excitations and by being periodic or irregular.
Yuan, Yi; Yan, Jiaqing; Ma, Zhitao; Li, Xiaoli
2016-01-01
Noninvasive focused ultrasound stimulation (FUS) can be used to modulate neural activity with high spatial resolution. Phase-amplitude coupling (PAC) between neuronal oscillations is tightly associated with cognitive processes, including learning, attention, and memory. In this study, we investigated the effect of FUS on PAC between neuronal oscillations and established the relationship between the PAC index and ultrasonic intensity. The rat hippocampus was stimulated using focused ultrasound at different spatial-average pulse-average ultrasonic intensities (3.9, 9.6, and 19.2 W/cm2). The local field potentials (LFPs) in the rat hippocampus were recorded before and after FUS. Then, we analyzed PAC between neuronal oscillations using a PAC calculation algorithm. Our results showed that FUS significantly modulated PAC between the theta (4–8 Hz) and gamma (30–80 Hz) bands and between the alpha (9–13 Hz) and ripple (81–200 Hz) bands in the rat hippocampus, and PAC increased with incremental increases in ultrasonic intensity. PMID:27499733
NASA Astrophysics Data System (ADS)
Gonze, Didier; Markadieu, Nicolas; Goldbeter, Albert
2008-09-01
On the basis of experimental observations, it has been suggested that glycolytic oscillations underlie the pulsatile secretion of insulin by pancreatic β cells, with a periodicity of about 13min. If β cells within an islet are synchronized through gap junctions, the question arises as to how β cells located in different islets of Langerhans synchronize to produce oscillations in plasma levels of insulin. We address this question by means of a minimal model that incorporates the secretion of insulin by cells undergoing glycolytic oscillations. Global coupling and synchronization result from the inhibition exerted by insulin on the production of glucose, which serves as the substrate for metabolic oscillations. Glycolytic oscillations are described by a simple two-variable model centered on the product-activated reaction catalyzed by the allosteric enzyme phosphofructokinase. We obtain bifurcation diagrams for the cases in which insulin secretion is controlled solely by the product or by the substrate of the metabolic oscillator. Remarkably, we find that the oscillating cells in these conditions synchronize, respectively, in phase or out of phase. Numerical simulations show that in-phase and out-of-phase synchronization can sometimes coexist when insulin release is controlled by both the substrate and the product of the metabolic oscillator. The results provide an example of a system in which the selection of in-phase or out-of-phase synchronization is governed by the nature of the coupling between the intracellular oscillations and the secretion of the biochemical signal through which the oscillating cells are globally coupled.
Experience with duplex bearings in narrow angle oscillating applications
NASA Technical Reports Server (NTRS)
Phinney, D. D.; Pollard, C. L.; Hinricks, J. T.
1988-01-01
Duplex ball bearings are matched pairs on which the abutting faces of the rings have been accurately ground so that when the rings are clamped together, a controlled amount of interference (preload) exists across the balls. These bearings are vulnerable to radial temperature gradients, blocking in oscillation and increased sensitivity to contamination. These conditions decrease the service life of these bearings. It was decided that an accelerated thermal vacuum life test should be conducted. The test apparatus and results are described and the rationale is presented for reducing a multiyear life test on oil lubricated bearings to less than a year.
Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder
NASA Astrophysics Data System (ADS)
Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.; Kofane, T. C.
2010-08-01
In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.
Al-Mekhlafi, Zeyad Ghaleb; Hanapi, Zurina Mohd; Othman, Mohamed; Zukarnain, Zuriati Ahmad
2017-01-01
Recently, Pulse Coupled Oscillator (PCO)-based travelling waves have attracted substantial attention by researchers in wireless sensor network (WSN) synchronization. Because WSNs are generally artificial occurrences that mimic natural phenomena, the PCO utilizes firefly synchronization of attracting mating partners for modelling the WSN. However, given that sensor nodes are unable to receive messages while transmitting data packets (due to deafness), the PCO model may not be efficient for sensor network modelling. To overcome this limitation, this paper proposed a new scheme called the Travelling Wave Pulse Coupled Oscillator (TWPCO). For this, the study used a self-organizing scheme for energy-efficient WSNs that adopted travelling wave biologically inspired network systems based on phase locking of the PCO model to counteract deafness. From the simulation, it was found that the proposed TWPCO scheme attained a steady state after a number of cycles. It also showed superior performance compared to other mechanisms, with a reduction in the total energy consumption of 25%. The results showed that the performance improved by 13% in terms of data gathering. Based on the results, the proposed scheme avoids the deafness that occurs in the transmit state in WSNs and increases the data collection throughout the transmission states in WSNs.
Hanapi, Zurina Mohd; Othman, Mohamed; Zukarnain, Zuriati Ahmad
2017-01-01
Recently, Pulse Coupled Oscillator (PCO)-based travelling waves have attracted substantial attention by researchers in wireless sensor network (WSN) synchronization. Because WSNs are generally artificial occurrences that mimic natural phenomena, the PCO utilizes firefly synchronization of attracting mating partners for modelling the WSN. However, given that sensor nodes are unable to receive messages while transmitting data packets (due to deafness), the PCO model may not be efficient for sensor network modelling. To overcome this limitation, this paper proposed a new scheme called the Travelling Wave Pulse Coupled Oscillator (TWPCO). For this, the study used a self-organizing scheme for energy-efficient WSNs that adopted travelling wave biologically inspired network systems based on phase locking of the PCO model to counteract deafness. From the simulation, it was found that the proposed TWPCO scheme attained a steady state after a number of cycles. It also showed superior performance compared to other mechanisms, with a reduction in the total energy consumption of 25%. The results showed that the performance improved by 13% in terms of data gathering. Based on the results, the proposed scheme avoids the deafness that occurs in the transmit state in WSNs and increases the data collection throughout the transmission states in WSNs. PMID:28056020
Entraining synthetic genetic oscillators
NASA Astrophysics Data System (ADS)
Wagemakers, Alexandre; Buldú, Javier M.; Sanjuán, Miguel A. F.; de Luis, Oscar; Izquierdo, Adriana; Coloma, Antonio
2009-09-01
We propose a new approach for synchronizing a population of synthetic genetic oscillators, which consists in the entrainment of a colony of repressilators by external modulation. We present a model where the repressilator dynamics is affected by periodic changes in temperature. We introduce an additional plasmid in the bacteria in order to correlate the temperature variations with the enhancement of the transcription rate of a certain gene. This can be done by introducing a promoter that is related to the heat shock response. This way, the expression of that gene results in a protein that enhances the overall oscillations. Numerical results show coherent oscillations of the population for a certain range of the external frequency, which is in turn related to the natural oscillation frequency of the modified repressilator. Finally we study the transient times related with the loss of synchronization and we discuss possible applications in biotechnology of large-scale production coupled to synchronization events induced by heat shock.
NASA Astrophysics Data System (ADS)
Hrkac, Gino; Keatley, Paul S.; Bryan, Matthew T.; Butler, Keith
2015-11-01
The magnetic vortex has sparked the interest of the academic and industrial communities over the last few decades. From their discovery in the 1970s for bubble memory devices to their modern application as radio frequency oscillators, magnetic vortices have been adopted to modern telecommunication and sensor applications. Basic properties of vortex structures in the static and dynamic regime, from a theoretical and experimental point of view, are presented as well as their application in spin torque driven nano-pillar and magnetic tunnel junction devices. Single vortex excitations and phase locking phenomena of coupled oscillators are discussed with an outlook of vortex oscillators in magnetic hybrid structures with imprinted domain confinement and dynamic encryption devices.
Gupta, Shamik; Bandyopadhyay, Malay
2011-10-01
We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.
Nagashima, Yoshihiko; Oosako, Takuya; Takase, Yuichi; Ejiri, Akira; Watanabe, Osamu; Kobayashi, Hiroaki; Adachi, Yuuki; Tojo, Hiroshi; Yamaguchi, Takashi; Kurashina, Hiroki; Yamada, Kotaro; An, Byung Il; Kasahara, Hiroshi; Shimpo, Fujio; Kumazawa, Ryuhei; Hayashi, Hiroyuki; Matsuzawa, Haduki; Hiratsuka, Junichi; Hanashima, Kentaro; Kakuda, Hidetoshi; Sakamoto, Takuya; Wakatsuki, Takuma
2010-06-18
We present an observation of beat oscillation generation by coupled modes associated with parametric decay instability (PDI) during radio frequency (rf) wave heating experiments on the Tokyo Spherical Tokamak-2. Nearly identical PDI spectra, which are characterized by the coexistence of the rf pump wave, the lower-sideband wave, and the low-frequency oscillation in the ion-cyclotron range of frequency, are observed at various locations in the edge plasma. A bispectral power analysis was used to experimentally discriminate beat oscillation from the resonant mode for the first time. The pump and lower-sideband waves have resonant mode components, while the low-frequency oscillation is exclusively excited by nonlinear coupling of the pump and lower-sideband waves. Newly discovered nonlocal transport channels in spectral space and in real space via PDI are described.
