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Sample records for coupled oscillators application

  1. Method for determining a coupling function in coupled oscillators with application to Belousov-Zhabotinsky oscillators.

    PubMed

    Miyazaki, J; Kinoshita, S

    2006-11-01

    A coupling function that describes the interaction between self-sustained oscillators in a phase equation is derived and applied experimentally to Belousov-Zhabotinsky (BZ) oscillators. It is demonstrated that the synchronous behavior of coupled BZ reactors is explained extremely well in terms of the coupling function thus obtained. This method does not require comprehensive knowledge of either the oscillation mechanism or the interaction among the oscillators, both of these being often difficult to elucidate in an actual system. These facts enable us to accurately analyze the weakly coupled entrainment phenomenon through the direct measurement of the coupling function.

  2. Control of coupled oscillator networks with application to microgrid technologies.

    PubMed

    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.

  3. Control of coupled oscillator networks with application to microgrid technologies.

    PubMed

    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. PMID:26601231

  4. Control of coupled oscillator networks with application to microgrid technologies

    PubMed Central

    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

  5. Phase patterns of coupled oscillators with application to wireless communication

    SciTech Connect

    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.

  6. Investigation of coupled optical parametric oscillators for novel applications

    NASA Astrophysics Data System (ADS)

    Ding, Yujie J.

    2016-03-01

    In this proceedings article, we summarize our previous results on the novel applications using the coupled optical parametric oscillators (OPO's). In a conventional OPO, a single pump wavelength is capable of generating a pair of the signal and idler beams by placing a bulk nonlinear crystal inside an OPO cavity. When a nonlinear crystal composite consisting of periodically-inverted KTiOPO4 (KTP) plates bonded together by the adhesive-free-bonded (AFB) technique is used instead of the bulk nonlinear crystal, the optical parametric oscillation takes place at two sets of the new wavelengths for the signal and idler beams due to the phase shifts occurring at the interfaces of the adjacent domains making up the composite. These two sets of the signal and idler waves are effectively generated by the two OPO's being coupled to each other. These signals and idlers exhibit ultrastability in terms of their frequency separation. We review the progress made by us on the applications being realized by using such coupled OPO's such as THz generation and restoration of the blurred images after propagating through a distortion plate and a phase plate simulating atmospheric turbulence.

  7. 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.

  8. A review of recent developments in the application of coupled oscillators to phased array antennas

    NASA Technical Reports Server (NTRS)

    Pogorzelski, R. J.

    2002-01-01

    Some years ago it was proposed that an array of electronic oscillators coupled to nearest neighbors can be made to mutually injection lock and oscillate as an ensemble thus implementing spatial power combining.

  9. Coupled Oscillators with Chemotaxis

    NASA Astrophysics Data System (ADS)

    Sawai, Satoshi; Aizawa, Yoji

    1998-08-01

    A simple coupled oscillator system with chemotaxis is introducedto study morphogenesis of cellular slime molds. The modelsuccessfuly explains the migration of pseudoplasmodium which hasbeen experimentally predicted to be lead by cells with higherintrinsic frequencies. Results obtained predict that its velocityattains its maximum value in the interface region between totallocking and partial locking and also suggest possible rolesplayed by partial synchrony during multicellular development.

  10. Synchronization of oscillators coupled through an environment

    NASA Astrophysics Data System (ADS)

    Katriel, Guy

    2008-11-01

    We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate synchronization of systems of oscillators which are weakly coupled, in the sense that the influence of the oscillators on the environment is weak. We prove that arbitrarily weak coupling will synchronize the oscillators, provided that this coupling is of the ‘right’ sign. We illustrate our general results by applications to a model of coupled GnRH neuron oscillators proposed by Khadra and Li [A. Khadra, Y.X. Li, A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons, Biophys. J. 91 (2006) 74-83.], and to indirectly weakly-coupled λ- ω oscillators.

  11. 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.

  12. 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.

  13. 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.

  14. Estimation of coupling between oscillators from short time series via phase dynamics modeling: Limitations and application to EEG data

    NASA Astrophysics Data System (ADS)

    Smirnov, D. A.; Bodrov, M. B.; Velazquez, J. L. Perez; Wennberg, R. A.; Bezruchko, B. P.

    2005-06-01

    We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D. A. Smirnov and B. P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and nonvanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.

  15. Phase-response curves of coupled oscillators.

    PubMed

    Ko, Tae-Wook; Ermentrout, G Bard

    2009-01-01

    Many real oscillators are coupled to other oscillators, and the coupling can affect the response of the oscillators to stimuli. We investigate phase-response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked oscillators are analytically obtained in terms of the PRC for uncoupled oscillators and the coupling function of the system. Through simulation and analytic methods, the PRCs for globally coupled oscillators are also discussed.

  16. 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).

  17. 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.

  18. Coupled Oscillatory Systems with 𝔻4 Symmetry and Application to van der Pol Oscillators

    NASA Astrophysics Data System (ADS)

    Murza, Adrian C.; Yu, Pei

    In this paper, we study the dynamics of autonomous ODE systems with 𝔻4 symmetry. First, we consider eight weakly-coupled oscillators and establish the condition for the existence of stable heteroclinic cycles in most generic 𝔻4-equivariant systems. Then, we analyze the action of 𝔻4 on ℂ2 and study the pattern of periodic solutions arising from Hopf bifurcation. We identify the type of periodic solutions associated with the pairs (H,K) of spatiotemporal or spatial symmetries, and prove their existence by using the HmodK Theorem due to Hopf bifurcation and the 𝔻4 symmetry. In particular, we give a rigorous proof for the existence of a fourth branch of periodic solutions in 𝔻4-equivariant systems. Further, we apply our theory to study a concrete case: two coupled van der Pol oscillators with 𝔻4 symmetry. We use normal form theory to analyze the periodic solutions arising from Hopf bifurcation. Among the families of the periodic solutions, we pay particular attention to the phase-locked oscillations, each of them being embedded in one of the invariant manifolds, and identify the in-phase, completely synchronized motions. We derive their explicit expressions and analyze their stability in terms of the parameters.

  19. 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…

  20. Determination of a coupling function in multicoupled oscillators.

    PubMed

    Miyazaki, Jun; Kinoshita, Shuichi

    2006-05-19

    A new method to determine a coupling function in a phase model is theoretically derived for coupled self-sustained oscillators and applied to Belousov-Zhabotinsky (BZ) oscillators. The synchronous behavior of two coupled BZ reactors is explained extremely well in terms of the coupling function thus obtained. This method is expected to be applicable to weakly coupled multioscillator systems, in which mutual coupling among nearly identical oscillators occurs in a similar manner. The importance of higher-order harmonic terms involved in the coupling function is also discussed.

  1. Oscillation death in diffusively coupled oscillators by local repulsive link.

    PubMed

    Hens, C R; Olusola, Olasunkanmi I; Pal, Pinaki; Dana, Syamal K

    2013-09-01

    A death of oscillation is reported in a network of coupled synchronized oscillators in the presence of additional repulsive coupling. The repulsive link evolves as an averaging effect of mutual interaction between two neighboring oscillators due to a local fault and the number of repulsive links grows in time when the death scenario emerges. Analytical condition for oscillation death is derived for two coupled Landau-Stuart systems. Numerical results also confirm oscillation death in chaotic systems such as a Sprott system and the Rössler oscillator. We explore the effect in large networks of globally coupled oscillators and find that the number of repulsive links is always fewer than the size of the network.

  2. The Dynamics of Coupled Oscillator Phase Control

    NASA Technical Reports Server (NTRS)

    Pogorzelski, R. J.; Maccarini, P. F.; York, R. A.

    1998-01-01

    Arrays of coupled oscillators have been proposed as means of realizing high power rf sources via coherent spatial power combining. In such applications, a uniform phase distribution over the aperture is usually desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Of particular interest among those achievable are linear phase distributions because these result in steering of the output rf beam away from the broadside direction. The theory describing the behavior of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. However, a simplified theory has been developed which facilitates intuitive understanding. This simplified theory is based on a "continuum model" in which the aperture phase is represented by a continuous function of the aperture coordinates. A challenging aspect of the development of this theory is the derivation of appropriate boundary conditions at the edges or ends of the array.

  3. Phase Diffusion in Unequally Noisy Coupled Oscillators.

    PubMed

    Amro, Rami M; Lindner, Benjamin; Neiman, Alexander B

    2015-07-17

    We consider the dynamics of two directionally coupled unequally noisy oscillators, the first oscillator being noisier than the second oscillator. We derive analytically the phase diffusion coefficient of both oscillators in a heterogeneous setup (different frequencies, coupling coefficients, and intrinsic noise intensities) and show that the phase coherence of the second oscillator depends in a nonmonotonic fashion on the noise intensity of the first oscillator: as the first oscillator becomes less coherent, i.e., worse, the second one becomes more coherent, i.e., better. This surprising effect is related to the statistics of the first oscillator which provides a source of noise for the second oscillator, that is non-Gaussian, bounded, and possesses a finite bandwidth. We verify that the effect is robust by numerical simulations of two coupled FitzHugh-Nagumo models.

  4. Stochastic switching in delay-coupled oscillators.

    PubMed

    D'Huys, Otti; Jüngling, Thomas; Kinzel, Wolfgang

    2014-09-01

    A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators we reduce the delay system to a nondelayed Langevin equation, which allows us to analytically compute the distribution of frequencies and their corresponding residence times. The number of stable periodic orbits scales with the roundtrip delay time and coupling strength, but the noisy system visits only a fraction of the orbits, which scales with the square root of the delay time and is independent of the coupling strength. In contrast, the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators, and only weakly dependent on the coupling delay. Finally we investigate the effect of a detuning between the oscillators. We demonstrate the generality of our results with delay-coupled FitzHugh-Nagumo oscillators.

  5. Synchronization regimes in conjugate coupled chaotic oscillators.

    PubMed

    Karnatak, Rajat; Ramaswamy, Ram; Prasad, Awadhesh

    2009-09-01

    Nonlinear oscillators that are mutually coupled via dissimilar (or conjugate) variables display distinct regimes of synchronous behavior. In identical chaotic oscillators diffusively coupled in this manner, complete synchronization occurs only by chaos suppression when the coupled subsystems drive each other into a regime of periodic dynamics. Furthermore, the coupling does not vanish but acts as an "internal" drive. When the oscillators are mismatched, phase synchronization occurs, while in a master slave configuration, generalized synchrony results. These effects are demonstrated in a system of coupled chaotic Rossler oscillators.

  6. Generalizing the transition from amplitude to oscillation death in coupled oscillators.

    PubMed

    Zou, Wei; Senthilkumar, D V; Koseska, Aneta; Kurths, Jürgen

    2013-11-01

    Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching types in coupled nonlinear oscillators. The transition from AD to OD has been recently realized due to the interplay between heterogeneity and coupling strength [A. Koseska et al., Phys. Rev. Lett. 111, 024103 (2013)]. We identify here the transition from AD to OD in nonlinear oscillators with couplings of distinct natures. It is demonstrated that the presence of time delay in the coupling cannot induce such a transition in identical oscillators, but it can indeed facilitate its occurrence with a low degree of heterogeneity. Moreover, it is further shown that the AD to OD transition is reliably observed in identical oscillators with dynamic and conjugate couplings. The coexistence of AD and OD and rich stable OD configurations after the transition are revealed, which are of great significance for potential applications in physics, biology, and control studies.

  7. Complex mode dynamics of coupled wave oscillators.

    PubMed

    Alexander, T J; Yan, D; Kevrekidis, P G

    2013-12-01

    We explore how nonlinear coherent waves localized in a few wells of a periodic potential can act analogously to a chain of coupled oscillators. We identify the small-amplitude oscillation modes of these "coupled wave oscillators" and find that they can be extended into the large amplitude regime, where some "ring" for long times. We also reveal the appearance of complex behavior such as the breakdown of Josephson-like oscillations, the destabilization of fundamental oscillation modes, and the emergence of chaotic oscillations for large amplitude excitations. We show that the dynamics may be accurately described by a discrete model with nearest-neighbor coupling, in which the lattice oscillators bear an effective mass.

  8. Dynamical robustness of coupled heterogeneous oscillators.

    PubMed

    Tanaka, Gouhei; Morino, Kai; Daido, Hiroaki; Aihara, Kazuyuki

    2014-05-01

    We study tolerance of dynamic behavior in networks of coupled heterogeneous oscillators to deterioration of the individual oscillator components. As the deterioration proceeds with reduction in dynamic behavior of the oscillators, an order parameter evaluating the level of global oscillation decreases and then vanishes at a certain critical point. We present a method to analytically derive a general formula for this critical point and an approximate formula for the order parameter in the vicinity of the critical point in networks of coupled Stuart-Landau oscillators. Using the critical point as a measure for dynamical robustness of oscillator networks, we show that the more heterogeneous the oscillator components are, the more robust the oscillatory behavior of the network is to the component deterioration. This property is confirmed also in networks of Morris-Lecar neuron models coupled through electrical synapses. Our approach could provide a useful framework for theoretically understanding the role of population heterogeneity in robustness of biological networks.