Application of matched filtering to identify behavioral modulation of brain oscillations
Stamoulis, Catherine; Richardson, Andrew G.
2009-01-01
Brain oscillations modulated by motor behaviors are coupled to steady-state and other potentially unrelated to movement oscillations, with energy in the same frequency bands as the signals of interest. We applied matched filtering, a quasi-optimum signal detection technique, to decouple and extract movement-related signals from local field potentials (LFPs) recorded in monkey motor cortical areas during the execution of a visually instructed reach-out task. Using a matched-filterbank, we examined coupling and interference of pre-movement and initial steady-state oscillations with movement-induced signals. Once these signal contributions were eliminated, we were able to identify significant correlations of the residual signals with behavioral parameters, which appeared attenuated by pre-movement signal interference in the raw LFPs. Specifically, the maximum and minimum amplitudes of filtered LFPs were directly modulated by peak movement velocity and micro-movements, respectively, identified in recorded hand velocity profiles. In addition, we identified phase correlations between signals during the delay (when the instructional cue was presented) and movement intervals, as well as modulation of LFP phase by movement direction. For pairs of orthogonal movement directions, corresponding LFP signals were consistently out of phase. Finally, β-band energy which is typically reduced during movement execution, possibly partly due to destructive interference between the modulated by behavior signal and unrelated oscillations, appeared to be recovered in the filtered signals. PMID:19424783
Harack, B.; Leary, A.; Coish, W. A.; Hilke, M.; Yu, G.; Gupta, J. A.; Payette, C.; Austing, D. G.
2013-12-04
We outline power spectra and auto correlation analysis performed on temporal oscillations in the tunneling current of coupled vertical quantum dots. The current is monitored for ∼2325 s blocks as the magnetic field is stepped through a high bias feature displaying hysteresis and switching: hallmarks of the hyperfine interaction. Quasi-periodic oscillations of ∼2 pA amplitude and of ∼100 s period are observed in the current inside the hysteretic feature. Compared to the baseline current outside the hysteretic feature the power spectral density is enhanced by up to three orders of magnitude and the auto correlation displays clear long lived oscillations about zero.
NASA Astrophysics Data System (ADS)
Xu, Shi-Min; Xu, Xing-Lei; Li, Hong-Qi
2008-06-01
The intermediate representation (namely intermediate coordinate-momentum representation) | x> λ, ν are introduced and employed to research the expression of the operator tauhat{p}+σhat{x} in intermediate representation | x> λ, ν . The systematic Hamilton operator hat{H} of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of λ, ν, τand σ were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator | x> λ, ν λ, ν < x|, and the Radon transformation of Wigner function is just a margin distribution.
Excitation of Earth's continuous free oscillations by atmosphere-ocean-seafloor coupling.
Rhie, Junkee; Romanowicz, Barbara
2004-09-30
The Earth undergoes continuous oscillations, and free oscillation peaks have been consistently identified in seismic records in the frequency range 2-7 mHz (refs 1, 2), on days without significant earthquakes. The level of daily excitation of this 'hum' is equivalent to that of magnitude 5.75 to 6.0 earthquakes, which cannot be explained by summing the contributions of small earthquakes. As slow or silent earthquakes have been ruled out as a source for the hum (except in a few isolated cases), turbulent motions in the atmosphere or processes in the oceans have been invoked as the excitation mechanism. We have developed an array-based method to detect and locate sources of the excitation of the hum. Our results demonstrate that the Earth's hum originates mainly in the northern Pacific Ocean during Northern Hemisphere winter, and in the Southern oceans during Southern Hemisphere winter. We conclude that the Earth's hum is generated by the interaction between atmosphere, ocean and sea floor, probably through the conversion of storm energy to oceanic infragravity waves that interact with seafloor topography.
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
Bocko, M.F.; Onofrio, R.
1996-07-01
Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves {ital et} {ital al}., 1980, Rev. Mod. Phys. {bold 52}, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. {copyright} {ital 1996 The American Physical Society.}
Synthetic free-oscillation spectra: an appraisal of various mode-coupling methods
NASA Astrophysics Data System (ADS)
Yang, Hsin-Ying; Tromp, Jeroen
2015-11-01
Normal-mode spectra may be used to investigate large-scale elastic and anelastic heterogeneity throughout the entire Earth. The relevant theory was developed a few decades ago, however-mainly due to computational limitations-several approximations are commonly employed, and thus far the full merits of the complete theory have not been taken advantage of. In this study, we present an exact algebraic form of the theory for an aspherical, anelastic and rotating Earth model in which either complex or real spherical harmonic bases are used. Physical dispersion is incorporated into the quadratic eigenvalue problem by expanding the logarithmic frequency term to second-order. Proper (re)normalization of modes in a 3-D Earth model is fully considered. Using a database of 41 earthquakes and more than 10 000 spectra containing 116 modes with frequencies less than 3 mHz, we carry out numerical experiments to quantitatively evaluate the accuracy of commonly used approximate mode synthetics. We confirm the importance of wideband coupling, that is, fully coupling all modes below a certain frequency. Neither narrowband coupling, in which nearby modes are grouped into isolated clusters, nor self-coupling, that is, incorporating coupling between singlets within the same multiplet, are sufficiently accurate approximations. Furthermore, we find that (1) effects of physical dispersion can be safely approximated based on either a fiducial frequency approximation or a quadratic approximation of the logarithmic dispersion associated with the absorption-band model; (2) neglecting the proper renormalization of the modes of a rotating, anelastic Earth model introduces only minor errors; (3) ignoring the frequency dependence of the Coriolis and kinematic matrices in a wideband coupling scheme can lead to ˜6 per cent errors in mode spectra at the lowest frequencies; notable differences also occur between narrowband coupling and quasi-degenerate perturbation theory, which linearizes the
Modeling Very Oscillating Signals. Application to Image Processing
Aubert, Gilles Aujol, Jean-Francois
2005-03-15
This article is a companion paper of a previous work where we have developed the numerical analysis of a variational model first introduced by Rudin et al. and revisited by Meyer for removing the noise and capturing textures in an image. The basic idea in this model is to decompose an image f into two components (u + v) and then to search for (u,v) as a minimizer of an energy functional. The first component u belongs to BV and contains geometrical information, while the second one v is sought in a space G which contains signals with large oscillations, i.e. noise and textures. In Meyer carried out his study in the whole R{sup 2} and his approach is rather built on harmonic analysis tools. We place ourselves in the case of a bounded set{omega} of R{sup 2} which is the proper setting for image processing and our approach is based upon functional analysis arguments. We define in this context the space G, give some of its properties, and then study in this continuous setting the energy functional which allows us to recover the components u and v. We present some numerical experiments to show the relevance of the model for image decomposition and for image denoising.
OSCILLATION MECHANICS OF THE RESPIRATORY SYSTEM: APPLICATIONS TO LUNG DISEASE
Kaczka, David W.; Dellacá, Raffaele L.
2011-01-01
Since its introduction in the 1950s, the forced oscillation technique (FOT) and the measurement of respiratory impedance have evolved into powerful tools for the assessment of various mechanical phenomena in the mammalian lung during health and disease. In this review, we highlight the most recent developments in instrumentation, signal processing, and modeling relevant to FOT measurements. We demonstrate how FOT provides unparalleled information on the mechanical status of the respiratory system compared to more widely-used pulmonary function tests. The concept of mechanical impedance is reviewed, as well as the various measurement techniques used to acquire such data. Emphasis is placed on the analysis of lower, physiologic frequency ranges (typically less than 10 Hz) that are most sensitive to normal physical processes as well as pathologic structural alterations. Various inverse modeling approaches used to interpret alterations in impedance are also discussed, specifically in the context of three common respiratory diseases: asthma, chronic obstructive pulmonary disease, and acute lung injury. Finally, we speculate on the potential role for FOT in the clinical arena. PMID:22011237
Braun, J; Buntkowsky, G; Bernarding, J; Tolxdorff, T; Sack, I
2001-06-01
New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.
Izhikevich, E M
1999-01-01
We study pulse-coupled neural networks that satisfy only two assumptions: each isolated neuron fires periodically, and the neurons are weakly connected. Each such network can be transformed by a piece-wise continuous change of variables into a phase model, whose synchronization behavior and oscillatory associative properties are easier to analyze and understand. Using the phase model, we can predict whether a given pulse-coupled network has oscillatory associative memory, or what minimal adjustments should be made so that it can acquire memory. In the search for such minimal adjustments we obtain a large class of simple pulse-coupled neural networks that can memorize and reproduce synchronized temporal patterns the same way a Hopfield network does with static patterns. The learning occurs via modification of synaptic weights and/or synaptic transmission delays.