  9. Averaging of globally coupled oscillators

    NASA Astrophysics Data System (ADS)

    Swift, James W.; Strogatz, Steven H.; Wiesenfeld, Kurt

    1992-03-01

    We study a specific system of symmetrically coupled oscillators using the method of averaging. The equations describe a series array of Josephson junctions. We concentrate on the dynamics near the splay-phase state (also known as the antiphase state, ponies on a merry-go-round, or rotating wave). We calculate the Floquet exponents of the splay-phase periodic orbit in the weak-coupling limit, and find that all of the Floquet exponents are purely imaginary; in fact, all the Floquet exponents are zero except for a single complex conjugate pair. Thus, nested two-tori of doubly periodic solutions surround the splay-phase state in the linearized averaged equations. We numerically integrate the original system, and find startling agreement with the averaging results on two counts: The observed ratio of frequencies is very close to the prediction, and the solutions of the full equations appear to be either periodic or doubly periodic, as they are in the averaged equations. Such behavior is quite surprising from the point of view of generic dynamical systems theory-one expects higher-dimensional tori and chaotic solutions. We show that the functional form of the equations, and not just their symmetry, is responsible for this nongeneric behavior.

  10. Capture into resonance of coupled Duffing oscillators

    NASA Astrophysics Data System (ADS)

    Kovaleva, Agnessa

    2015-08-01

    In this paper we investigate capture into resonance of a pair of coupled Duffing oscillators, one of which is excited by periodic forcing with a slowly varying frequency. Previous studies have shown that, under certain conditions, a single oscillator can be captured into persistent resonance with a permanently growing amplitude of oscillations (autoresonance). This paper demonstrates that the emergence of autoresonance in the forced oscillator may be insufficient to generate oscillations with increasing amplitude in the attachment. A parametric domain, in which both oscillators can be captured into resonance, is determined. The quasisteady states determining the growth of amplitudes are found. An agreement between the theoretical and numerical results is demonstrated.

  11. Capture into resonance of coupled Duffing oscillators.

    PubMed

    Kovaleva, Agnessa

    2015-08-01

    In this paper we investigate capture into resonance of a pair of coupled Duffing oscillators, one of which is excited by periodic forcing with a slowly varying frequency. Previous studies have shown that, under certain conditions, a single oscillator can be captured into persistent resonance with a permanently growing amplitude of oscillations (autoresonance). This paper demonstrates that the emergence of autoresonance in the forced oscillator may be insufficient to generate oscillations with increasing amplitude in the attachment. A parametric domain, in which both oscillators can be captured into resonance, is determined. The quasisteady states determining the growth of amplitudes are found. An agreement between the theoretical and numerical results is demonstrated. PMID:26382478

  12. Capture into resonance of coupled Duffing oscillators.

    PubMed

    Kovaleva, Agnessa

    2015-08-01

    In this paper we investigate capture into resonance of a pair of coupled Duffing oscillators, one of which is excited by periodic forcing with a slowly varying frequency. Previous studies have shown that, under certain conditions, a single oscillator can be captured into persistent resonance with a permanently growing amplitude of oscillations (autoresonance). This paper demonstrates that the emergence of autoresonance in the forced oscillator may be insufficient to generate oscillations with increasing amplitude in the attachment. A parametric domain, in which both oscillators can be captured into resonance, is determined. The quasisteady states determining the growth of amplitudes are found. An agreement between the theoretical and numerical results is demonstrated.

  13. Transitory behaviors in diffusively coupled nonlinear oscillators.

    PubMed

    Tadokoro, Satoru; Yamaguti, Yutaka; Fujii, Hiroshi; Tsuda, Ichiro

    2011-03-01

    We study collective behaviors of diffusively coupled oscillators which exhibit out-of-phase synchrony for the case of weakly interacting two oscillators. In large populations of such oscillators interacting via one-dimensionally nearest neighbor couplings, there appear various collective behaviors depending on the coupling strength, regardless of the number of oscillators. Among others, we focus on an intermittent behavior consisting of the all-synchronized state, a weakly chaotic state and some sorts of metachronal waves. Here, a metachronal wave means a wave with orderly phase shifts of oscillations. Such phase shifts are produced by the dephasing interaction which produces the out-of-phase synchronized states in two coupled oscillators. We also show that the abovementioned intermittent behavior can be interpreted as in-out intermittency where two saddles on an invariant subspace, the all-synchronized state and one of the metachronal waves play an important role.

  14. A Fresh Look at Coupled-Oscillator Spatial Power Combining

    NASA Technical Reports Server (NTRS)

    Pearson, L.W.; Pogorzelski, R. J.

    1998-01-01

    Quasi-optical oscillators were proposed a little more than ten years ago as a means of developing the power levels needed for applications at millimeter frequencies using large numbers of individual semiconductor devices each of which produces only a modest amount of power [J.W. Mink, IEEE Trans. MTT., vol. 34, p. 273, 19861. An operating system was demonstrated soon after [Z.B. Popovic et. al, Int. J. Infrared and Millimeter Waves, v. 9, p. 647, 1988] in the form of a so-called grid oscillator. This device constituted a rectangular array of oscillating devices that are mutually coupled so that they oscillator coherently. The interconnecting lines in one direction serve as radiators so that the oscillators radiate directly, and the radiated fields add. Subsequently, coupled oscillators using resonant transmission line lengths was demonstrated by Mortazawi and Itoh [IEEE Trans. MTT., vol. 38, p. 86,1990). In recent work, coupled-oscillator power combiners have received less attention, with amplifier/combiners receiving more attention. Specific weaknesses of spatial-combining oscillators have motivated this transition. Namely, the oscillators employ low-Q resonators (resulting in low signal quality) and no clear means of modulation has been identified until recently. In this presentation, we review coupled-oscillator combiners in broad terms, indicating the features that make particular systems viable. We indicate how these features can be reconciled to functional requirements for system applications. Comparisons are drawn between two approaches to obtain mutual coupling: One employs low-Q oscillator circuits at each site, with concomitantly high propensity for the oscillators to couple. The other approach employs moderate-Q oscillators at each site with the concomitant requirement to tune the oscillators so that they share a range of frequencies over which they can couple and lock. In either case, precise frequency control and modulation can be achieved through

  15. 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.

  16. Collective phase response curves for heterogeneous coupled oscillators.

    PubMed

    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.

  17. Oscillation death in asymmetrically delay-coupled oscillators.

    PubMed

    Zou, Wei; Tang, Yang; Li, Lixiang; Kurths, Jürgen

    2012-04-01

    Symmetrically coupled oscillators represent a limiting case for studying the dynamics of natural systems. Therefore, we here investigate the effect of coupling asymmetry on delay-induced oscillation death (OD) in coupled nonlinear oscillators. It is found that the asymmetrical coupling substantially enlarges the domain of the OD island in the parameter space. Specifically, when the intensity of asymmetry is enhanced by turning down the value of the coupling asymmetry parameter α, the OD island gradually expands along two directions of both the coupling delay and the coupling strength. The expansion behavior of the OD region is well characterized by a power law scaling, R=α(γ) with γ≈-1.19. The minimum value of the intrinsic frequency, for which OD is possible, monotonically decreases with decreasing α and saturates around a constant value in the limit of α→0. The generality of the conducive effect of coupling asymmetry is confirmed in a numerical study of two delay-coupled chaotic Rössler oscillators. Our findings shed an improved light on the understanding of dynamics in asymmetrically delay-coupled systems.

  18. A Simplified Theory of Coupled Oscillator Array Phase Control

    NASA Technical Reports Server (NTRS)

    Pogorzelski, R. J.; York, R. A.

    1997-01-01

    Linear and planar arrays of coupled oscillators have been proposed as means of achieving high power rf sources through coherent spatial power combining. In such - applications, a uniform phase distribution over the aperture is desired. However, it has been shown that by detuning some of the oscillators away from the oscillation frequency of the ensemble of oscillators, one may achieve other useful aperture phase distributions. Notable among these are linear phase distributions resulting in steering of the output rf beam away from the broadside direction. The theory describing the operation of such arrays of coupled oscillators is quite complicated since the phenomena involved are inherently nonlinear. This has made it difficult to develop an intuitive understanding of the impact of oscillator tuning on phase control and has thus impeded practical application. In this work a simpl!fied theory is developed which facilitates intuitive understanding by establishing an analog of the phase control problem in terms of electrostatics.

  19. 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.

  20. Reentrant transition in coupled noisy oscillators.

    PubMed

    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. PMID:25679676

  1. Synchronization in chaotic oscillators by cyclic coupling

    NASA Astrophysics Data System (ADS)

    Olusola, O. I.; Njah, A. N.; Dana, S. K.

    2013-07-01

    We introduce a type of cyclic coupling to investigate synchronization of chaotic oscillators. We derive analytical solutions of the critical coupling for stable synchronization under the cyclic coupling for the Rössler system and the Lorenz oscillator as paradigmatic illustration. Based on the master stability function (MSF) approach, the analytical results on critical coupling are verified numerically. An enhancing effect in terms of lowering the critical coupling or enlarging the synchronization window in a critical coupling space is noticed. The cyclic coupling is also applied in other models, Hindmarsh-Rose model, Sprott system, Chen system and forced Duffing system to confirm the enhancing effect. The cyclic coupling allows tuning of two coupling constants in reverse directions when an optimal control of synchronization is feasible.

  2. Recent Developments in the Analysis of Couple Oscillator Arrays

    NASA Technical Reports Server (NTRS)

    Pogorzelski, Ronald J.

    2000-01-01

    This presentation considers linear arrays of coupled oscillators. Our purpose in coupling oscillators together is to achieve high radiated power through the spatial power combining which results when the oscillators are injection locked to each other. York, et. al. have shown that, left to themselves, the ensemble of injection locked oscillators oscillate at the average of the tuning frequencies of all the oscillators. Coupling these arrays achieves high radiated power through coherent spatial power combining. The coupled oscillators are usually designed to produce constant aperture phase. Oscillators are injection locked to each other or to a master oscillator to produce coherent radiation. Oscillators do not necessarily oscillate at their tuning frequency.

  3. Pulse-coupled BZ oscillators with unequal coupling strengths.

    PubMed

    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.

  4. 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.

  5. Arrays of coupled chemical oscillators.

    PubMed

    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

  6. Arrays of coupled chemical oscillators

    PubMed Central

    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

  7. Arrays of coupled chemical oscillators.

    PubMed

    Forrester, Derek Michael

    2015-11-19

    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.

  8. Chimera States in populations of nonlocally coupled chemical oscillators.

    PubMed

    Nkomo, Simbarashe; Tinsley, Mark R; Showalter, Kenneth

    2013-06-14

    Chimera states occur spontaneously in populations of coupled photosensitive chemical oscillators. Experiments and simulations are carried out on nonlocally coupled oscillators, with the coupling strength decreasing exponentially with distance. Chimera states with synchronized oscillators, phase waves, and phase clusters coexisting with unsynchronized oscillators are analyzed. Irregular motion of the cores of asynchronous oscillators is found in spiral-wave chimeras.

  9. Oscillations death revisited; coupling of identical chemical oscillators.

    PubMed

    Bar-Eli, Kedma

    2011-06-28

    The coupling of identical reactors containing chemical oscillators is discussed. The coupling is executed by means of transferring chemical species from one cell (reactor) to the other in a diffusion like manner i.e. in proportion to the concentration difference between the cells. The coupling rate constant, however, is the same for all species. The individual, uncoupled, cells may be oscillating or in a stable steady state (the same for all reactors). In both cases, depending on the initial conditions, the symmetry breaks, and the cells may end up-contrary to intuition-in a stable steady state in which the final concentrations are not equal in the various reactors. The Brusselator and Oregonator mechanisms are examined and they behave in the manner described. On the other hand, the Lotka-Volterra mechanism, being conservative, keeps, when coupled, only the homogeneous solutions. PMID:21594295

  10. Designing the Dynamics of Globally Coupled Oscillators

    NASA Astrophysics Data System (ADS)

    Orosz, G.; Moehlis, J.; Ashwin, P.

    2009-09-01

    A method for designing cluster states with prescribed stability is presented for coupled phase oscillator systems with all-to-all coupling. We determine criteria for the coupling function that ensure the existence and stability of a large variety of clustered configurations. We show that such criteria can be satisfied by choosing Fourier coefficients of the coupling function. We demonstrate that using simple trigonometric and localized coupling functions one can realize arbitrary patterns of stable clusters and that the designed systems are capable of performing finite state computation. The design principles may be relevant when engineering complex dynamical behavior of coupled systems, e.g. the emergent dynamics of artificial neural networks, coupled chemical oscillators and robotic swarms.

  11. Synchronization of coupled Boolean phase oscillators.

    PubMed

    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.

  12. Autoresonance versus localization in weakly coupled oscillators

    NASA Astrophysics Data System (ADS)

    Kovaleva, Agnessa; Manevitch, Leonid I.

    2016-04-01

    We study formation of autoresonance (AR) in a two-degree of freedom oscillator array including a nonlinear (Duffing) oscillator (the actuator) weakly coupled to a linear attachment. Two classes of systems are studied. In the first class of systems, a periodic force with constant (resonance) frequency is applied to a nonlinear oscillator (actuator) with slowly time-decreasing stiffness. In the systems of the second class a nonlinear time-invariant oscillator is subjected to an excitation with slowly increasing frequency. In both cases, the attached linear oscillator and linear coupling are time-invariant, and the system is initially engaged in resonance. This paper demonstrates that in the systems of the first type AR in the nonlinear actuator entails oscillations with growing amplitudes in the linear attachment while in the system of the second type energy transfer from the nonlinear actuator is insufficient to excite high-energy oscillations of the attachment. It is also shown that a slow change of stiffness may enhance the response of the actuator and make it sufficient to support oscillations with growing energy in the attachment even beyond the linear resonance. Explicit asymptotic approximations of the solutions are obtained. Close proximity of the derived approximations to exact (numerical) results is demonstrated.

  13. Dispersion dipoles for coupled Drude oscillators.

    PubMed

    Odbadrakh, Tuguldur T; Jordan, Kenneth D

    2016-01-21

    We present the dispersion-induced dipole moments of coupled Drude oscillators obtained from two approaches. The first approach evaluates the dipole moment using the second-order Rayleigh-Schrödinger perturbation theory wave function allowing for dipole-dipole and dipole-quadrupole coupling. The second approach, based on response theory, employs an integral of the dipole-dipole polarizability of one oscillator and the dipole-dipole-quadrupole hyperpolarizability of the other oscillator over imaginary frequencies. The resulting dispersion dipoles exhibit an R(-7) dependence on the separation between the two oscillators and are connected to the leading-order C6/R(6) dispersion energy through the electrostatic Hellmann-Feynman theorem. PMID:26801024

  14. Dispersion dipoles for coupled Drude oscillators.

    PubMed

    Odbadrakh, Tuguldur T; Jordan, Kenneth D

    2016-01-21

    We present the dispersion-induced dipole moments of coupled Drude oscillators obtained from two approaches. The first approach evaluates the dipole moment using the second-order Rayleigh-Schrödinger perturbation theory wave function allowing for dipole-dipole and dipole-quadrupole coupling. The second approach, based on response theory, employs an integral of the dipole-dipole polarizability of one oscillator and the dipole-dipole-quadrupole hyperpolarizability of the other oscillator over imaginary frequencies. The resulting dispersion dipoles exhibit an R(-7) dependence on the separation between the two oscillators and are connected to the leading-order C6/R(6) dispersion energy through the electrostatic Hellmann-Feynman theorem.

  15. Mode coupling in spin torque oscillators

    NASA Astrophysics Data System (ADS)

    Zhang, Steven S.-L.; Zhou, Yan; Li, Dong; Heinonen, Olle

    2016-09-01

    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. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature.

  16. Susceptibility of large populations of coupled oscillators.

    PubMed

    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.

  17. Deck the Halls. Animated Displays: Coupled Mechanical Oscillators.

    ERIC Educational Resources Information Center

    Pizzo, Joe, Ed.

    1992-01-01

    Describes a set of displays on the theme of coupled mechanical oscillators. Displays encompass three common demonstrations: (1) a coupled pair of identical pendulums; (2) a multiple-pendulum resonance demonstration; and (3) a Wilberforce coupled oscillator. (MDH)

  18. 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.

  19. Dynamics of weakly coupled parametrically forced oscillators

    NASA Astrophysics Data System (ADS)

    Salgado Sánchez, P.; Porter, J.; Tinao, I.; Laverón-Simavilla, A.

    2016-08-01

    The dynamics of two weakly coupled parametric oscillators are studied in the neighborhood of the primary subharmonic instability. The nature of both primary and secondary instabilities depends in a critical way on the permutation symmetries, if any, that remain after coupling is considered, and this depends on the relative phases of the parametric forcing terms. Detailed bifurcation sets, revealing a complex series of transitions organized in part by Bogdanov-Takens points, are calculated for representative sets of parameters. In the particular case of out-of-phase forcing the predictions of the coupled oscillator model are compared with direct numerical simulations and with recent experiments on modulated cross waves. Both the initial Hopf bifurcation and the subsequent saddle-node heteroclinic bifurcation are confirmed.

  20. Dynamics of weakly coupled parametrically forced oscillators.

    PubMed

    Salgado Sánchez, P; Porter, J; Tinao, I; Laverón-Simavilla, A

    2016-08-01

    The dynamics of two weakly coupled parametric oscillators are studied in the neighborhood of the primary subharmonic instability. The nature of both primary and secondary instabilities depends in a critical way on the permutation symmetries, if any, that remain after coupling is considered, and this depends on the relative phases of the parametric forcing terms. Detailed bifurcation sets, revealing a complex series of transitions organized in part by Bogdanov-Takens points, are calculated for representative sets of parameters. In the particular case of out-of-phase forcing the predictions of the coupled oscillator model are compared with direct numerical simulations and with recent experiments on modulated cross waves. Both the initial Hopf bifurcation and the subsequent saddle-node heteroclinic bifurcation are confirmed.

  1. 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

  2. Wave formation by time delays in randomly coupled oscillators.

    PubMed

    Ko, Tae-Wook; Jeong, Seong-Ok; Moon, Hie-Tae

    2004-05-01

    We study the dynamics of randomly coupled oscillators when interactions between oscillators are time delayed due to the finite and constant speed of coupling signals. Numerical simulations show that the time delays, proportional to the Euclidean distances between interacting oscillators, can induce near regular waves in addition to near in-phase synchronous oscillations even though oscillators are randomly coupled. We discuss the stability conditions for the wave states and the in-phase synchronous states.

  3. 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

  4. 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.

  5. Heterogeneity of time delays determines synchronization of coupled oscillators

    NASA Astrophysics Data System (ADS)

    Petkoski, Spase; Spiegler, Andreas; Proix, Timothée; Aram, Parham; Temprado, Jean-Jacques; Jirsa, Viktor K.

    2016-07-01

    Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.

  6. Heterogeneity of time delays determines synchronization of coupled oscillators.

    PubMed

    Petkoski, Spase; Spiegler, Andreas; Proix, Timothée; Aram, Parham; Temprado, Jean-Jacques; Jirsa, Viktor K

    2016-07-01

    Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations. PMID:27575125

  7. Heterogeneity of time delays determines synchronization of coupled oscillators.

    PubMed

    Petkoski, Spase; Spiegler, Andreas; Proix, Timothée; Aram, Parham; Temprado, Jean-Jacques; Jirsa, Viktor K

    2016-07-01

    Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial distribution of time delays with regard to synchronization, by decomposing it into patterns and therefore reducing the stability analysis into the tractable problem of a finite set of delay-coupled differential equations. We analyze delay-structured networks of phase oscillators and we find that, depending on the heterogeneity of the delays, the oscillators group in phase-shifted, anti-phase, steady, and non-stationary clusters, and analytically compute their stability boundaries. These results find direct application in the study of brain oscillations.

  8. Isochronal chaos synchronization of delay-coupled optoelectronic oscillators.

    PubMed

    Illing, Lucas; Panda, Cristian D; Shareshian, Lauren

    2011-07-01

    We study experimentally chaos synchronization of nonlinear optoelectronic oscillators with time-delayed mutual coupling and self-feedback. Coupling three oscillators in a chain, we find that the outer two oscillators always synchronize. In contrast, isochronal synchronization of the mediating middle oscillator is found only when self-feedback is added to the middle oscillator. We show how the stability of the isochronal solution of any network, including the case of three coupled oscillators, can be determined by measuring the synchronization threshold of two unidirectionally coupled systems. In addition, we provide a sufficient condition that guarantees global asymptotic stability of the synchronized solution.

  9. Dynamics of learning in coupled oscillators tutored with delayed reinforcements.

    PubMed

    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.

  10. 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.

  11. Dynamics of learning in coupled oscillators tutored with delayed reinforcements.

    PubMed

    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. PMID:16090001

  12. Synchronization between two weakly coupled delay-line oscillators.

    PubMed

    Levy, Etgar C; Horowitz, Moshe

    2012-12-01

    We study theoretically the generation of a continuous-wave signal by two weakly coupled delay-line oscillators. In such oscillators, the cavity length is longer than the wavelength of the signal. We show by using an analytical solution and comprehensive numerical simulations that in delay-line oscillators, the dynamics of the amplitude response cannot be neglected even when the coupling between the oscillators is weak. Therefore, weakly coupled delay-line oscillators cannot be accurately modeled by using coupled phase-oscillator models. In particular, we show that synchronization between the oscillators can be obtained in cases that are not allowed by coupled phase-oscillator models. We study the stability of the continuous-wave solutions. In delay-line oscillators, several cavity modes can potentially oscillate. To ensure stability, the bandwidth of the delay-line oscillator should be limited. We show that the weakly coupled delay-line oscillator model that is described in this paper can be used to accurately model the synchronization between two weakly coupled optoelectronic oscillators. A very good quantitative agreement is obtained between a comprehensive numerical model to study optoelectronic oscillators and the model results given in this paper.

  13. Predicting synchrony in heterogeneous pulse coupled oscillators.

    PubMed

    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.

  14. Four mass coupled oscillator guitar model.

    PubMed

    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.

  15. Four mass coupled oscillator guitar model.

    PubMed

    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. PMID:22280705

  16. Energy current magnification in coupled oscillator loops

    NASA Astrophysics Data System (ADS)

    Marathe, Rahul; Dhar, Abhishek; Jayannavar, A. M.

    2010-09-01

    Motivated by studies on current magnification in quantum mesoscopic systems, we consider sound and heat transmission in classical models of oscillator chains. A loop of coupled oscillators is connected to two leads through which one can either transmit monochromatic waves or white-noise signal from heat baths. We look for the possibility of current magnification in this system due to some asymmetry introduced between the two arms in the loop. We find that current magnification is indeed obtained for particular frequency ranges. However, the integrated current shows the effect only in the presence of a pinning potential for the atoms in the leads. We also study the effect of anharmonicity on current magnification.

  17. Reconstruction of two-dimensional phase dynamics from experiments on coupled oscillators.

    PubMed

    Blaha, Karen A; Pikovsky, Arkady; Rosenblum, Michael; Clark, Matthew T; Rusin, Craig G; Hudson, John L

    2011-10-01

    Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the two-dimensional approach relative to the one-dimensional approach using phase difference. We quantify the dependence of the coupling functions on the coupling magnitude and coupling time delay. We show differences in synchronization predictions of the two models using a toy model. We show that the two-dimensional approach reveals behavior not detected by the one-dimensional model in a driven experimental oscillator. This approach is broadly applicable to quantify interactions between nonlinear oscillators, especially where intrinsic oscillator sensitivity and coupling evolve with time.

  18. Quantum dissipative effect of one dimension coupled anharmonic oscillator

    SciTech Connect

    Sulaiman, A.; Zen, Freddy P.

    2015-04-16

    Quantum dissipative effect of one dimension coupled anharmonic oscillator is investigated. The systems are two coupled harmonic oscillator with the different masses. The dissipative effect is studied based on the quantum state diffusion formalism. The result show that the anharmonic effect increase the amplitude but the lifetime of the oscillation depend on the damping coefficient and do not depend on the temperature.

  19. Control of Oscillation Patterns in a Symmetric Coupled Biological Oscillator System

    NASA Astrophysics Data System (ADS)

    Takamatsu, Atsuko; Tanaka, Reiko; Yamamoto, Takatoki; Fujii, Teruo

    2003-08-01

    A chain of three-oscillator system was constructed with living biological oscillators of phasmodial slime mold, Physarum polycehalum and the oscillation patterns were analyzed by the symmetric Hopf bifurcation theory using group theory. Multi-stability of oscillation patterns was observed, even when the coupling strength was fixed. This suggests that the coupling strength is not an effective parameter to obtain a desired oscillation pattern among the multiple patterns. Here we propose a method to control oscillation patterns using resonance to external stimulus and demonstrate pattern switching induced by frequency resonance given to only one of oscillators in the system.

  20. The Coupled Harmonic Oscillator: Not Just for Seniors Anymore.

    ERIC Educational Resources Information Center

    Preyer, Norris W.

    1996-01-01

    Presents experiments that use Microcomputer Based Laboratory (MBL) techniques to enable freshmen physics students to investigate complex systems, such as nonlinear oscillators or coupled harmonic oscillators, at a level appropriate for an independent project. (JRH)

  1. 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.

  2. Spontaneous mode switching in coupled oscillators competing for constant amounts of resources

    NASA Astrophysics Data System (ADS)

    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.

  3. Spontaneous mode switching in coupled oscillators competing for constant amounts of resources.

    PubMed

    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. PMID:20370272

  4. 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.

  5. Chaos in generically coupled phase oscillator networks with nonpairwise interactions

    NASA Astrophysics Data System (ADS)

    Bick, Christian; Ashwin, Peter; Rodrigues, Ana

    2016-09-01

    The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling—including three and four-way interactions of the oscillator phases—that appears generically at the next order in normal-form based calculations can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.

  6. Dynamical recurrence and the quantum control of coupled oscillators.

    PubMed

    Genoni, Marco G; Serafini, Alessio; Kim, M S; Burgarth, Daniel

    2012-04-13

    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.

  7. Non-conventional synchronization of weakly coupled active oscillators

    NASA Astrophysics Data System (ADS)

    Manevitch, L. I.; Kovaleva, M. A.; Pilipchuk, V. N.

    2013-03-01

    We present a new type of self-sustained vibrations in the fundamental physical model covering a broad area of applications from wave generation in radiophysics and nonlinear optics to the heart muscle contraction and eyesight disorder in biophysics. Such a diversity of applications is due to the universal physical phenomenon of synchronization. Previous studies of this phenomenon, originating from Huygens famous observation, are based mainly on the model of two weakly coupled Van der Pol oscillators and usually deal with their synchronization in the regimes close to nonlinear normal modes (NNMs). In this work, we show for the first time that, in the important case of threshold excitation, an alternative synchronization mechanism can develop when the conventional synchronization becomes impossible. We identify this mechanism as an appearance of dynamic attractor with the complete periodic energy exchange between the oscillators, which is the dissipative analogue of highly intensive beats in a conservative system. This type of motion is therefore opposite to the NNM-type synchronization with no energy exchange by definition. The analytical description of these vibrations employs the concept of Limiting Phase Trajectories (LPTs) introduced by one of the authors earlier for conservative systems. Finally, within the LPT approach, we describe the transition from the complete energy exchange between the oscillators to the energy localization mostly on one of the two oscillators. The localized mode is an attractor in the range of model parameters wherein the LPT as well as the in-phase and out-of-phase NNMs become unstable.