NASA Technical Reports Server (NTRS)
Espinosa, Ismael; Gonzalez, Hortensia; Quiza, Jorge; Gonazalez, J. Jesus; Arroyo, Ruben; Lara, Ritaluz
1995-01-01
Oscillation of electrical activity has been found in many nervous systems, from invertebrates to vertebrates including man. There exists experimental evidence of very simple circuits with the capability of oscillation. Neurons with intrinsic oscillation have been found and also neural circuits where oscillation is a property of the network. These two types of oscillations coexist in many instances. It is nowadays hypothesized that behind synchronization and oscillation there is a system of coupled oscillators responsible for activities that range from locomotion and feature binding in vision to control of sleep and circadian rhythms. The huge knowledge that has been acquired on oscillators from the times of Lord Rayleigh has made the simulation of neural oscillators a very active endeavor. This has been enhanced with more recent physiological findings about small neural circuits by means of intracellular and extracellular recordings as well as imaging methods. The future of this interdisciplinary field looks very promising; some researchers are going into quantum mechanics with the idea of trying to provide a quantum description of the brain. In this work we describe some simulations using neuron models by means of which we form simple neural networks that have the capability of oscillation. We analyze the oscillatory activity with root locus method, cross-correlation histograms, and phase planes. In the more complicated neural network models there is the possibility of chaotic oscillatory activity and we study that by means of Lyapunov exponents. The companion paper shows an example of that kind.
NASA Astrophysics Data System (ADS)
Liu, F.; Hossein-Zadeh, M.
2013-05-01
We study the RF spectrum of radiation pressure driven optomechanical oscillators (OMO). Using experiments and theoretical estimations we have characterized the relative amplitude of OMO's spectral components as a function of optical detuning and optical input power. We have identified a regime where the optical resonance shift can be directly extracted from the RF spectrum for resonant optical sensing applications.
Dynamics of two arbitrary qubits strongly coupled to a quantum oscillator
NASA Astrophysics Data System (ADS)
Dong, Kun
2016-12-01
Using adiabatic approximation, a two arbitrary qubits Rabi model has been studied in ultra-strong coupling. The analytical expressions of the eigenvalues and the eigenvalues are obtained. They are in accordance with the numerical determined results. The dynamical behavior of the system and the evolution of entanglement have also been discussed. The collapse and revival phenomena has garnered particular attention. The influence of inconsistent coupling strength on them is studied. These results will be applied in quantum information processing. Project supported by the National Natural Science Foundation of China (Grant No. 10875018).
NASA Astrophysics Data System (ADS)
Dalir, Hamed; Koyama, Fumio
2014-02-01
A novel approach for bandwidth augmentation for direct modulation of VCSELs using transverse-coupled-cavity (TCC) scheme is raised, which enables us to tailor the modulation-transfer function. The base structure is similar to that of 3QW VCSELs with 980 nm wavelength operation. While the bandwidth of conventional VCSELs was limited by 9-10 GHz, the 3-dB bandwidth of TCC VCSEL with aperture diameters of 8.5×8.5μm2 and 3×3μm2 are increased by a factor of 3 far beyond the relaxation-oscillation frequency. Our current bandwidth achievement on the larger aperture size is 29 GHz which is limited by the used photo-detector. To the best of our knowledge this is the fastest 980 nm VCSEL.
The Atlantic Multi-Decadal Oscillation Climate Impact - Zonal and Meridional Coupling
NASA Astrophysics Data System (ADS)
Werner, Rolf; Kirillov, Andrey; Valev, Dimitar; Atanassov, Atanas; Danov, Dimitar; Guineva, Veneta
2016-07-01
The Atlantic multi-decadal oscillation (AMO) shows a period of about 60-70 years. Over the time span from 1860 up to 2014 the AMO has had a strong climate impact on the Northern Hemisphere. The AMO is considered to be related to the Atlantic overturning circulation, but the origin of the oscillation is not fully understood up till now. To study the AMO impact on climate, the Hadcrut4, Crut4 and HadSST3 temperature data sets have been employed in the current study. The influence of the AMO on the zonal and meridional temperature distribution has been investigated in detail. The strongest zonal AMO impact was obtained in the Arctic region. The results indicated that the AMO influence on temperature at Southern latitudes was opposite in phase compared to the temperature influence in the Northern Hemisphere, in agreement with the well known heat transfer phenomenon from South to North Atlantic. In the Northern Hemisphere the strongest AMO temperature impact was found over the Atlantic and America. In the West from American continent, over the Pacific, the AMO impact was the lowest obtained over the whole Northern Hemisphere. The Rocky Mountains and Sierra Madre, connected with it southwards, built up an atmospheric circulation barrier preventing a strong propagation of the AMO temperature signal westerly. The amplitude of the AMO index itself was greater during summer-fall. However stronger AMO influence on the Northern Hemisphere temperatures was found during the fall-winter season, when the differences between the Northern Hemisphere temperatures and the temperatures in the tropics were the greatest.
Demonstration of Double EIT Using Coupled Harmonic Oscillators and RLC Circuits
ERIC Educational Resources Information Center
Harden, Joshua; Joshi, Amitabh; Serna, Juan D.
2011-01-01
Single and double electromagnetically induced transparencies (EIT) in a medium, consisting of four-level atoms in the inverted-Y configuration, are discussed using mechanical and electrical analogies. A three-coupled spring-mass system subject to damping and driven by an external force is used to represent the four-level atom mechanically. The…
Liu, Jingliang; Yang, Hujiang; Wang, Chuan; Xu, Kun; Xiao, Jinghua
2016-01-01
Here we experimentally demonstrated the electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) effects in mechanical coupled pendulums. The analogue of EIT and ATS has been studied in mechanical systems and the intrinsic physics between these two phenomena are also been discussed. Exploiting the Akaike Information Criterion, we discern the ATS effect from EIT effect in our experimental results. PMID:26751738
Theoretical realization and application of parity-time-symmetric oscillators in a quantum regime
NASA Astrophysics Data System (ADS)
Li, Wenlin; Li, Chong; Song, Heshan
2017-02-01
In the existing parity-time (PT ) symmetry with the balanced gain and loss, the gain is derived from semiclassical but not full quantum theories, which significantly restricts the applications of PT symmetry in quantum fields. In this work, we propose and analyze a theoretical scheme to realize full quantum oscillator PT symmetry. The quantum gain is provided by a dissipation optical cavity with a blue-detuned laser field. After adiabatically eliminating the cavity modes, we give an effective master equation, which is a complete quantum description compared with the non-Hermitian Hamiltonian, to reveal the quantum behaviors of such a gain oscillator. This kind of PT symmetry can eliminate the dissipation effect in the quantum regime. As an example, we apply PT -symmetric oscillators to enhance optomechanically induced transparency.
Coupling, Q-Factor, and Integration Aspects of Microsphere Applications
NASA Technical Reports Server (NTRS)
Ilchenko, V. S.; Yao, X. S.; Maleki, L.
2000-01-01
With suggested applications varying from microlaser and cavity QED through optical locking of diode lasers to modulators and sensors, high-Q silica microspheres with whispering-gallery (WG) modes so far remain the subject of tabletop feasibility demonstrations. Despite the uniquely high quality-factor and submillimeter dimensions suitable for tight packaging, this novel type of high-finesse cavity still has to be adapted to fiber- and integrated-optic hardware. In the visible and near infrared-band experiments (633-850nm) measuring the ringdown time tau of free oscillations, Q = (0.6 to 0.8 ) x 10(exp 10) has been obtained in silica spheres of diameter -800 microns (corresponding tau = 3 to 4 microseconds). It was proved that under normal laboratory conditions, quality-factor is subject to deterioration within several-minute scale down to (2 ... 3 ) x 10(exp 9). The responsible mechanism was identified as adsorption of a monolayer of atmospheric water, so that preservation of the ultimate Q requires manipulation in dry environment, or fast packaging into sealed devices. Larger Q can be expected closer to minimum of attenuation in fused silica alpha = 0.2 dB/km; Q greater than or equal to 1 x 10(exp 11) at lambda=1.55 microns, with corresponding energy storage time tau approx. 0.1ms. Experiments are currently underway to determine whether this high Q can be realized experimentally. The evident difficulty is that OH-related optical absorption has its peaks located near the reported minimum of attenuation in silica. We can also mention here that some of proposed fiber materials, yet not ready for fiber drawing, have been predicted to have smaller attenuation than fused silica and may be suitable for microsphere fabrication (sodium-magnesium silicate glass, alpha = 0.06dB/km). WG modes possess very small radiative loss (it does not prevent Q-10(exp 20) and more) and therefore are electromagnetically isolated and cannot be excited by free-space beams. If no modification
NASA Astrophysics Data System (ADS)
Yuan, L. H.; Wang, C. N.; Zhang, Z. Z.
2016-10-01
Based on the Lyapunov stability theory, an improved Lyapunov function scheme is used to understand the complete synchronization of hyperchaotic systems by imposing pulse linear coupling on the response system. According to this scheme, the controller begins to control the response system in a period when the output error variables are increasing; otherwise, the controller turns off. The distribution of conditional Lyapunov exponent versus coupling intensity, and the synchronization cost (averaged power consumption of controller) is calculated, respectively. By designing an exponential type of Lyapunov function, it is found that complete synchronization could be realized between two Chen hyperchaotic systems and two 4-dimensional LC hyperchaotic systems. Our numerical results are consistent with the previous theoretical discussion.
Towards a quasi-periodic mean field theory for globally coupled oscillators
NASA Astrophysics Data System (ADS)
Banaji, Murad; Glendinning, Paul
1999-02-01
We show how a quasi-periodic mean field theory may be used to understand the chaotic dynamics and geometry of globally coupled complex Ginzburg-Landau equations. The Poincaré map of the mean field equations appears to have saddlenode-homoclinic bifurcations leading to chaotic motion, and the attractor has the characteristic ρ shape identified by numerical experiments on the full equations.
The effect of temperature on the coupled slow and fast dynamics of an electrochemical oscillator
Zülke, Alana A.; Varela, Hamilton
2016-01-01
The coupling among disparate time-scales is ubiquitous in many chemical and biological systems. We have recently investigated the effect of fast and, long-term, slow dynamics in surface processes underlying some electrocatalytic reactions. Herein we report on the effect of temperature on the coupled slow and fast dynamics of a model system, namely the electro-oxidation of formic acid on platinum studied at five temperatures between 5 and 45 °C. The main result was a turning point found at 25 °C, which clearly defines two regions for the temperature dependency on the overall kinetics. In addition, the long-term evolution allowed us to compare reaction steps related to fast and slow evolutions. Results were discussed in terms of the key role of PtO species, which chemically couple slow and fast dynamics. In summary we were able to: (a) identify the competition between two reaction steps as responsible for the occurrence of two temperature domains; (b) compare the relative activation energies of these two steps; and (c) suggest the role of a given reaction step on the period-increasing set of reactions involved in the oscillatory dynamics. The introduced methodology could be applied to other systems to uncover the temperature dependence of complex chemical networks. PMID:27079514
The effect of temperature on the coupled slow and fast dynamics of an electrochemical oscillator
NASA Astrophysics Data System (ADS)
Zülke, Alana A.; Varela, Hamilton
2016-04-01
The coupling among disparate time-scales is ubiquitous in many chemical and biological systems. We have recently investigated the effect of fast and, long-term, slow dynamics in surface processes underlying some electrocatalytic reactions. Herein we report on the effect of temperature on the coupled slow and fast dynamics of a model system, namely the electro-oxidation of formic acid on platinum studied at five temperatures between 5 and 45 °C. The main result was a turning point found at 25 °C, which clearly defines two regions for the temperature dependency on the overall kinetics. In addition, the long-term evolution allowed us to compare reaction steps related to fast and slow evolutions. Results were discussed in terms of the key role of PtO species, which chemically couple slow and fast dynamics. In summary we were able to: (a) identify the competition between two reaction steps as responsible for the occurrence of two temperature domains; (b) compare the relative activation energies of these two steps; and (c) suggest the role of a given reaction step on the period-increasing set of reactions involved in the oscillatory dynamics. The introduced methodology could be applied to other systems to uncover the temperature dependence of complex chemical networks.
Terahertz oscillators using resonant tunneling diodes and their functions for various applications
NASA Astrophysics Data System (ADS)
Asada, M.; Suzuki, S.
2016-04-01
Compact and coherent source is a key component for various applications of the terahertz wave. We report on our recent results of terahertz oscillators using resonant tunneling diodes (RTDs). The RTD is an InGaAs/AlAs double-barrier structure on InP substrate, and integrated with a planar slot antenna as a resonator and radiator. The output power is obtained from the substrate side through a Si lens. To achieve high-frequency oscillation, a narrow quantum well and an optimized collector spacer thickness were used. The former reduces the electron dwell time in the resonant tunneling region and the latter simultaneously reduces the electron transit time and the capacitance at the collector depletion region. The conduction loss of the slot antenna was also reduced with an optimized antenna length and an improved air bridge structure between the RTD and antenna. By these structures, fundamental oscillation up to 1.92 THz were obtained at room temperature. Oscillation above 2 THz is further expected in theoretical calculation. An oscillator with patch antenna, in which a Si lens is unnecessary, was fabricated. In a preliminary experiment, output power of 55 μW was obtained at 1 THz in a three-element array. Wireless data transmission using direct intensity modulation was demonstrated with the data rate of 30 Gbp/s and the bit error rate below the forward error correction limit. By integrating a varactor into the slot antenna, electrical frequency tuning was achieved with a tuning range of 580-900 GHz in an array device. Application of frequency-tunable RTD oscillators to measurements of absorption spectra was also demonstrated.
NASA Astrophysics Data System (ADS)
Chatterjee, A.; Anderson, J. L.; Moncrieff, M.; Collins, N.; Danabasoglu, G.; Hoar, T.; Karspeck, A. R.; Neale, R. B.; Raeder, K.; Tribbia, J. J.
2014-12-01
We present a quantitative evaluation of the simulated MJO in analyses produced with a coupled data assimilation (CDA) framework developed at the National Center for Atmosphere Research. This system is based on the Community Earth System Model (CESM; previously known as the Community Climate System Model -CCSM) interfaced to a community facility for ensemble data assimilation (Data Assimilation Research Testbed - DART). The system (multi-component CDA) assimilates data into each of the respective ocean/atmosphere/land model components during the assimilation step followed by an exchange of information between the model components during the forecast step. Note that this is an advancement over many existing prototypes of coupled data assimilation systems, which typically assimilate observations only in one of the model components (i.e., single-component CDA). The more realistic treatment of air-sea interactions and improvements to the model mean state in the multi-component CDA recover many aspects of MJO representation, from its space-time structure and propagation (see Figure 1) to the governing relationships between precipitation and sea surface temperature on intra-seasonal scales. Standard qualitative and process-based diagnostics identified by the MJO Task Force (currently under the auspices of the Working Group on Numerical Experimentation) have been used to detect the MJO signals across a suite of coupled model experiments involving both multi-component and single-component DA experiments as well as a free run of the coupled CESM model (i.e., CMIP5 style without data assimilation). Short predictability experiments during the boreal winter are used to demonstrate that the decay rates of the MJO convective anomalies are slower in the multi-component CDA system, which allows it to retain the MJO dynamics for a longer period. We anticipate that the knowledge gained through this study will enhance our understanding of the MJO feedback mechanisms across the air
Lansman, Jeffry B
2015-01-01
An absence of utrophin in muscle from mdx mice prolongs the open time of single mechanosensitive channels. On a time scale much longer than the duration of individual channel activations, genetic depletion of utrophin produces low frequency oscillations of channel open probability. Oscillatory channel opening occurred in the dystrophin/utrophin mutants, but was absent in wild-type and mdx fibers. By contrast, small conductance channels showed random gating behavior when present in the same patch. Applying a negative pressure to a patch on a DKO fiber produced a burst of mode II activity, but channels subsequently closed and remained silent for tens of seconds during the maintained pressure stimulus. In addition, simultaneous opening of multiple MS channels could be frequently observed in recordings from patches on DKO fibers, but only rarely in wild-type and mdx muscle. A model which accounts for the single-channel data is proposed in which utrophin acts as gating spring which maintains the mechanical stability a caveolar-like compartment. The state of this compartment is suggested to be dynamic; its continuity with the extracellular surface varying over seconds to minutes. Loss of the mechanical stability of this compartment contributes to pathogenic Ca(2+) entry through MS channels in Duchenne dystrophy.
Rat, V.; Coudert, J. F.