  8. Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators.

    PubMed

    Zhou, Brian B; Roy, Rajarshi

    2007-02-01

    We propose a basic mechanism for isochronal synchrony and communication with mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators, mutually coupled with a propagation delay, synchronize isochronally when both are symmetrically driven by a third Ikeda oscillator. This synchronous operation, unstable in the two delay-coupled oscillators alone, facilitates simultaneous, bidirectional communication of messages with chaotic carrier wave forms. This approach to combine both bidirectional and unidirectional coupling represents an application of generalized synchronization using a mediating drive signal for a spatially distributed and internally synchronized multicomponent system.

  9. 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.

  10. 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.

  11. 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…

  12. Cooperative dynamics in coupled systems of fast and slow phase oscillators.

    PubMed

    Sakaguchi, Hidetsugu; Okita, Takayuki

    2016-02-01

    We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasiperiodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is derived using the Ott-Antonsen ansatz. The applicability of the ansatz is checked by the comparison of numerical results of the coupled oscillator system and the reduced low-dimensional equation. We investigate further several interesting phenomena in which mutual interactions between the fast and slow oscillators play an essential role. Fast oscillations appear intermittently as a result of excitatory interactions with slow oscillators in a certain parameter range. Slow oscillators experience an oscillator-death phenomenon owing to their interaction with fast oscillators. This oscillator death is explained as a result of saddle-node bifurcation in a simple phase equation obtained using the temporal average of the fast oscillations. Finally, we show macroscopic synchronization of the order 1:m between the slow and fast oscillators.

  13. Dynamics of a network of phase oscillators with plastic couplings

    NASA Astrophysics Data System (ADS)

    Nekorkin, V. I.; Kasatkin, D. V.

    2016-06-01

    The processes of synchronization and phase cluster formation are investigated in a complex network of dynamically coupled phase oscillators. Coupling weights evolve dynamically depending on the phase relations between the oscillators. It is shown that the network exhibits several types of behavior: the globally synchronized state, two-cluster and multi-cluster states, different synchronous states with a fixed phase relationship between the oscillators and chaotic desynchronized state.

  14. Effect of mixed coupling on relay-coupled Rössler and Lorenz oscillators.

    PubMed

    Sharma, Amit; Shrimali, Manish Dev; Aihara, K

    2014-12-01

    The complete synchronization between the outermost oscillators using the mixed coupling in relay coupled systems is studied. Mixed coupling has two types of coupling functions: coupling between similar or dissimilar variables. We examine the complete synchronization in relay-coupled systems by the largest transverse Lyapunov exponent and synchronization error. We show numerically for Rössler and Lorenz oscillators that the combination of these two types of coupling functions is able to decrease the critical coupling strength for complete synchronization as well as it also suppress oscillations for larger coupling strength.

  15. Amplitude death of identical oscillators in networks with direct coupling.

    PubMed

    Illing, Lucas

    2016-08-01

    It is known that amplitude death can occur in networks of coupled identical oscillators if they interact via diffusive time-delayed coupling links. Here we consider networks of oscillators that interact via direct time-delayed coupling links. It is shown analytically that amplitude death is impossible for directly coupled Stuart-Landau oscillators, in contradistinction to the case of diffusive coupling. We demonstrate that amplitude death in the strict sense does become possible in directly coupled networks if the node dynamics is governed by second-order delay differential equations. Finally, we analyze in detail directly coupled nodes whose dynamics are described by first-order delay differential equations and find that, while amplitude death in the strict sense is impossible, other interesting oscillation quenching scenarios exist. PMID:27627306

  16. Amplitude death of identical oscillators in networks with direct coupling

    NASA Astrophysics Data System (ADS)

    Illing, Lucas

    2016-08-01

    It is known that amplitude death can occur in networks of coupled identical oscillators if they interact via diffusive time-delayed coupling links. Here we consider networks of oscillators that interact via direct time-delayed coupling links. It is shown analytically that amplitude death is impossible for directly coupled Stuart-Landau oscillators, in contradistinction to the case of diffusive coupling. We demonstrate that amplitude death in the strict sense does become possible in directly coupled networks if the node dynamics is governed by second-order delay differential equations. Finally, we analyze in detail directly coupled nodes whose dynamics are described by first-order delay differential equations and find that, while amplitude death in the strict sense is impossible, other interesting oscillation quenching scenarios exist.

  17. Stable and transient multicluster oscillation death in nonlocally coupled networks.

    PubMed

    Schneider, Isabelle; Kapeller, Marie; Loos, Sarah; Zakharova, Anna; Fiedler, Bernold; Schöll, Eckehard

    2015-11-01

    In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multicluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation, which works well for large coupling ranges but fails for coupling ranges, which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results. PMID:26651770

  18. Stable and transient multicluster oscillation death in nonlocally coupled networks

    NASA Astrophysics Data System (ADS)

    Schneider, Isabelle; Kapeller, Marie; Loos, Sarah; Zakharova, Anna; Fiedler, Bernold; Schöll, Eckehard

    2015-11-01

    In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multicluster patterns, depending on the cluster distribution prescribed by the initial conditions. Besides stable oscillation death, we also find a regime of long transients asymptotically approaching synchronized oscillations. To explain these phenomena analytically in dependence on the coupling range and the coupling strength, we first use a mean-field approximation, which works well for large coupling ranges but fails for coupling ranges, which are small compared to the cluster size. Going beyond standard mean-field theory, we predict the boundaries of the different stability regimes as well as the transient times analytically in excellent agreement with numerical results.

  19. 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.

  20. Coevolution of synchronous activity and connectivity in coupled chaotic oscillators.

    PubMed

    Chen, Li; Qiu, Can; Huang, Hongbin; Qi, Guanxiao; Wang, Haijun

    2010-11-01

    We investigate the coevolution dynamics of node activities and coupling strengths in coupled chaotic oscillators via a simple threshold adaptive scheme. The coupling strength is synchronous activity regulated, which in turn is able to boost the synchronization remarkably. In the case of weak coupling, the globally coupled oscillators present a highly clustered functional connectivity with a power-law distribution in the tail with γ≃3.1 , while for strong coupling, they self-organize into a network with a heterogeneously rich connectivity at the onset of synchronization but exhibit rather sparse structure to maintain the synchronization in noisy environment. The relevance of the results is briefly discussed.

  1. 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.

  2. Symmetry-broken states on networks of coupled oscillators.

    PubMed

    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.

  3. Coupling cold atoms with mechanical oscillators

    NASA Astrophysics Data System (ADS)

    Montoya, Cris; Valencia, Jose; Geraci, Andrew; Eardley, Matthew; Kitching, John

    2014-05-01

    Macroscopic systems, coupled to quantum systems with well understood coherence properties, can enable the study of the boundary between quantum microscopic phenomena and macroscopic systems. Ultra-cold atoms can be probed and manipulated with micro-mechanical resonators that provide single-spin sensitivity and sub-micron spatial resolution, facilitating studies of decoherence and quantum control. In the future, hybrid quantum systems consisting of cold atoms interfaced with mechanical devices may have applications in quantum information science. We describe our experiment to couple laser-cooled Rb atoms to a magnetic cantilever tip. This cantilever is precisely defined on the surface of a chip with lithography and the atoms are trapped at micron-scale distances from this chip. To match cantilever mechanical resonances, atomic magnetic resonances are tuned with a magnetic field.

  4. Spontaneous oscillations in two 2-component cells coupled by diffusion.

    PubMed

    Alexander, J C

    1986-01-01

    Mathematical examples are presented of oscillators with two variables which do not oscillate in isolation, but which do oscillate stably when coupled with a twin via diffusion. Two examples are presented, the Lefever-Prigogine Brusselator and a system used to model glycolytic oscillations. The mathematical method is not the usual bifurcation theory, but rather a type of singular perturbation theory combined with bifurcation theory. For both examples, it is shown that all stationary solutions are unstable for appropriate parameter settings. In the case of the Brusselator, it is further shown that there exist limit cycles; i.e. stable oscillations, in this parameter range. A numerical example is presented. PMID:3958635

  5. Nonlinear transient waves in coupled phase oscillators with inertia

    NASA Astrophysics Data System (ADS)

    Jörg, David J.

    2015-05-01

    Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.

  6. Nonlinear transient waves in coupled phase oscillators with inertia.

    PubMed

    Jörg, David J

    2015-05-01

    Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.

  7. 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.

  8. Statistics of Lyapunov exponent spectrum in randomly coupled Kuramoto oscillators.

    PubMed

    Patra, Soumen K; Ghosh, Anandamohan

    2016-03-01

    Characterization of spatiotemporal dynamics of coupled oscillatory systems can be done by computing the Lyapunov exponents. We study the spatiotemporal dynamics of randomly coupled network of Kuramoto oscillators and find that the spectral statistics obtained from the Lyapunov exponent spectrum show interesting sensitivity to the coupling matrix. Our results indicate that in the weak coupling limit the gap distribution of the Lyapunov spectrum is Poissonian, while in the limit of strong coupling the gap distribution shows level repulsion. Moreover, the oscillators settle to an inhomogeneous oscillatory state, and it is also possible to infer the random network properties from the Lyapunov exponent spectrum.

  9. Amplitude death, oscillation death, wave, and multistability in identical Stuart-Landau oscillators with conjugate coupling

    NASA Astrophysics Data System (ADS)

    Han, Wenchen; Cheng, Hongyan; Dai, Qionglin; Li, Haihong; Ju, Ping; Yang, Junzhong

    2016-10-01

    In this work, we investigate the dynamics in a ring of identical Stuart-Landau oscillators with conjugate coupling systematically. We analyze the stability of the amplitude death and find the stability independent of the number of oscillators. When the amplitude death state is unstable, a large number of states such as homogeneous oscillation death, heterogeneous oscillation death, homogeneous oscillation, and wave propagations are found and they may coexist. We also find that all of these states are related to the unstable spatial modes to the amplitude death state.

  10. 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.

  11. A common lag scenario in quenching of oscillation in coupled oscillators.

    PubMed

    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. PMID:27586600

  12. A common lag scenario in quenching of oscillation in coupled oscillators.

    PubMed

    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.

  13. 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.

  14. Classification of attractors for systems of identical coupled Kuramoto oscillators.

    PubMed

    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.

  15. Classification of attractors for systems of identical coupled Kuramoto oscillators

    SciTech Connect

    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.

  16. Pulse coupled oscillators and the phase resetting curve.

    PubMed

    Canavier, Carmen C; Achuthan, Srisairam

    2010-08-01

    Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.

  17. Creation and localization of entanglement in a simple configuration of coupled harmonic oscillators

    SciTech Connect

    Leandro, J. F.; Semiao, F. L.

    2009-05-15

    We investigate a simple arrangement of coupled harmonic oscillators which brings out some interesting effects concerning creation of entanglement. It is well known that if each member in a linear chain of coupled harmonic oscillators is prepared in a 'classical state', such as a pure coherent state or a mixed thermal state, no entanglement is created in the rotating wave approximation. On the other hand, if one of the oscillators is prepared in a nonclassical state (pure squeezed state, for instance), entanglement may be created between members of the chain. In the setup considered here, we found that a great family of nonclassical (squeezed) states can localize entanglement in such a way that distant oscillators never become entangled. We present a detailed study of this particular localization phenomenon. Our results may find application in future solid state implementations of quantum computers, and we suggest an electromechanical system consisting of an array of coupled micromechanical oscillators as a possible implementation.

  18. Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators.

    PubMed

    Senthilkumar, D V; Suresh, K; Chandrasekar, V K; Zou, Wei; Dana, Syamal K; Kathamuthu, Thamilmaran; Kurths, Jürgen

    2016-04-01

    We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results. PMID:27131491

  19. Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators

    NASA Astrophysics Data System (ADS)

    Senthilkumar, D. V.; Suresh, K.; Chandrasekar, V. K.; Zou, Wei; Dana, Syamal K.; Kathamuthu, Thamilmaran; Kurths, Jürgen

    2016-04-01

    We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.

  20. A quantitative analysis of coupled oscillations using mobile accelerometer sensors

    NASA Astrophysics Data System (ADS)

    Castro-Palacio, Juan Carlos; Velázquez-Abad, Luisberis; Giménez, Fernando; Monsoriu, Juan A.

    2013-05-01

    In this paper, smartphone acceleration sensors were used to perform a quantitative analysis of mechanical coupled oscillations. Symmetric and asymmetric normal modes were studied separately in the first two experiments. In the third, a coupled oscillation was studied as a combination of the normal modes. Results indicate that acceleration sensors of smartphones, which are very familiar to students, represent valuable measurement instruments for introductory and first-year physics courses.

  1. Oscillations and Synchronization in a System of Three Reactively Coupled Oscillators

    NASA Astrophysics Data System (ADS)

    Kuznetsov, Alexander P.; Turukina, Ludmila V.; Chernyshov, Nikolai Yu.; Sedova, Yuliya V.

    We consider a system of three interacting van der Pol oscillators with reactive coupling. Phase equations are derived, using proper order of expansion over the coupling parameter. The dynamics of the system is studied by means of the bifurcation analysis and with the method of Lyapunov exponent charts. Essential and physically meaningful features of the reactive coupling are discussed.

  2. Fluctuations in a coupled-oscillator model of the cardiovascular system

    NASA Astrophysics Data System (ADS)

    González, Jorge A.; Suárez-Vargas, Jose J.; Stefanovska, Aneta; McClintock, Peter V. E.

    2007-06-01

    We present a model of the cardiovascular system (CVS) based on a system of coupled oscillators. Using this approach we can describe several complex physiological phenomena that can have a range of applications. For instance, heart rate variability (HRV), can have a new deterministic explanation. The intrinsic dynamics of the HRV is controlled by deterministic couplings between the physiological oscillators in our model and without the need to introduce external noise as is commonly done. This new result provides potential applications not only for physiological systems but also for the design of very precise electronic generators where the frequency stability is crucial. Another important phenomenon is that of oscillation death. We show that in our CVS model the mechanism leading to the quenching of the oscillations can be controlled, not only by the coupling parameter, but by a more general scheme. In fact, we propose that a change in the relative current state of the cardiovascular oscillators can lead to a cease of the oscillations without actually changing the strength of the coupling among them. We performed real experiments using electronic oscillators and show them to match the theoretical and numerical predictions. We discuss the relevance of the studied phenomena to real cardiovascular systems regimes, including the explanation of certain pathologies, and the possible applications in medical practice.

  3. 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.

  4. Corticothalamic Projections Control Synchronization in Locally Coupled Bistable Thalamic Oscillators

    NASA Astrophysics Data System (ADS)

    Mayer, Jörg; Schuster, Heinz Georg; Claussen, Jens Christian; Mölle, Matthias

    2007-08-01

    Thalamic circuits are able to generate state-dependent oscillations of different frequencies and degrees of synchronization. However, little is known about how synchronous oscillations, such as spindle oscillations in the thalamus, are organized in the intact brain. Experimental findings suggest that the simultaneous occurrence of spindle oscillations over widespread territories of the thalamus is due to the corticothalamic projections, as the synchrony is lost in the decorticated thalamus. In this Letter we study the influence of corticothalamic projections on the synchrony in a thalamic network, and uncover the underlying control mechanism, leading to a control method which is applicable for several types of oscillations in the central nervous system.

  5. Weak chimeras in minimal networks of coupled phase oscillators.

    PubMed

    Ashwin, Peter; Burylko, Oleksandr

    2015-01-01

    We suggest a definition for a type of chimera state that appears in networks of indistinguishable phase oscillators. Defining a "weak chimera" as a type of invariant set showing partial frequency synchronization, we show that this means they cannot appear in phase oscillator networks that are either globally coupled or too small. We exhibit various networks of four, six, and ten indistinguishable oscillators, where weak chimeras exist with various dynamics and stabilities. We examine the role of Kuramoto-Sakaguchi coupling in giving degenerate (neutrally stable) families of weak chimera states in these example networks.

  6. Suppression and revival of oscillation in indirectly coupled limit cycle oscillators

    NASA Astrophysics Data System (ADS)

    Sharma, P. R.; Kamal, N. K.; Verma, U. K.; Suresh, K.; Thamilmaran, K.; Shrimali, M. D.

    2016-09-01

    We study the phenomena of suppression and revival of oscillations in a system of limit cycle oscillators coupled indirectly via a dynamic local environment. The dynamics of the environment is assumed to decay exponentially with time. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). We also show that introducing a feedback factor in the diffusion term revives the oscillations in this system. The critical curves for the regions of different emergent states as a function of coupling strength, decay parameter of the environment and feedback factor in the coupling are obtained analytically using linear stability analysis. These results are found to be consistent with the numerics and are also observed experimentally.

  7. Deterministic coherence resonance in coupled chaotic oscillators with frequency mismatch.

    PubMed

    Pisarchik, A N; Jaimes-Reátegui, R

    2015-11-01

    A small mismatch between natural frequencies of unidirectionally coupled chaotic oscillators can induce coherence resonance in the slave oscillator for a certain coupling strength. This surprising phenomenon resembles "stabilization of chaos by chaos," i.e., the chaotic driving applied to the chaotic system makes its dynamics more regular when the natural frequency of the slave oscillator is a little different than the natural frequency of the master oscillator. The coherence is characterized with the dominant component in the power spectrum of the slave oscillator, normalized standard deviations of both the peak amplitude and the interpeak interval, and Lyapunov exponents. The enhanced coherence is associated with increasing negative both the third and the fourth Lyapunov exponents, while the first and second exponents are always positive and zero, respectively.

  8. Speech encoding by coupled cortical theta and gamma oscillations.

    PubMed

    Hyafil, Alexandre; Fontolan, Lorenzo; Kabdebon, Claire; Gutkin, Boris; Giraud, Anne-Lise

    2015-05-29

    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.

  9. Amplitude death in networks of delay-coupled delay oscillators.

    PubMed

    Höfener, Johannes M; Sethia, Gautam C; Gross, Thilo

    2013-09-28

    Amplitude death is a dynamical phenomenon in which a network of oscillators settles to a stable state as a result of coupling. Here, we study amplitude death in a generalized model of delay-coupled delay oscillators. We derive analytical results for degree homogeneous networks which show that amplitude death is governed by certain eigenvalues of the network's adjacency matrix. In particular, these results demonstrate that in delay-coupled delay oscillators amplitude death can occur for arbitrarily large coupling strength k. In this limit, we find a region of amplitude death which already occurs at small coupling delays that scale with 1/k. We show numerically that these results remain valid in random networks with heterogeneous degree distribution.

  10. Resonant-tunnelling diode oscillator using a slot-coupled quasioptical open resonator

    NASA Technical Reports Server (NTRS)

    Stephan, K. D.; Brown, E. R.; Parker, C. D.; Goodhue, W. D.; Chen, C. L.

    1991-01-01

    A resonant-tunneling diode has oscillated at X-band frequencies in a microwave circuit consisting of a slot antenna coupled to a semiconfocal open resonator. Coupling between the open resonator and the slot oscillator improves the noise-to-carrier ratio by about 36 dB relative to that of the slot oscillator alone in the 100-200 kHz range. A circuit operating near 10 GHz has been designed as a scale model for millimeter- and submillimeter-wave applications.

  11. 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.

  12. Synchronization-based computation through networks of coupled oscillators

    PubMed Central

    Malagarriga, Daniel; García-Vellisca, Mariano A.; Villa, Alessandro E. P.; Buldú, Javier M.; García-Ojalvo, Jordi; Pons, Antonio J.

    2015-01-01

    The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates. PMID:26300765

  13. Synchronization-based computation through networks of coupled oscillators.

    PubMed

    Malagarriga, Daniel; García-Vellisca, Mariano A; Villa, Alessandro E P; Buldú, Javier M; García-Ojalvo, Jordi; Pons, Antonio J

    2015-01-01

    The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates.

  14. Coupled chemical oscillators and emergent system properties.

    PubMed

    Epstein, Irving R

    2014-09-25

    We review recent work on a variety of systems, from the nanometre to the centimetre scale, including microemulsions, microfluidic droplet arrays, gels and flow reactors, in which chemical oscillators interact to generate novel spatiotemporal patterns and/or mechanical motion. PMID:24835430

  15. Semi-passivity and synchronization of diffusively coupled neuronal oscillators

    NASA Astrophysics Data System (ADS)

    Steur, Erik; Tyukin, Ivan; Nijmeijer, Henk

    2009-11-01

    We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks using the theory of semi-passive and passive systems. We show that the conductance based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (electrical) energy is bounded. As a result, for a wide range of coupling configurations, networks of these oscillators are guaranteed to possess ultimately bounded solutions. Moreover, we demonstrate that when the coupling is strong enough the oscillators become synchronized. Our theoretical conclusions are confirmed by computer simulations with coupled Hindmarsh-Rose and Morris-Lecar oscillators. Finally we discuss possible “instabilities” in networks of oscillators induced by the diffusive coupling.

  16. Coupled electron and ion nonlinear oscillations in a collisionless plasma

    SciTech Connect

    Karimov, A. R.

    2013-05-15

    Dynamics of coupled electrostatic electron and ion nonlinear oscillations in a collisionless plasma is studied with reference to a kinetic description. Proceeding from the exact solution of Vlasov-Maxwell equations written as a function of linear functions in the electron and ion velocities, we arrive at the two coupled nonlinear equations which describe the evolution of the system.

  17. Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators

    PubMed Central

    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

  18. Limits to detection of generalized synchronization in delay-coupled chaotic oscillators.

    PubMed

    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.

  19. Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators.

    PubMed

    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

    2015-11-26

    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.

  20. Efficient Synchronization of Dipolarly Coupled Vortex-Based Spin Transfer Nano-Oscillators.

    PubMed

    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

  1. Erosion of synchronization in networks of coupled oscillators.

    PubMed

    Skardal, Per Sebastian; Taylor, Dane; Sun, Jie; Arenas, Alex

    2015-01-01

    We report erosion of synchronization in networks of coupled phase oscillators, a phenomenon where perfect phase synchronization is unattainable in steady state, even in the limit of infinite coupling. An analysis reveals that the total erosion is separable into the product of terms characterizing coupling frustration and structural heterogeneity, both of which amplify erosion. The latter, however, can differ significantly from degree heterogeneity. Finally, we show that erosion is marked by the reorganization of oscillators according to their node degrees rather than their natural frequencies.

  2. Periodic and aperiodic regimes in coupled dissipative chemical oscillators

    NASA Astrophysics Data System (ADS)

    Schreiber, Igor; Holodniok, Martin; Kubíček, Milan; Marek, Miloš

    1986-05-01

    Dynamic behavior of two identical reaction cells with linear symmetric coupling is studied in detail. The standard model reaction scheme "Brusselator" is used as the description of the kinetics. The uncoupled cells can exhibit either a stable stationary state or stable periodic oscillations. A number of stationary and periodic oscillatory patterns arise as a result of the coupling. A non-homogeneous spatio-temporal organization includes homoclinic and heteroclinic oscillations as well as chaotic regimes. Numerical continuation algorithms are used to determine the dependence of stationary and periodic solutions on parameters. Stable stationary nonhomogeneous regimes exist typically at intermediate levels of coupling intensity. The nonhomogeneous periodic solutions arise either via Hopf bifurcatios from stationary solutions or via period-doubling bifurcations from the homogeneous periodic solutions. The results obtained may serve as a standard for the study of the behavior of other coupled systems in which either a stable stationary state or stable oscillations exist in the single cell.

  3. Synchronization of weakly nonlinear oscillators with Huygens' coupling.

    PubMed

    Ramirez, J Pena; Fey, Rob H B; Nijmeijer, H

    2013-09-01

    In this paper, the occurrence of synchronization in pairs of weakly nonlinear self-sustained oscillators that interact via Huygens' coupling, i.e., a suspended rigid bar, is treated. In the analysis, a generalized version of the classical Huygens' experiment of synchronization of two coupled pendulum clocks is considered, in which the clocks are replaced by arbitrary self-sustained oscillators. Sufficient conditions for the existence and stability of synchronous solutions in the coupled system are derived by using the Poincaré method. The obtained results are supported by computer simulations and experiments conducted on a dedicated experimental platform. It is demonstrated that the mass of the coupling bar is an important parameter with respect to the limit synchronous behaviour in the oscillators.

  4. Hopf normal form with SN symmetry and reduction to systems of nonlinearly coupled phase oscillators

    NASA Astrophysics Data System (ADS)

    Ashwin, Peter; Rodrigues, Ana

    2016-06-01

    Coupled oscillator models where N oscillators are identical and symmetrically coupled to all others with full permutation symmetry SN are found in a variety of applications. Much, but not all, work on phase descriptions of such systems consider the special case of pairwise coupling between oscillators. In this paper, we show this is restrictive-and we characterize generic multi-way interactions between oscillators that are typically present, except at the very lowest order near a Hopf bifurcation where the oscillations emerge. We examine a network of identical weakly coupled dynamical systems that are close to a supercritical Hopf bifurcation by considering two parameters, ɛ (the strength of coupling) and λ (an unfolding parameter for the Hopf bifurcation). For small enough λ > 0 there is an attractor that is the product of N stable limit cycles; this persists as a normally hyperbolic invariant torus for sufficiently small ɛ > 0. Using equivariant normal form theory, we derive a generic normal form for a system of coupled phase oscillators with SN symmetry. For fixed N and taking the limit 0 < ɛ ≪ λ ≪ 1, we show that the attracting dynamics of the system on the torus can be well approximated by a coupled phase oscillator system that, to lowest order, is the well-known Kuramoto-Sakaguchi system of coupled oscillators. The next order of approximation generically includes terms with up to four interacting phases, regardless of N. Using a normalization that maintains nontrivial interactions in the limit N → ∞, we show that the additional terms can lead to new phenomena in terms of coexistence of two-cluster states with the same phase difference but different cluster size.

  5. Beam splitter coupled CDSE optical parametric oscillator

    DOEpatents

    Levinos, Nicholas J.; Arnold, George P.

    1980-01-01

    An optical parametric oscillator is disclosed in which the resonant radiation is separated from the pump and output radiation so that it can be manipulated without interfering with them. Thus, for example, very narrow band output may readily be achieved by passing the resonant radiation through a line narrowing device which does not in itself interfere with either the pump radiation or the output radiation.

  6. Coupled domain wall oscillations in magnetic cylindrical nanowires

    SciTech Connect

    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.

  7. Network oscillations of inferior olive neurons: entrainment and phase-locking of locally-coupled oscillators

    NASA Astrophysics Data System (ADS)

    Chartrand, Thomas; Goldman, Mark S.; Lewis, Timothy J.