2010-08-15
This work is devoted to the instabilities occurring in a plasma torch, such as those found in plasma spraying. These instabilities are responsible for a lack of reproducibility of coatings properties, especially in the case of suspension plasma spraying that is an innovative way to obtain thin coatings of submicron-sized particles. Strong Helmholtz oscillations are highlighted in the plasma flow and it is demonstrated that they overlap with different acoustic modes in addition with the more commonly admitted ''restrike'' mode, the later being due to rearcing events in the arc region. The instabilities occur in the arc voltage but it is experimentally shown in this paper that the pressure within the torch body presents the same kind of instabilities. Besides, a numerical filtering technique has been adapted to isolate the different instability components. The operating parameters of the plasma torch were varied in order to highlight their influence on the amplitude of the different modes, both for the arc voltage and the pressure.
NASA Astrophysics Data System (ADS)
Adames, Á. F.; Kim, D.
2015-12-01
A linear wave theory for the Madden-Julian Oscillation (MJO), previously developed by Sobel and Maloney, is extended upon in this study. Using column-integrated moisture as a prognostic variable, a dispersion relation is derived that solely depends on the convective adjustment timescale, a parameter that indicates the amount of moisture available for propagation and the distance that free Kelvin waves are able to travel in the presence of dissipation. The dispersion relation adequately describes the MJO's signal in the wavenumber-frequency spectrum and defines the MJO as a dispersive equatorial moist wave with a westward group velocity. On the basis of linear regression analysis of the time varying field of outgoing longwave radiation, it is estimated that that the MJO's group velocity is 2/5 as large as its eastward phase speed. This dispersion is the result of the anomalous winds in the Kelvin and Rossby wave responses modulating the mean distribution of moisture such that the moisture anomaly propagates eastward while wave energy propagates westward. Additionally, it is found that cloud-radiation feedbacks cause growth of the moist wave to be largest at the planetary scales. It is hypothesized that this scale selection mechanism is the result of upper-level cloudiness exhibiting a larger zonal extent than precipitation. The longwave radiative heating from these upper-level clouds causes an expansion of the region of ascent under weak-temperature gradient balance.
NASA Astrophysics Data System (ADS)
Napitu, A. M.; Gordon, A. L.; Pujiana, K.
2014-12-01
The intraseasonal SST characteristics within the Indonesian Seas and their responses to the Madden-Julian Oscillations [MJO] are examined through analyses of observed and reanalysis datasets. Intraseasonal variation accounts for about 30% of SST variability, with the strongest signature is observed in Banda and Timor seas. The MJO signature in SST is evident in the form of energy peak at 35-45 days, amplification during the Northwest Monsoon (boreal winter), and eastward propagation. SST responds to sea-air heat flux associated with MJO with net heat flux into the ocean (atmosphere) characterizing the suppressed (active) phase of MJO. The influence of MJO on Banda Sea SST is greatest during La Niña periods, which are favorable for deeper thermocline conditions, which diminish the role of ocean processes driving vertical heat transfer between subsurface and surface layers. Diminished influence of ocean processes results in dominance of surface heat fluxes associated with MJO in governing intraseasonal SST variability. During El Niño, the role of ocean processes is favorable to mediate heat transfer between lower and upper layer of the ocean surface as thermocline is shallower. The ocean component heat fluxes then compete with MJO forced heat fluxes in governing SST variability as indicated by less pronounced eastward propagation.
NASA Astrophysics Data System (ADS)
Zhang, Kai-Chun; Wu, Zhen-Hua; Liu, Sheng-Gang
2008-09-01
An extended interaction oscillator (EIO) generating 120 GHz wave in sub-terahertz waves is studied by using the three-dimensional electromagnetic simulation software CST and PIC codes. A rectangular reentrant coupled-cavity is proposed as the slow-wave structure of EIO. By CST, the circuit parameters including frequency-phase dispersion, interaction impedance and characteristic impedance are simulated and calculated. The operation mode of EIO is chosen very close to the point where β L = 2π with corresponding frequency 120 GHz, the beam voltage 12 kV and the dimensions of the cavity with the period 0.5 mm, the height 3 mm and the width 1.4 mm. Simulation results of beam-wave interaction by PIC show that the exciting frequency is 120.85 GHz and output peak power 465 W with 12-period coupled-cavity with the perveance 0.17μP. Simulation results indicate that the EIO has very wide range of the operation voltage.
NASA Astrophysics Data System (ADS)
Hu, Xinguang; Yuan, Shuai; Armghan, Ammar; Liu, Yang; Jiao, Zheng; Lv, Haijiang; Zeng, Cheng; Huang, Ying; Huang, Qingzhong; Wang, Yi; Xia, Jinsong
2017-01-01
A radiating two-oscillator model is developed to describe plasmon-induced transparency (PIT) and absorption (PIA) spectral responses in a two-bright mode coupling system, from which the analytical expressions of the scattering parameters are derived. To verify the validity of the model, the scattering parameters are used to fit with corresponding numerical data obtained from finite difference time domain simulations by using a simple planar structure. The transmission and reflection spectra can be well reproduced simultaneously, indicating that the model is effective and convenient for describing two-bright mode coupling. By analyzing the transmission phase of the bright modes, the physical regime behind the PIT effect is revealed. Successful reproduction of group delay shows that the model can be used in analyzing slow light effects. In addition, a study on resonance detuning and the damping factor indicates that the two parameters should be considered simultaneously in the PIT effect. PIA-like phenomenon can also be achieved in the system but with a smaller detuning compared with the PIT effect. The results obtained here may be useful for designing active devices in the future.
Dynamically Maintained Spike Timing Sequences in Networks of Pulse-Coupled Oscillators with Delays
NASA Astrophysics Data System (ADS)
Gong, Pulin; van Leeuwen, Cees
2007-01-01
We demonstrate the widespread occurrence of dynamically maintained spike timing sequences in recurrent networks of pulse-coupled spiking neurons with large time delays. The sequences occur in transient, quasistable phase-locking states. The system spontaneously jumps between these states. This collective dynamics enables the system to generate a large number of distinct precise spike timing sequences. Distributed time delays play a constructive role by enhancing the dominance in parameter space of the dynamics responsible for producing the large variety of spike timing sequences.
NASA Astrophysics Data System (ADS)
Bayr, Tobias; Wengel, Christian; Latif, Mojib
2016-04-01
Dommenget (2010) found that El Niño-like variability, termed Slab Ocean El Niño, can exist in the absence of ocean dynamics and is driven by the interaction of the atmospheric surface heat fluxes and the heat content of the upper ocean. Further, Dommenget et al. (2014) report the Slab Ocean El Niño is not an artefact of the ECHAM5-AGCM coupled to a slab ocean model. In fact, atmospheric feedbacks crucial to the Slab Ocean El Niño can also be found in many state-of-the-art coupled climate models participating in CMIP3 and CMIP5, so that ENSO in many CMIP models can be understood as a mixed recharge oscillator/Slab Ocean El Niño mode. Here we show further analysis of the Slab Ocean El Niño atmospheric feedbacks in coupled models. The BCCR_CM2.0 climate model from the CMIP3 data base, which has a very large equatorial cold bias, has an El Niño that is mostly driven by Slab Ocean El Niño atmospheric feedbacks and is used as an example to describe Slab Ocean El Niño atmospheric feedbacks in a coupled model. In the BCCR_CM2.0, the ENSO-related variability in the 20°C isotherm (Z20), a measure of upper ocean heat content, is decoupled from the first mode of the seasonal cycle-related variability, while the two are coupled in observations, with ENSO being phase-locked to the seasonal cycle. Further analysis of the seasonal cycle in Z20 using SODA Ocean Reanalysis reveals two different regimes in the seasonal cycle along the equator: The first regime, to which ENSO is phase-locked, extends over the west and central equatorial Pacific and is driven by subsurface ocean dynamics. The second regime, extending in observations only over the cold tongue region, is driven by the seasonal cycle at the sea surface and is shifted by roughly six months relative to the first regime. In a series of experiments with the Kiel Climate Model (KCM) with different mean states due to tuning in the convection parameters, we can show that the strength of the equatorial cold bias and the
NASA Technical Reports Server (NTRS)
Tratt, David M.; Mansour, Kamjou; Menzies, Robert T.; Qiu, Yueming; Forouhar, Siamak; Maker, Paul D.; Muller, Richard E.