    2015-03-01

    Although the inferior olive is known to contribute to the generation of timing and error signals for motor control, the specific role of its distinctive spatiotemporal activity patterns is still controversial. Olivary neurons display regular, sometimes synchronized oscillations of subthreshold membrane potential, driven in part by the highest density of electrical coupling of any brain region. We show that a reduced model of coupled phase oscillators is sufficient to reproduce and study experimental observations previously only demonstrated in more complex models. These include stable phase differences, variability of entrainment frequency, wave propagation, and cluster formation. Using the phase-response curve (PRC) of a conductance-based model of olivary neurons, we derive our phase model according to the theory of weakly-coupled oscillators. We retain the heterogeneity of intrinsic frequencies and heterogeneous, spatially constrained coupling as weak perturbations to the limit-cycle dynamics. Generalizing this model to an ensemble of coupled oscillator lattices with frequency and coupling disorder, we study the onset of entrainment and phase-locking as coupling is strengthened, including the scaling of cluster sizes with coupling strength near each phase transition.

  8. Dynamical regimes of four almost identical chemical oscillators coupled via pulse inhibitory coupling with time delay.

    PubMed

    Vanag, Vladimir K; Smelov, Pavel S; Klinshov, Vladimir V

    2016-02-21

    The dynamic regimes in networks of four almost identical spike oscillators with pulsatile coupling via inhibitor are systematically studied. We used two models to describe individual oscillators: a phase-oscillator model and a model for the Belousov-Zhabotinsky reaction. A time delay τ between a spike in one oscillator and the spike-induced inhibitory perturbation of other oscillators is introduced. Diagrams of all rhythms found for three different types of connectivities (unidirectional on a ring, mutual on a ring, and all-to-all) are built in the plane C(inh)-τ, where C(inh) is the coupling strength. It is shown analytically and numerically that only four regular rhythms are stable for unidirectional coupling: walk (phase shift between spikes of neighbouring oscillators equals the quarter of the global period T), walk-reverse (the same as walk but consecutive spikes take place in the direction opposite to the direction of connectivity), anti-phase (any two neighbouring oscillators are anti-phase), and in-phase oscillations. In the case of mutual on the ring coupling, an additional in-phase-anti-phase mode emerges. For all-to-all coupling, two new asymmetrical patterns (two-cluster and three-cluster modes) have been found. More complex rhythms are observed at large C(inh), when some oscillators are suppressed completely or generate smaller number of spikes than others.

  9. Solvable Model for Chimera States of Coupled Oscillators

    NASA Astrophysics Data System (ADS)

    Abrams, Daniel M.; Mirollo, Rennie; Strogatz, Steven H.; Wiley, Daniel A.

    2008-08-01

    Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.

  10. Solvable model for chimera states of coupled oscillators.

    PubMed

    Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A

    2008-08-22

    Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.

  11. Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators.

    PubMed

    O'Keeffe, Kevin P; Krapivsky, P L; Strogatz, Steven H

    2015-08-01

    We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators progressively coalesce into larger ones. Using tools from the study of aggregation phenomena, we obtain exact results for the time-dependent distribution of cluster sizes as the system evolves from disorder to synchrony.

  12. Bloch oscillations of THz acoustic phonons in coupled nanocavity structures.

    PubMed

    Lanzillotti-Kimura, N D; Fainstein, A; Perrin, B; Jusserand, B; Mauguin, O; Largeau, L; Lemaître, A

    2010-05-14

    Nanophononic Bloch oscillations and Wannier-Stark ladders have been recently predicted to exist in specifically tailored structures formed by coupled nanocavities. Using pump-probe coherent phonon generation techniques we demonstrate that Bloch oscillations of terahertz acoustic phonons can be directly generated and probed in these complex nanostructures. In addition, by Fourier transforming the time traces we had access to the proper eigenmodes in the frequency domain, thus evidencing the related Wannier-Stark ladder. The observed Bloch oscillation dynamics are compared with simulations based on a model description of the coherent phonon generation and photoelastic detection processes.

  13. Link weight evolution in a network of coupled chemical oscillators.

    PubMed

    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.

  14. 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.

  15. Enhancing the stability of the synchronization of multivariable coupled oscillators.

    PubMed

    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.

  16. Sensory segmentation with coupled neural oscillators.

    PubMed

    von der Malsburg, C; Buhmann, J

    1992-01-01

    We present a model of sensory segmentation that is based on the generation and processing of temporal tags in the form of oscillations, as suggested by the Dynamic Link Architecture. The model forms the basis for a natural solution to the sensory segmentation problem. It can deal with multiple segments, can integrate different cues and has the potential for processing hierarchical structures. Temporally tagged segments can easily be utilized in neural systems and form a natural basis for object recognition and learning. The model consists of a "cortical" circuit, an array of units that act as local feature detectors. Units are formulated as neural oscillators. Knowledge relevant to segmentation is encoded by connections. In accord with simple Gestalt laws, our concrete model has intracolumnar connections, between all units with overlapping receptive fields, and intercolumnar connections, between units responding to the same quality in different positions. An inhibitory connection system prevents total correlation and controls the grain of the segmentation. In simulations with synthetic input data we show the performance of the circuit, which produces signal correlation within segments and anticorrelation between segments.

  17. 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.

  18. Local dissipation and coupling properties of cellular oscillators: a case study on calcium oscillations.

    PubMed

    Perc, Matjaz; Marhl, Marko

    2004-04-01

    Synchronised signal transduction between cells is crucial, since it assures fast and immutable information processing, which is vital for flawless functioning of living organisms. The question arises how to recognise the ability of a cell to be easily coupled with other cells. In the present paper, we investigate the system properties that determine best coupling abilities and assure the most efficient signal transduction between cells. A case study is done for intercellular calcium oscillations. For a particular diffusion-like coupled system of cellular oscillators, we determined the minimal gap-junctional permeability that is necessary for synchronisation of initially asynchronous oscillators. Our results show that dissipation is a crucial system property that determines the coupling ability of cellular oscillators. We found that low dissipation assures synchronisation of coupled cells already at very low gap-junctional permeability, whereas highly dissipative oscillators require much higher gap-junctional permeability in order to synchronise. The results are discussed in the sense of their biological importance for systems where the synchronous responses of cells were recognised to be indispensable for appropriate physiological functioning of the tissue.

  19. Phase and amplitude dynamics of nonlinearly coupled oscillators.

    PubMed

    Cudmore, P; Holmes, C A

    2015-02-01

    This paper addresses the amplitude and phase dynamics of a large system of nonlinearly coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the existence and stability of collective behaviour which occurs due to a play-off between the distribution of individual oscillator frequency and the type of nonlinear coupling. We show that this system exhibits synchronisation, where all oscillators are rotating at the same rate, and that in the synchronised state the system has a regular structure related to the distribution of the frequencies of the individual oscillators. Using a geometric description, we show how changes in the non-linear coupling function can cause pitchfork and saddle-node bifurcations which create or destroy stable and unstable synchronised solutions. We apply these results to show how in-phase and anti-phase solutions are created in a system with a bi-modal distribution of frequencies.

  20. 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.

  1. Chimera states in purely local delay-coupled oscillators.

    PubMed

    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.

  2. Bicritical scaling behavior in unidirectionally coupled oscillators.

    PubMed

    Kim, S Y; Lim, W

    2001-03-01

    We study the scaling behavior of period doublings in a system of two unidirectionally coupled parametrically forced pendulums near a bicritical point where two critical lines of period-doubling transition to chaos in both subsystems meet. When crossing a bicritical point, a hyperchaotic attractor with two positive Lyapunov exponents appears, i.e., a transition to hyperchaos occurs. Varying the control parameters of the two subsystems, the unidirectionally coupled parametrically forced pendulums exhibit multiple period-doubling transitions to hyperchaos. For each transition to hyperchaos, using both a "residue-matching" renormalization group method and a direct numerical method, we make an analysis of the bicritical scaling behavior. It is thus found that the second response subsystem exhibits a new type of non-Feigenbaum scaling behavior, while the first drive subsystem is in the usual Feigenbaum critical state. The universality of the bicriticality is also examined for several different types of unidirectional couplings.

  3. Persistent chimera states in nonlocally coupled phase oscillators

    NASA Astrophysics Data System (ADS)

    Suda, Yusuke; Okuda, Koji

    2015-12-01

    Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this Rapid Communication, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that chimera states can be stable even without taking the continuous limit, which we call the persistent chimera state.

  4. Persistent chimera states in nonlocally coupled phase oscillators.

    PubMed

    Suda, Yusuke; Okuda, Koji

    2015-12-01

    Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this Rapid Communication, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that chimera states can be stable even without taking the continuous limit, which we call the persistent chimera state.

  5. 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.

  6. Phase-lag synchronization in networks of coupled chemical oscillators.

    PubMed

    Totz, Jan F; Snari, Razan; Yengi, Desmond; Tinsley, Mark R; Engel, Harald; Showalter, Kenneth

    2015-08-01

    Chemical oscillators with a broad frequency distribution are photochemically coupled in network topologies. Experiments and simulations show that the network synchronization occurs by phase-lag synchronization of clusters of oscillators with zero- or nearly zero-lag synchronization. Symmetry also plays a role in the synchronization, the extent of which is explored as a function of coupling strength, frequency distribution, and the highest frequency oscillator location. The phase-lag synchronization occurs through connected synchronized clusters, with the highest frequency node or nodes setting the frequency of the entire network. The synchronized clusters successively "fire," with a constant phase difference between them. For low heterogeneity and high coupling strength, the synchronized clusters are made up of one or more clusters of nodes with the same permutation symmetries. As heterogeneity is increased or coupling strength decreased, the phase-lag synchronization occurs partially through clusters of nodes sharing the same permutation symmetries. As heterogeneity is further increased or coupling strength decreased, partial synchronization and, finally, independent unsynchronized oscillations are observed. The relationships between these classes of behavior are explored with numerical simulations, which agree well with the experimentally observed behavior.

  7. 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.

  8. Intercommunity resonances in multifrequency ensembles of coupled oscillators.

    PubMed

    Komarov, Maxim; Pikovsky, Arkady

    2015-07-01

    We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to the resonance 2:1 is considered in detail. We construct uniformly rotating solutions describing synchronization inside communities and between them. Remarkably, cross coupling across the frequencies can promote synchrony even when ensembles are separately asynchronous. We also show that the transition to synchrony due to the cross coupling is accompanied by a huge multiplicity of distinct synchronous solutions, which is directly related to a multibranch entrainment. On the other hand, for synchronous populations, the cross-frequency coupling can destroy phase locking and lead to chaos of mean fields.

  9. A coupled optoelectronic oscillator with three resonant cavities

    NASA Astrophysics Data System (ADS)

    Shan, Yuan-yuan; Jiang, Yang; Bai, Guang-fu; Ma, Chuang; Li, Hong-xia; Liang, Jian-hui

    2015-01-01

    A new single-mode optoelectronic oscillator (OEO) with three coupled cavities is proposed and demonstrated. A Fabry-Perot (F-P) cavity fiber laser and an optical-electrical feedback branch are coupled together to construct an optoelectronic oscillator, where the F-P cavity fiber laser serves as a light source, and a modulator is placed in the laser cavity to implement reciprocating modulation, which simultaneously splits the laser cavity into two parts and forms a dual-loop configuration. To complete an optoelectronic oscillator, part of optical signal is output from the F-P cavity to implement the feedback modulation, which constructs the third cavity. Since only the oscillation signal satisfies the requirements of all the three cavities, a single-mode oscillation can be finally achieved. Three resonant cavities are successfully designed without adding more optoelectronic devices, and the side-modes can be well suppressed with low cost. The oscillation condition is theoretically analyzed. In the experimental demonstration, a 20 GHz single longitudinal mode microwave signal is successfully obtained.

  10. Search for an Atomic EDM with Optical-Coupling Nuclear Spin Oscillator

    SciTech Connect

    Asahi, K.; Uchida, M.; Inoue, T.; Hatakeyama, N.; Yoshimi, A.

    2007-06-13

    We have constructed a nuclear spin oscillator of a new type, that employs a feedback scheme based on an optical spin detection and suceeding spin control by a transverse field application. This spin oscillator parallels the conventional spin maser in many points, but exhibits advantages and requirements that are different from those with the spin maser. By means of the optical-coupling nuclear spin oscillator, an experimental setup to search for an electric dipole moment (EDM) in a spin 1/2 diamagnetic atom 129Xe is being developed.

  11. Inhomogeneous stationary and oscillatory regimes in coupled chaotic oscillators.

    PubMed

    Liu, Weiqing; Volkov, Evgeny; Xiao, Jinghua; Zou, Wei; Zhan, Meng; Yang, Junzhong

    2012-09-01

    The dynamics of linearly coupled identical Lorenz and Pikovsky-Rabinovich oscillators are explored numerically and theoretically. We concentrate on the study of inhomogeneous stable steady states ("oscillation death (OD)" phenomenon) and accompanying periodic and chaotic regimes that emerge at an appropriate choice of the coupling matrix. The parameters, for which OD occurs, are determined by stability analysis of the chosen steady state. Three model-specific types of transitions to and from OD are observed: (1) a sharp transition to OD from a nonsymmetric chaotic attractor containing random intervals of synchronous chaos; (2) transition to OD from the symmetry-breaking chaotic regime created by negative coupling; (3) supercritical bifurcation of OD into inhomogeneous limit cycles and further evolution of the system to inhomogeneous chaotic regimes that coexist with complete synchronous chaos. These results may fill a gap in the understanding of the mechanism of OD in coupled chaotic systems.