2001-01-01
The NASA Earth Science Enterprise Advanced Technology Initiatives Program is supporting a program for the development of semiconductor laser reference oscillators for application to coherent optical remote sensing from Earth orbit. Local oscillators provide the frequency reference required for active spaceborne optical remote sensing concepts that involve heterodyne (coherent) detection. Two recent examples of such schemes are Doppler wind lidar and tropospheric carbon dioxide measurement by laser absorption spectrometry, both of which are being proposed at a wavelength of 2.05 microns. Frequency-agile local oscillator technology is important to such applications because of the need to compensate for large platform-induced Doppler components that would otherwise interfere with data interpretation. Development of frequency-agile local oscillator approaches has heretofore utilized the same laser material as the transmitter laser (Tm,Ho:YLF in the case of the 2.05-micron wavelength mentioned above). However, a semiconductor laser-based frequency-agile local oscillator offers considerable scope for reduced mechanical complexity and improved frequency agility over equivalent crystal laser devices, while their potentially faster tuning capability suggest the potential for greater scanning versatility. The program we report on here is specifically tasked with the development of prototype novel architecture semiconductor lasers with the power, tunability, and spectral characteristics required for coherent Doppler lidar. The baseline approach for this work is the distributed feedback (DFB) laser, in which gratings are etched into the semiconductor waveguide structures along the entire length of the laser cavity. However, typical DFB lasers at the wavelength of interest have linewidths that exhibit unacceptable growth when driven at the high currents and powers that are required for the Doppler lidar application. Suppression of this behavior by means of corrugation pitch
Bills, Bruce G.; James, Thomas S.; Mengel, John G.
1999-01-01
Precessional motion of Earth's rotation axis relative to its orbit is a well-known source of long-period climatic variation. It is less well appreciated that growth and decay of polar ice sheets perturb the symmetry of the global mass distribution enough that the geographic location of the rotation axis will change by at least 15 km and possibly as much as 100 km during a single glacial cycle. This motion of the pole will change the seasonal and latitudinal pattern of temperatures. We present calculations, based on a diurnal average energy balance, which compare the summer and winter temperature anomalies due to a 1° decrease in obliquity with those due to a 1° motion of the rotation pole toward Hudson Bay. Both effects result in peak temperature perturbations of about 1° Celsius. The obliquity change primarily influences the amplitude of the seasonal cycle, while the polar motion primarily changes the annual mean temperatures. The polar motion induced temperature anomaly is such that it will act as a powerful negative feedback on ice sheet growth. We also explore the evolution of the coupled system composed of ice sheet mass and pole position. Oscillatory solutions result from the conflicting constraints of rotational and thermal stability. A positive mass anomaly on an otherwise featureless Earth is in rotational equilibrium only at the poles or the equator. The two polar equilibria are rotationally unstable, and the equatorial equilibrium, though rotationally stable, is thermally unstable. We find that with a plausible choice for the strength of coupling between the thermal and rotational systems, relatively modest external forcing can produce significant response at periods of 104–106 years, but it strongly attenuates polar motion at longer periods. We suggest that these coupled oscillations may contribute to the observed dominance of 100 kyr glacial cycles since the mid-Pleistocene and will tend to stabilize geographic patterns that are suitable to
Partial Synchronization in Pulse-Coupled Oscillator Networks II: A Numerical Study
NASA Astrophysics Data System (ADS)
Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato
We use high-precision numerical simulations, to compute the dynamics of N identical integrate and fire model neurons coupled in an all-to-all network through α-function pulses. In particular, we determine the discrete evolution of the state of our system from spike to spike. In addition to traditional fully synchronous and splay states, we exhibit multiple competing partially synchronized ordered states, which are fixed points and limit cycles in the phase space. Close examinations reveal the bifurcations among different states. By varying the parameters, we map out the phase diagram of stable fixed points. Our results illustrate the power of dimensional reduction in complex dynamical systems, and shed light on the collective behaviors of neural networks. Work supported by NSF DMS 1413020.
Low-frequency, self-sustained oscillations in inductively coupled plasmas used for optical pumping
Coffer, J.; Encalada, N.; Huang, M.; Camparo, J.
2014-10-28
We have investigated very low frequency, on the order of one hertz, self-pulsing in alkali-metal inductively-coupled plasmas (i.e., rf-discharge lamps). This self-pulsing has the potential to significantly vary signal-to-noise ratios and (via the ac-Stark shift) resonant frequencies in optically pumped atomic clocks and magnetometers (e.g., the atomic clocks now flying on GPS and Galileo global navigation system satellites). The phenomenon arises from a nonlinear interaction between the atomic physics of radiation trapping and the plasma's electrical nature. To explain the effect, we have developed an evaporation/condensation theory (EC theory) of the self-pulsing phenomenon.
Low-frequency, self-sustained oscillations in inductively coupled plasmas used for optical pumping
NASA Astrophysics Data System (ADS)
Coffer, J.; Encalada, N.; Huang, M.; Camparo, J.
2014-10-01
We have investigated very low frequency, on the order of one hertz, self-pulsing in alkali-metal inductively-coupled plasmas (i.e., rf-discharge lamps). This self-pulsing has the potential to significantly vary signal-to-noise ratios and (via the ac-Stark shift) resonant frequencies in optically pumped atomic clocks and magnetometers (e.g., the atomic clocks now flying on GPS and Galileo global navigation system satellites). The phenomenon arises from a nonlinear interaction between the atomic physics of radiation trapping and the plasma's electrical nature. To explain the effect, we have developed an evaporation/condensation theory (EC theory) of the self-pulsing phenomenon.
Quantum treatment of the time-dependent coupled oscillators under the action of a random force
Abdalla, M. Sebawe Nassar, M.M.
2009-03-15
In this communication we introduce the problem of time-dependent frequency converter under the action of external random force. We have assumed that the coupling parameter and the phase pump are explicitly time dependent. Using the equations of motion in the Heisenberg picture the dynamical operators are obtained, however, under a certain integrability condition. When the system is initially prepared in the even coherent states the squeezing phenomenon is discussed. The correlation function is also considered and it has been shown that the nonclassical properties are apparent and sensitive to any variation in the integrability parameter. Furthermore, the wave function in Schroedinger picture is calculated and used it to derive the wave function in the coherent states. The accurate definition of the creation and annihilation operators are also introduced and employed to diagonalize the Hamiltonian system.
Conference on Charge-Coupled Device Technology and Applications
NASA Technical Reports Server (NTRS)
1976-01-01
Papers were presented from the conference on charge coupled device technology and applications. The following topics were investigated: data processing; infrared; devices and testing; electron-in, x-ray, radiation; and applications. The emphasis was on the advances of mutual relevance and potential significance both to industry and NASA's current and future requirements in all fields of imaging, signal processing and memory.
Diode pumped solid-state laser oscillators for spectroscopic applications
NASA Technical Reports Server (NTRS)
Byer, R. L.; Basu, S.; Fan, T. Y.; Kozlovsky, W. J.; Nabors, C. D.; Nilsson, A.; Huber, G.
1987-01-01
The rapid improvement in diode laser pump sources has led to the recent progress in diode laser pumped solid state lasers. To date, electrical efficiencies of greater than 10 percent were demonstrated. As diode laser costs decrease with increased production volume, diode laser and diode laser array pumped solid state lasers will replace the traditional flashlamp pumped Nd:YAG laser sources. The use of laser diode array pumping of slab geometry lasers will allow efficient, high peak and average power solid state laser sources to be developed. Perhaps the greatest impact of diode laser pumped solid state lasers will be in spectroscopic applications of miniature, monolithic devices. Single-stripe diode-pumped operation of a continuous-wave 946 nm Nd:YAG laser with less than 10 m/w threshold was demonstrated. A slope efficiency of 16 percent near threshold was shown with a projected slope efficiency well above a threshold of 34 percent based on results under Rhodamine 6G dye-laser pumping. Nonlinear crystals for second-harmonic generation of this source were evaluated. The KNbO3 and periodically poled LiNbO3 appear to be the most promising.
Initial Coupling of the RELAP-7 and PRONGHORN Applications
J. Ortensi; D. Andrs; A.A. Bingham; R.C. Martineau; J.W. Peterson
2012-10-01
Modern nuclear reactor safety codes require the ability to solve detailed coupled neutronic- thermal fluids problems. For larger cores, this implies fully coupled higher dimensionality spatial dynamics with appropriate feedback models that can provide enough resolution to accurately compute core heat generation and removal during steady and unsteady conditions. The reactor analysis code PRONGHORN is being coupled to RELAP-7 as a first step to extend RELAP’s current capabilities. This report details the mathematical models, the type of coupling, and the testing results from the integrated system. RELAP-7 is a MOOSE-based application that solves the continuity, momentum, and energy equations in 1-D for a compressible fluid. The pipe and joint capabilities enable it to model parts of the power conversion unit. The PRONGHORN application, also developed on the MOOSE infrastructure, solves the coupled equations that define the neutron diffusion, fluid flow, and heat transfer in a full core model. The two systems are loosely coupled to simplify the transition towards a more complex infrastructure. The integration is tested on a simplified version of the OECD/NEA MHTGR-350 Coupled Neutronics-Thermal Fluids benchmark model.
Collins, M.