  12. Synchronization of Coupled Oscillators on a Two-Dimensional Plane.

    PubMed

    Guo, Dameng; Fu, Yong Qing; Zheng, Bo

    2016-08-01

    The effect of the transfer rate of signal molecules on coupled chemical oscillators arranged on a two-dimensional plane was systematically investigated in this paper. A microreactor equipped with a surface acoustic wave (SAW) mixer was applied to adjust the transfer rate of the signal molecules in the microreactor. The SAW mixer with adjustable input powers provided a simple means to generate different mixing rates in the microreactor. A robust synchronization of the oscillators was found at an input radio frequency power of 20 dBm, with which the chemical waves were initiated at a fixed site of the oscillator system. With increasing input power, the frequency of the chemical waves was increased, which agreed well with the prediction given by the time-delayed phase oscillator model. Results from the finite element simulation agreed well with the experimental results. PMID:27124217

  13. Synchronization of Coupled Oscillators on a Two-Dimensional Plane.

    PubMed

    Guo, Dameng; Fu, Yong Qing; Zheng, Bo

    2016-08-01

    The effect of the transfer rate of signal molecules on coupled chemical oscillators arranged on a two-dimensional plane was systematically investigated in this paper. A microreactor equipped with a surface acoustic wave (SAW) mixer was applied to adjust the transfer rate of the signal molecules in the microreactor. The SAW mixer with adjustable input powers provided a simple means to generate different mixing rates in the microreactor. A robust synchronization of the oscillators was found at an input radio frequency power of 20 dBm, with which the chemical waves were initiated at a fixed site of the oscillator system. With increasing input power, the frequency of the chemical waves was increased, which agreed well with the prediction given by the time-delayed phase oscillator model. Results from the finite element simulation agreed well with the experimental results.

  14. Phase clustering in complex networks of delay-coupled oscillators

    NASA Astrophysics Data System (ADS)

    Pérez, Toni; Eguíluz, Víctor M.; Arenas, Alex

    2011-06-01

    We study the clusterization of phase oscillators coupled with delay in complex networks. For the case of diffusive oscillators, we formulate the equations relating the topology of the network and the phases and frequencies of the oscillators (functional response). We solve them exactly in directed networks for the case of perfect synchronization. We also compare the reliability of the solution of the linear system for non-linear couplings. Taking advantage of the form of the solution, we propose a frequency adaptation rule to achieve perfect synchronization. We also propose a mean-field theory for uncorrelated random networks that proves to be pretty accurate to predict phase synchronization in real topologies, as for example, the Caenorhabditis elegans or the autonomous systems connectivity.

  15. Weakly coupled oscillators in a slowly varying world.

    PubMed

    Park, Youngmin; Ermentrout, Bard

    2016-06-01

    We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a pair of oscillators. We apply this to the simple Hopf oscillator and then to a biophysical model. The latter represents the behavior of a neuron that is subject to slow modulation of a muscarinic current such as would occur during transient attention through cholinergic activation. Our method extends and simplifies the recent work of Kurebayashi (Physical Review Letters, 111, 214101, 2013) to include coupling. We apply the method to an all-to-all network and show that there is a waxing and waning of synchrony of modulated neurons.

  16. 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.

  17. Clustering in delay-coupled smooth and relaxational chemical oscillators

    NASA Astrophysics Data System (ADS)

    Blaha, Karen; Lehnert, Judith; Keane, Andrew; Dahms, Thomas; Hövel, Philipp; Schöll, Eckehard; Hudson, John L.

    2013-12-01

    We investigate cluster synchronization in networks of nonlinear systems with time-delayed coupling. Using a generic model for a system close to the Hopf bifurcation, we predict the order of appearance of different cluster states and their corresponding common frequencies depending upon coupling delay. We may tune the delay time in order to ensure the existence and stability of a specific cluster state. We qualitatively and quantitatively confirm these results in experiments with chemical oscillators. The experiments also exhibit strongly nonlinear relaxation oscillations as we increase the voltage, i.e., go further away from the Hopf bifurcation. In this regime, we find secondary cluster states with delay-dependent phase lags. These cluster states appear in addition to primary states with delay-independent phase lags observed near the Hopf bifurcation. Extending the theory on Hopf normal-form oscillators, we are able to account for realistic interaction functions, yielding good agreement with experimental findings.

  18. Franck-Condon transitions in a system with large-amplitude anharmonic vibrations coupled to a harmonic-oscillator bath: Application to the C 1s photoelectron spectrum of ethanol

    SciTech Connect

    Abu-samha, M.; Boerve, K. J.

    2006-10-15

    A vibrational adiabatic approach to Franck-Condon analysis is presented for systems with a few highly displaced oscillators coupled to a bath of harmonic oscillators. The model reduces the many-coupled-oscillator problem to few-body problems, albeit with corrections due to coupling to harmonic modes. The theory is applied with very good results to the carbon 1s photoelectron spectrum of ethanol, which is strongly influenced by change in conformation from gauche to anti when ethanol is ionized at the methyl site.

  19. 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.

  20. 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)

  1. The pervasiveness and plasticity of circadian oscillations: the coupled circadian-oscillators framework

    PubMed Central

    Patel, Vishal R.; Ceglia, Nicholas; Zeller, Michael; Eckel-Mahan, Kristin; Sassone-Corsi, Paolo; Baldi, Pierre

    2015-01-01

    Motivation: Circadian oscillations have been observed in animals, plants, fungi and cyanobacteria and play a fundamental role in coordinating the homeostasis and behavior of biological systems. Genetically encoded molecular clocks found in nearly every cell, based on negative transcription/translation feedback loops and involving only a dozen genes, play a central role in maintaining these oscillations. However, high-throughput gene expression experiments reveal that in a typical tissue, a much larger fraction (∼10%) of all transcripts oscillate with the day–night cycle and the oscillating species vary with tissue type suggesting that perhaps a much larger fraction of all transcripts, and perhaps also other molecular species, may bear the potential for circadian oscillations. Results: To better quantify the pervasiveness and plasticity of circadian oscillations, we conduct the first large-scale analysis aggregating the results of 18 circadian transcriptomic studies and 10 circadian metabolomic studies conducted in mice using different tissues and under different conditions. We find that over half of protein coding genes in the cell can produce transcripts that are circadian in at least one set of conditions and similarly for measured metabolites. Genetic or environmental perturbations can disrupt existing oscillations by changing their amplitudes and phases, suppressing them or giving rise to novel circadian oscillations. The oscillating species and their oscillations provide a characteristic signature of the physiological state of the corresponding cell/tissue. Molecular networks comprise many oscillator loops that have been sculpted by evolution over two trillion day–night cycles to have intrinsic circadian frequency. These oscillating loops are coupled by shared nodes in a large network of coupled circadian oscillators where the clock genes form a major hub. Cells can program and re-program their circadian repertoire through epigenetic and other mechanisms

  2. Mechanism for intensity-induced chimera states in globally coupled oscillators.

    PubMed

    Chandrasekar, V K; Gopal, R; Venkatesan, A; Lakshmanan, M

    2014-12-01

    We identify the mechanism behind the existence of intensity-induced chimera states in globally coupled oscillators. We find that the effect of intensity in the system is to cause multistability by increasing the number of fixed points. This in turn increases the number of multistable attractors, and we find that their stability is determined by the strength of coupling. This causes the coexistence of different collective states in the system depending upon the initial state. We demonstrate that intensity-induced chimera is generic to both periodic and chaotic systems. We discuss possible applications of our results to real-world systems like the brain and spin torque nano-oscillators.

  3. Amplitude-phase coupling in a spin-torque nano-oscillator

    NASA Astrophysics Data System (ADS)

    Kudo, Kiwamu; Nagasawa, Tazumi; Sato, Rie; Mizushima, Koichi

    2009-04-01

    The spin-torque nano-oscillator in the presence of thermal fluctuation is described by the normal form of the Hopf bifurcation with an additive white noise. By the application of the reduction method, the amplitude-phase coupling factor, which has a significant effect on the power spectrum of the spin-torque nano-oscillator, is calculated from the Landau-Lifshitz-Gilbert-Slonczewski equation with the nonlinear Gilbert damping. The amplitude-phase coupling factor exhibits a large variation depending on an in-plane anisotropy under the practical external fields.

  4. Three people can synchronize as coupled oscillators during sports activities.

    PubMed

    Yokoyama, Keiko; Yamamoto, Yuji

    2011-10-01

    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.

  5. Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators

    PubMed Central

    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

  6. Collective cell movement promotes synchronization of coupled genetic oscillators.

    PubMed

    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.

  7. Compact heterodyne NEMS oscillator for sensing applications

    NASA Astrophysics Data System (ADS)

    Sansa, Marc; Gourlat, Guillaume; Jourdan, Guillaume; Gely, Marc; Villard, Patrick; Sicard, Gilles; Hentz, Sébastien

    2016-11-01

    We present a novel topology of heterodyne nanoelectromechanical self-oscillator, aimed at the dense integration of resonator arrays for sensing applications. This oscillator is based on an original measurement method, suitable for both open loop and closed loop operations, which simplifies current down-mixing set-ups. When implemented on-chip, it will allow the reduction of the size and power consumption of readout CMOS circuitry. This is today the limiting factor for the integration density of NEMS oscillators for real-life applications. Here we characterize this method in both open-loop and closed-loop, and evaluate its frequency stability.

  8. Travelling waves in arrays of delay-coupled phase oscillators

    NASA Astrophysics Data System (ADS)

    Laing, Carlo R.

    2016-09-01

    We consider the effects of several forms of delays on the existence and stability of travelling waves in non-locally coupled networks of Kuramoto-type phase oscillators and theta neurons. By passing to the continuum limit and using the Ott/Antonsen ansatz, we derive evolution equations for a spatially dependent order parameter. For phase oscillator networks, the travelling waves take the form of uniformly twisted waves, and these can often be characterised analytically. For networks of theta neurons, the waves are studied numerically.

  9. Data Synchronization in a Network of Coupled Phase Oscillators

    NASA Astrophysics Data System (ADS)

    Miyano, Takaya; Tsutsui, Takako

    2007-01-01

    We devised a new method of data mining for a large-scale database. In the method, a network of locally coupled phase oscillators subject to Kuramoto’s model substitutes for given multivariate data to generate major features through phase locking of the oscillators, i.e., phase transition of the data set. We applied the method to the national database of care needs certification for the Japanese public long-term care insurance program, and found three major patterns in the aging process of the frail elderly. This work revealed the latent utility of Kuramoto’s model for data processing.

  10. Time Delay Effect in a Living Coupled Oscillator System with the Plasmodium of Physarum polycephalum

    NASA Astrophysics Data System (ADS)

    Takamatsu, Atsuko; Fujii, Teruo; Endo, Isao

    2000-08-01

    A living coupled oscillator system was constructed by a cell patterning method with a plasmodial slime mold, in which parameters such as coupling strength and distance between the oscillators can be systematically controlled. Rich oscillation phenomena between the two-coupled oscillators, namely, desynchronizing and antiphase/in-phase synchronization were observed according to these parameters. Both experimental and theoretical approaches showed that these phenomena are closely related to the time delay effect in interactions between the oscillators.

  11. Universal lineshapes at the crossover between weak and strong critical coupling in Fano-resonant coupled oscillators

    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.

  12. Universal lineshapes at the crossover between weak and strong critical coupling in Fano-resonant coupled oscillators

    PubMed Central

    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

  13. Reviving oscillation with optimal spatial period of frequency distribution in coupled oscillators

    NASA Astrophysics Data System (ADS)

    Deng, Tongfa; Liu, Weiqing; Zhu, Yun; Xiao, Jinghua; Kurths, Jürgen

    2016-09-01

    The spatial distributions of system's frequencies have significant influences on the critical coupling strengths for amplitude death (AD) in coupled oscillators. We find that the left and right critical coupling strengths for AD have quite different relations to the increasing spatial period m of the frequency distribution in coupled oscillators. The left one has a negative linear relationship with m in log-log axis for small initial frequency mismatches while remains constant for large initial frequency mismatches. The right one is in quadratic function relation with spatial period m of the frequency distribution in log-log axis. There is an optimal spatial period m0 of frequency distribution with which the coupled system has a minimal critical strength to transit from an AD regime to reviving oscillation. Moreover, the optimal spatial period m0 of the frequency distribution is found to be related to the system size √{ N } . Numerical examples are explored to reveal the inner regimes of effects of the spatial frequency distribution on AD.

  14. 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.

  15. Experiments on oscillator ensemble with global nonlinear coupling

    NASA Astrophysics Data System (ADS)

    Rosenblum, Michael; Temirbayev, Amirkhan; Zhanabaev, Zeinulla; Tarasov, Stanislav; Ponomarenko, Vladimir

    2012-02-01

    We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a linear or nonlinear phase-shifting unit in the global feedback loop. With linear unit we observe, with increase of the coupling strength, a standard Kuramoto-like transition to a fully synchronous state; the threshold of the transition depends on the phase shift. In case of nonlinear global coupling we first observe a transition to a state when approximately half of the population forms a synchronous cluster. With further increase of the coupling strength we observe destruction of this cluster and formation of a self-organized quasiperiodic state, predicted in [M. Rosenblum and A. Pikovsky, PRL, 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. The transition is characterized by a non-monotonic dependence of the order parameter on the coupling strength. We demonstrate a good correspondence between theory and experiment.

  16. 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.