2000-04-01
This paper describes El Nino-Southern Oscillation (ENSO) interannual variability simulated in the second Handley Centre coupled model under control and greenhouse warming scenarios. The model produces a very reasonable simulation of ENSO in the control experiment--reproducing the amplitude, spectral characteristics, and phase locking to the annual cycle that are observed in nature. The mechanism for the model ENSO is shown to be a mixed SST-ocean dynamics mode that can be interpreted in terms of the ocean recharge paradigm of Jin. In experiments with increased levels of greenhouse gases, no statistically significant changes in ENSO are seen until these levels approach four times preindustrial values. In these experiments, the model ENSO has an approximately 20% larger amplitude, a frequency that is approximately double that of the current ENSO (implying more frequent El Ninos and La Ninas), and phase locks to the annual cycle at a different time of year. It is shown that the increase in the vertical gradient of temperature in the thermocline region, associated with the model's response to increased greenhouse gases, is responsible for the increase in the amplitude of ENSO, while the increase in meridional temperature gradients on either side of the equator, again associated with the models response to increasing greenhouse gases, is responsible for the increased frequency of ENSO events.
Monier, Erwan; Weare, Bryan C.; Gustafson, William I.
2009-07-24
The realism of the Madden-Julian Oscillation (MJO) produced by the MM5 regional model is investigated using systematic and standardized statistical diagnostics. This study expands on previous work by choosing a larger domain and a different input dataset (ECMWF ERA-40 reanalysis) to force the initial and boundary conditions of the model. Results show that upper- and lower-level zonal winds display the correct MJO structure, phase speed (8 m s ^{-1}) and space-time power spectrum. However, the simulated free atmosphere moisture, Outgoing Longwave Radation (OLR) and precipitation do not exhibit any clear MJO signal. Yet, the boundary layer moisture, the moist static energy and the atmospheric instability, measured using a moist static energy instability index have clear MJO signals. A significant finding of this study is the ability of MM5 to simulate a realistic MJO phase speed in the winds without reproducing the MJO wind-convection coupling or a realistic propagation in the free atmosphere water vapor. This study suggests that the convergence of boundary layer moisture and the discharge and recharge of the moist static energy and atmospheric instability may be responsible for controlling the speed of propagation of the MJO circulation.
NASA Technical Reports Server (NTRS)
Wilson, T. G.; Lee, F. C. Y.; Burns, W. W., III; Owen, H. A., Jr.
1975-01-01
It recently has been shown in the literature that many dc-to-square-wave parallel inverters which are widely used in power-conditioning applications can be grouped into one of two families. Each family is characterized by an equivalent RLC network. Based on this approach, a classification procedure is presented for self-oscillating parallel inverters which makes evident natural relationships which exist between various inverter configurations. By utilizing concepts from the basic theory of negative resistance oscillators and the principle of duality as applied to nonlinear networks, a chain of relationships is established which enables a methodical transfer of knowledge gained about one family of inverters to any of the other families in the classification array.
NASA Astrophysics Data System (ADS)
Schilling, Osvaldo F.
2004-03-01
We discuss theoretically the properties of an electromechanical oscillating system whose operation is based upon the cyclic conservative conversion between gravitational potential, kinetic and magnetic energies. The system consists of a superconducting coil subjected to a constant external force and to magnetic fields. The coil oscillates and has induced in it a rectified electrical current whose magnitude may reach hundreds of amperes. The design differs from that of most conventional superconductor machines since the motion is linear (and practically unnoticeable depending on frequency) rather than rotatory and it does not involve high speeds. Furthermore, there is no need for an external electrical power source to start up the system. We also show that the losses for such a system can be made extremely small for certain operational conditions, so that by reaching and keeping resonance the system's main application should be in the generation and storage of electromagnetic energy.
NASA Astrophysics Data System (ADS)
De Vita, P.; Allocca, V.; Manna, F.; Fabbrocino, S.
2012-05-01
Thus far, studies on climate change have focused mainly on the variability of the atmospheric and surface components of the hydrologic cycle, investigating the impact of this variability on the environment, especially with respect to the risks of desertification, droughts and floods. Conversely, the impacts of climate change on the recharge of aquifers and on the variability of groundwater flow have been less investigated, especially in Mediterranean karst areas whose water supply systems depend heavily upon groundwater exploitation. In this paper, long-term climatic variability and its influence on groundwater recharge were analysed by examining decadal patterns of precipitation, air temperature and spring discharges in the Campania region (southern Italy), coupled with the North Atlantic Oscillation (NAO). The time series of precipitation and air temperature were gathered over 90 yr, from 1921 to 2010, using 18 rain gauges and 9 air temperature stations with the most continuous functioning. The time series of the winter NAO index and of the discharges of 3 karst springs, selected from those feeding the major aqueducts systems, were collected for the same period. Regional normalised indexes of the precipitation, air temperature and karst spring discharges were calculated, and different methods were applied to analyse the related time series, including long-term trend analysis using smoothing numerical techniques, cross-correlation and Fourier analysis. The investigation of the normalised indexes highlighted the existence of long-term complex periodicities, from 2 to more than 30 yr, with differences in average values of up to approximately ±30% for precipitation and karst spring discharges, which were both strongly correlated with the winter NAO index. Although the effects of the North Atlantic Oscillation (NAO) had already been demonstrated in the long-term precipitation and streamflow patterns of different European countries and Mediterranean areas, the results
Wireless power using magnetic resonance coupling for neural sensing applications
NASA Astrophysics Data System (ADS)
Yoon, Hargsoon; Kim, Hyunjung; Choi, Sang H.; Sanford, Larry D.; Geddis, Demetris; Lee, Kunik; Kim, Jaehwan; Song, Kyo D.
2012-04-01
Various wireless power transfer systems based on electromagnetic coupling have been investigated and applied in many biomedical applications including functional electrical stimulation systems and physiological sensing in humans and animals. By integrating wireless power transfer modules with wireless communication devices, electronic systems can deliver data and control system operation in untethered freely-moving conditions without requiring access through the skin, a potential source of infection. In this presentation, we will discuss a wireless power transfer module using magnetic resonance coupling that is specifically designed for neural sensing systems and in-vivo animal models. This research presents simple experimental set-ups and circuit models of magnetic resonance coupling modules and discusses advantages and concerns involved in positioning and sizing of source and receiver coils compared to conventional inductive coupling devices. Furthermore, the potential concern of tissue heating in the brain during operation of the wireless power transfer systems will also be addressed.
Synchronization of genetic oscillators
NASA Astrophysics Data System (ADS)
Zhou, Tianshou; Zhang, Jiajun; Yuan, Zhanjiang; Chen, Luonan
2008-09-01
Synchronization of genetic or cellular oscillators is a central topic in understanding the rhythmicity of living organisms at both molecular and cellular levels. Here, we show how a collective rhythm across a population of genetic oscillators through synchronization-induced intercellular communication is achieved, and how an ensemble of independent genetic oscillators is synchronized by a common noisy signaling molecule. Our main purpose is to elucidate various synchronization mechanisms from the viewpoint of dynamics, by investigating the effects of various biologically plausible couplings, several kinds of noise, and external stimuli. To have a comprehensive understanding on the synchronization of genetic oscillators, we consider three classes of genetic oscillators: smooth oscillators (exhibiting sine-like oscillations), relaxation oscillators (displaying jump dynamics), and stochastic oscillators (noise-induced oscillation). For every class, we further study two cases: with intercellular communication (including phase-attractive and repulsive coupling) and without communication between cells. We find that an ensemble of smooth oscillators has different synchronization phenomena from those in the case of relaxation oscillators, where noise plays a different but key role in synchronization. To show differences in synchronization between them, we make comparisons in many aspects. We also show that a population of genetic stochastic oscillators have their own synchronization mechanisms. In addition, we present interesting phenomena, e.g., for relaxation-type stochastic oscillators coupled to a quorum-sensing mechanism, different noise intensities can induce different periodic motions (i.e., inhomogeneous limit cycles).
Cooling Mechanical Oscillators by Coherent Control
NASA Astrophysics Data System (ADS)
Frimmer, Martin; Gieseler, Jan; Novotny, Lukas
2016-10-01
In optomechanics, electromagnetic fields are harnessed to control a single mode of a mechanically compliant system, while other mechanical degrees of freedom remain unaffected due to the modes' mutual orthogonality and high quality factor. Extension of the optical control beyond the directly addressed mode would require a controlled coupling between mechanical modes. Here, we introduce an optically controlled coupling between two oscillation modes of an optically levitated nanoparticle. We sympathetically cool one oscillation mode by coupling it coherently to the second mode, which is feedback cooled. Furthermore, we demonstrate coherent energy transfer between mechanical modes and discuss its application for ground-state cooling.
Marinelli, Agostino; Hemsing, Erik; Rosenzweig, James B.
2012-06-15
In this paper, we study the initial value problem of longitudinal plasma oscillations in a relativistic electron beam. Our analysis is based on the formalism developed in Marinelli et al.[Phys. Plasmas 18, 103105 (2011)]. We study the evolution of an arbitrary six-dimensional phase-space perturbation under the effect of longitudinal space-charge forces, with the inclusion of three-dimensional effects due to the finite size of the beam, transverse betatron motion, and longitudinal thermal motion induced by both energy-spread and transverse emittance. We expand the phase-space perturbation in a series of eigenmodes of a Schroedinger-like equation, corresponding to a set of propagating space-charge waves. We develop a general formalism, which we use to find explicit expressions for the evolution of an initial perturbation coupled to the fundamental plasma eigenmode. This work has important applications in the theory of space-charge instabilities in high brightness electron beams and control of shot-noise in seeded free-electron lasers. We discuss the application of the present theory to a specific experimental scenario corresponding to a shot-noise suppression scheme at optical wavelengths.
NASA Astrophysics Data System (ADS)
Jiao, Zongxia; Wang, Tianyi; Yan, Liang
2016-12-01
A linear oscillating motor is an electromagnetic actuator that can achieve short-stroke reciprocating movement directly without auxiliary transmission mechanisms. It has been widely used in linear pump applications as the source of power and motion. However, because of the demand of high power density in a linear actuation system, the performance of linear oscillating motors has been the focus of studies and deserves further research for high power density. In this paper, a general framework of linear oscillating motor design and optimization is addressed in detail, including the electromagnetic, dynamics, and thermal aspects. First, the electromagnetic and dynamics characteristics are modeled to reveal the principle for optimization. Then, optimization and analysis on magnetic structure, resonant system, and thermal features are conducted, which provide the foundation for prototype development. Finally, experimental results are provided for validation. As a whole, this process offers complete guidance for high power density linear oscillating motors in linear pump applications.
A drifting impact oscillator with periodic impulsive loading: Application to percussive drilling
NASA Astrophysics Data System (ADS)
Depouhon, A.; Denoël, V.; Detournay, E.
2013-09-01
Percussive drilling is extensively used to drill hard rocks in the earth resource industry, where it performs best compared to other drilling technologies. In this paper, we propose a novel model of the process that consists of a drifting oscillator under impulsive loading coupled with a bilinear force/penetration interface law, together with a kinetic energy threshold for continuous bit penetration. Following the formulation of the model, we analyze its steady-state response and show that there exists a parallel between theoretical and experimental predictions, as both exhibit a maximum of the average penetration rate with respect to the vertical load on bit. In addition, the existence of complex long-term dynamics with the coexistence of periodic solutions in certain parameter ranges is demonstrated.
Resonant tunnelling diode oscillator as an alternative LO for SIS receiver applications
NASA Technical Reports Server (NTRS)
Blundell, R.; Papa, D. C.; Brown, E. R.; Parker, C. D.
1993-01-01
The resonant tunnelling diode (RTD) oscillator has been demonstrated for the first time as a local oscillator (LO) in a heterodyne receiver. Noise measurements made on a sensitive 200 GHz superconductor-insulator-superconductor receiver using both a multiplied Gunn diode and an RTD oscillator as the LO revealed no difference in receiver noise as a function of oscillator type.
NASA Astrophysics Data System (ADS)
Corsaro, E.; De Ridder, J.
2014-11-01
Context. Thanks to the advent of the space-based missions CoRoT and NASA's Kepler, the asteroseismology of solar-like oscillations is now at the base of our understanding about stellar physics. The Kepler spacecraft, especially, is releasing excellent photometric observations of more than three years length in high duty cycle, which contain a large amount of information that has not yet been investigated. Aims: To exploit the full potential of Kepler light curves, sophisticated and robust analysis tools are now required more than ever. Characterizing single stars with an unprecedented level of accuracy and subsequently analyzing stellar populations in detail are fundamental to further constrain stellar structure and evolutionary models. Methods: We developed a new code, termed Diamonds, for Bayesian parameter estimation and model comparison by means of the nested sampling Monte Carlo (NSMC) algorithm, an efficient and powerful method very suitable for high-dimensional and multi-modal problems. A detailed description of the features implemented in the code is given with a focus on the novelties and differences with respect to other existing methods based on NSMC. Diamonds is then tested on the bright F8 V star KIC 9139163, a challenging target for peak-bagging analysis due to its large number of oscillation peaks observed, which are coupled to the blending that occurs between ℓ = 2,0 peaks, and the strong stellar background signal. We further strain the performance of the approach by adopting a 1147.5 days-long Kepler light curve, accounting for more than 840 000 data bins in the power spectrum of the star. Results: The Diamonds code is able to provide robust results for the peak-bagging analysis of KIC 9139163, while preserving a considerable computational efficiency for identifying the solution at the same time. We test the detection of different astrophysical backgrounds in the star and provide a criterion based on the Bayesian evidence for assessing the peak
Vecchiarelli, Anthony G; Li, Min; Mizuuchi, Michiyo; Hwang, Ling Chin; Seol, Yeonee; Neuman, Keir C; Mizuuchi, Kiyoshi
2016-03-15
The Escherichia coli Min system self-organizes into a cell-pole to cell-pole oscillator on the membrane to prevent divisions at the cell poles. Reconstituting the Min system on a lipid bilayer has contributed to elucidating the oscillatory mechanism. However, previous in vitro patterns were attained with protein densities on the bilayer far in excess of those in vivo and failed to recapitulate the standing wave oscillations observed in vivo. Here we studied Min protein patterning at limiting MinD concentrations reflecting the in vivo conditions. We identified "burst" patterns--radially expanding and imploding binding zones of MinD, accompanied by a peripheral ring of MinE. Bursts share several features with the in vivo dynamics of the Min system including standing wave oscillations. Our data support a patterning mechanism whereby the MinD-to-MinE ratio on the membrane acts as a toggle switch: recruiting and stabilizing MinD on the membrane when the ratio is high and releasing MinD from the membrane when the ratio is low. Coupling this toggle switch behavior with MinD depletion from the cytoplasm drives a self-organized standing wave oscillator.
NASA Astrophysics Data System (ADS)
Fallahazad, Babak; Movva, Hema Chandra Prakash; Kim, Kyounghwan; Larentis, Stefano; Taniguchi, Takashi; Watanabe, Kenji; Banerjee, Sanjay K.; Tutuc, Emanuel
We study the magnetotransport properties of high mobility holes in monolayer and bilayer WSe2, measured in dual-gated samples with top and bottom hexagonal boron-nitride dielectrics, and using platinum bottom contacts. Thanks to the Pt high work-function combined with the a high hole density induced electrostatically by an applied top gate bias, the contacts remain ohmic down to low (1.5 K) temperatures. The samples display well defined Shubnikov-de Haas (SdH) oscillations, and quantum Hall states (QHS) in high magnetic fields. In both mono and bilayer WSe2, the SdH oscillations and the QHSs occur predominantly at even filling factors, evincing a two-fold Landau level degeneracy consistent with spin-valley locking. The Fourier transform analysis of the SdH oscillations in dual-gated bilayer WSe2 reveal the presence of two subbands, each localized in the top or the bottom layer, as well as negative compressibility. From the temperature dependence of the SdH oscillation amplitude we determine a hole effective mass of 0.45me for both mono and bilayer WSe2. The top and bottom layer densities can be independently tuned using the top and bottom gates, respectively, evincing a weak interlayer coupling. This work has been supported by NRI-SWAN and Intel corporation.
Exchange coupling and its applications in magnetic data storage.
Li, Kebin; Wu, Yihong; Guo, Zaibing; Zheng, Yuankai; Han, Guchang; Qiu, Jinjun; Luo, Ping; An, Lihua; Zhou, Tiejun
2007-01-01
The continuing scaling of magnetic recording is facing more and more scientific and technological challenges because both the read sensor and recording bit are approaching sub-50 nm regime with the ever increasing areal density in hard disk drives. One of the key and indispensable elements for both high-sensitivity sensors and high-density media is the exchange bias between a ferromagnetic and an antiferromagnetic layer or the exchange coupling between two ferromagnets via a non-magnetic spacer. In the nanometer regime, the exchange coupling between ferromagnet and antiferromagnet or two ferromagnets through a conductive spacer is governed by the intergrain exchange interaction which has its origin in electron spins. Interlayer exchange coupling in multilayer or trilayer essentially originates from the quantum confinement effect. In this paper, we first review the physical origin and various theoretical models of the two types of exchange couplings, followed by a review of the applications of the exchange bias and interlayer exchange coupling in data storage with emphasis on the advanced read sensor and advanced media including perpendicular media and patterned media.