  17. Coupled bloch-phonon oscillations in semiconductor superlattices

    PubMed

    Dekorsy; Bartels; Kurz; Kohler; Hey; Ploog

    2000-07-31

    We investigate coherent Bloch oscillations in GaAs/AlxGa1-xAs superlattices with electronic miniband widths larger than the optical phonon energy. In these superlattices the Bloch frequency can be tuned into resonance with the optical phonon. Close to resonance a direct coupling of Bloch oscillations to LO phonons is observed which gives rise to the coherent excitation of LO phonons. The density necessary for driving coherent LO phonons via Bloch oscillations is about 2 orders of magnitude smaller than the density necessary to drive coherent LO phonons in bulk GaAs. The experimental observations are confirmed by the theoretical description of this phenomenon [A.W. Ghosh et al., Phys. Rev. Lett. 85, 1084 (2000)].

  18. Experimental observation of a transition from amplitude to oscillation death in coupled oscillators.

    PubMed

    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)]. 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.

  19. Impulsive synchronization of coupled dynamical networks with nonidentical Duffing oscillators and coupling delays.

    PubMed

    Wang, Zhengxin; Duan, Zhisheng; Cao, Jinde

    2012-03-01

    This paper aims to investigate the synchronization problem of coupled dynamical networks with nonidentical Duffing-type oscillators without or with coupling delays. Different from cluster synchronization of nonidentical dynamical networks in the previous literature, this paper focuses on the problem of complete synchronization, which is more challenging than cluster synchronization. By applying an impulsive controller, some sufficient criteria are obtained for complete synchronization of the coupled dynamical networks of nonidentical oscillators. Furthermore, numerical simulations are given to verify the theoretical results. PMID:22463016

  20. Delta-Beta Coupled Oscillations Underlie Temporal Prediction Accuracy.

    PubMed

    Arnal, Luc H; Doelling, Keith B; Poeppel, David

    2015-09-01

    The ability to generate temporal predictions is fundamental for adaptive behavior. Precise timing at the time-scale of seconds is critical, for instance to predict trajectories or to select relevant information. What mechanisms form the basis for such accurate timing? Recent evidence suggests that (1) temporal predictions adjust sensory selection by controlling neural oscillations in time and (2) the motor system plays an active role in inferring "when" events will happen. We hypothesized that oscillations in the delta and beta bands are instrumental in predicting the occurrence of auditory targets. Participants listened to brief rhythmic tone sequences and detected target delays while undergoing magnetoencephalography recording. Prior to target occurrence, we found that coupled delta (1-3 Hz) and beta (18-22 Hz) oscillations temporally align with upcoming targets and bias decisions towards correct responses, suggesting that delta-beta coupled oscillations underpin prediction accuracy. Subsequent to target occurrence, subjects update their decisions using the magnitude of the alpha-band (10-14 Hz) response as internal evidence of target timing. These data support a model in which the orchestration of oscillatory dynamics between sensory and motor systems is exploited to accurately select sensory information in time. PMID:24846147

  1. Spiral wave chimeras in locally coupled oscillator systems.

    PubMed

    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. PMID:26986275

  2. 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.

  3. Partially coherent twisted states in arrays of coupled phase oscillators

    SciTech Connect

    Omel'chenko, Oleh E.; Wolfrum, Matthias; Laing, Carlo R.

    2014-06-15

    We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorentzian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly “twisted” in space. To analyze these, we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies, and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system.

  4. Partially coherent twisted states in arrays of coupled phase oscillators.

    PubMed

    Omel'chenko, Oleh E; Wolfrum, Matthias; Laing, Carlo R

    2014-06-01

    We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorentzian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly "twisted" in space. To analyze these, we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies, and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system.

  5. Finite-size scaling in globally coupled phase oscillators with a general coupling scheme

    NASA Astrophysics Data System (ADS)

    Nishikawa, Isao; Iwayama, Koji; Tanaka, Gouhei; Horita, Takehiko; Aihara, Kazuyuki

    2014-02-01

    We investigate the critical exponent of correlation size, related to synchronization transition, in globally coupled nonidentical phase oscillators. The critical exponent has so far been identified for sinusoidal coupling, but has not been fully studied for other coupling schemes. Herein, for a general coupling function including a negative second harmonic term in addition to the sinusoidal term, we numerically estimate the critical exponent of the correlation size, denoted by ν _+, in a synchronized regime of the system by employing a non-conventional statistical quantity. First, we confirm that the estimated value of ν _+ is approximately 5/2 for the sinusoidal coupling case, which is consistent with the well known theoretical result. Second, we show that the value of ν _+ increases with an increase in the strength of the second harmonic term. Our result means that the universality of a critical exponent can break down in the globally coupled phase oscillators.

  6. Coupling a small torsional oscillator to large optical angular momentum

    NASA Astrophysics Data System (ADS)

    Shi, Hao; Bhattacharya, Mishkatul

    2013-05-01

    We propose a new optomechanical system to achieve torsional optomechanics. Our system is composed of a windmill-shaped dielectric optically trapped within a cavity interacting with Laguerre-Gaussian cavity modes with both angular and radial nodes. Compared to existing configurations, our proposal enables small mechanical oscillators to interact with the in-principle unlimited orbital angular momentum that can be carried by a single photon, and therefore allows the generation of scalable optomechanical coupling. Supported by Research Corporation for Science Advancement.

  7. Coupling a small torsional oscillator to large optical angular momentum

    NASA Astrophysics Data System (ADS)

    Shi, H.; Bhattacharya, M.

    2013-03-01

    We propose a new configuration for realizing torsional optomechanics: an optically trapped windmill-shaped dielectric interacting with Laguerre-Gaussian cavity modes containing both angular and radial nodes. In contrast to existing schemes, our method can couple mechanical oscillators smaller than the optical beam waist to the in-principle unlimited orbital angular momentum that can be carried by a single photon, and thus generate substantial optomechanical interactions. Combining the advantages of small mass, large coupling, and low clamping losses, our work conceptually opens the way for the observation of quantum effects in torsional optomechanics.

  8. 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.

  9. Entanglement of mechanical oscillators coupled to a nonequilibrium environment

    SciTech Connect

    Ludwig, Max; Hammerer, K.; Marquardt, Florian

    2010-07-15

    Recent experiments aim at cooling nanomechanical resonators to the ground state by coupling them to nonequilibrium environments in order to observe quantum effects such as entanglement. This raises the general question of how such environments affect entanglement. Here we show that there is an optimal dissipation strength for which the entanglement between two coupled oscillators is maximized. Our results are established with the help of a general framework of exact quantum Langevin equations valid for arbitrary bath spectra, in and out of equilibrium. We point out why the commonly employed Lindblad approach fails to give even a qualitatively correct picture.

  10. 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.

  11. Environmental coupling in ecosystems: From oscillation quenching to rhythmogenesis.

    PubMed

    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. PMID:27627297

  12. Intercommunity resonances in multifrequency ensembles of coupled oscillators.

    PubMed

    Komarov, Maxim; Pikovsky, Arkady

    2015-07-01

    We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to the resonance 2:1 is considered in detail. We construct uniformly rotating solutions describing synchronization inside communities and between them. Remarkably, cross coupling across the frequencies can promote synchrony even when ensembles are separately asynchronous. We also show that the transition to synchrony due to the cross coupling is accompanied by a huge multiplicity of distinct synchronous solutions, which is directly related to a multibranch entrainment. On the other hand, for synchronous populations, the cross-frequency coupling can destroy phase locking and lead to chaos of mean fields. PMID:26274246

  13. Tune Determination of Strongly Coupled Betatron Oscillations in a Fast-Ramping Synchrotron

    SciTech Connect

    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.

  14. 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.

  15. Coupled-oscillator theory of dispersion and Casimir-Polder interactions.

    PubMed

    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(-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.

  16. Coupled-oscillator theory of dispersion and Casimir-Polder interactions

    NASA Astrophysics Data System (ADS)

    Berman, P. R.; Ford, G. W.; Milonni, P. W.

    2014-10-01

    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-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.

  17. 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.

  18. Dendritic and synaptic effects in systems of coupled cortical oscillators.

    PubMed

    Crook, S M; Ermentrout, G B; Bower, J M

    1998-07-01

    We explore the influence of synaptic location and form on the behavior of networks of coupled cortical oscillators. First, we develop a model of two coupled somatic oscillators that includes passive dendritic cables. Using a phase model approach, we show that the synchronous solution can change from a stable solution to an unstable one as the cable lengthens and the synaptic position moves further from the soma. We confirm this prediction using a system of coupled compartmental models. We also demonstrate that when the synchronous solution becomes unstable, a bifurcation occurs and a pair of asynchronous stable solutions appear, causing a phase lag between the cells in the system. Then using a variety of coupling functions and different synaptic positions, we show that distal connections and broad synaptic time courses encourage phase lags that can be reduced, eliminated, or enhanced by the presence of active currents in the dendrite. This mechanism may appear in neural systems where proximal connections could be used to encourage synchrony, and distal connections and broad synaptic time courses could be used to produce phase lags that can be modulated by active currents.

  19. Synchronization of phase oscillators with frequency-weighted coupling

    PubMed Central

    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

  20. Different kinds of chimera death states in nonlocally coupled oscillators.

    PubMed

    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. PMID:27300886

  1. Different kinds of chimera death states in nonlocally coupled oscillators.

    PubMed

    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.

  2. Multiphysics Application Coupling Toolkit

    SciTech Connect

    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.

  3. Multiphysics Application Coupling Toolkit

    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, openmore » 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.« less

  4. Experiments on oscillator ensembles with global nonlinear coupling.

    PubMed

    Temirbayev, Amirkhan A; Zhanabaev, Zeinulla Zh; Tarasov, Stanislav B; Ponomarenko, Vladimir I; Rosenblum, Michael

    2012-01-01

    We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett. 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.

  5. Experiments on oscillator ensembles with global nonlinear coupling

    NASA Astrophysics Data System (ADS)

    Temirbayev, Amirkhan A.; Zhanabaev, Zeinulla Zh.; Tarasov, Stanislav B.; Ponomarenko, Vladimir I.; Rosenblum, Michael

    2012-01-01

    We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.064101 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.

  6. Tunable, continuous-wave single-resonant optical parametric oscillator with output coupling for resonant wave

    NASA Astrophysics Data System (ADS)

    Xiong-Hua, Zheng; Bao-Fu, Zhang; Zhong-Xing, Jiao; Biao, Wang

    2016-01-01

    We present a continuous-wave singly-resonant optical parametric oscillator with 1.5% output coupling of the resonant signal wave, based on an angle-polished MgO-doped periodically poled lithium niobate (MgO:PPLN), pumped by a commercial Nd:YVO4 laser at 1064 nm. The output-coupled optical parametric oscillator delivers a maximum total output power of 4.19 W with 42.8% extraction efficiency, across a tuning range of 1717 nm in the near- and mid-infrared region. This indicates improvements of 1.87 W in output power, 19.1% in extraction efficiency and 213 nm in tuning range extension in comparison with the optical parametric oscillator with no output coupling, while at the expense of increasing the oscillation threshold by a factor of ˜ 2. Moreover, it is confirmed that the finite output coupling also contributes to the reduction of the thermal effects in crystal. Project supported by the National Natural Science Foundation of China (Grant Nos. 61308056, 11204044, 11232015, and 11072271), the Research Fund for the Doctoral Program of Higher Education of China (Grant Nos. 20120171110005 and 20130171130003), the Fundamental Research Funds for the Central Universities of China (Grant No. 14lgpy07), and the Opening Project of Science and Technology on Reliability Physics and Application Technology of Electronic Component Laboratory, China (Grant No. ZHD201203).

  7. Coupled Oscillator Based Agile Beam Transmitters and Receivers: A Review of Work at JPL

    NASA Technical Reports Server (NTRS)

    Pogorzelski, Ronald J.

    2006-01-01

    This is a review of the work done at Caltech's Jet Propulsion Laboratory during the past decade on development of the coupled oscillator technology in phased array applications to spacecraft telecommunications. First, some historical background is provided to set the work in context. However, this is by no means intended to be a comprehensive review of all work in this area. Rather, the focus is on the JPL contribution with some mention of other work which provided either insight or motivation. In the mid 1990's, R. A. York, and collaborators proposed that an array of mutually injection locked electronic oscillators could provide appropriately phased signals to the radiating elements of an array antenna such that the radiated beam could be steered merely by tuning the end or perimeter oscillators of the array. York, et al. also proposed a receiving system based on such oscillator arrays in which the oscillators provide properly phased local oscillator signals to be mixed with the signals received by the array elements to remove the phase due to angle of arrival of the incident wave. These concepts were viewed as a promising simplification of the beam steering control system that could result in significant cost, mass, and prime power reduction and were therefore attractive for possible space application.

  8. Coupled Vortex Oscillations in Spatially Separated Permalloy Squares

    SciTech Connect

    Vogel, Andreas; Kamionka, Thomas; Martens, Michael; Meier, Guido; Drews, Andre; Chou, Kang Wei; Tyliszczak, Tolek; Stoll, Hermann; Van Waeyenberge, Bartel

    2011-04-01

    We experimentally study the magnetization dynamics of pairs of micron-sized permalloy squares coupled via their stray fields. The trajectories of the vortex cores in the Landau-domain patterns of the squares are mapped in real space using time-resolved scanning transmission x-ray microscopy. After excitation of one of the vortex cores with a short magnetic-field pulse, the system behaves like coupled harmonic oscillators. The coupling strength depends on the separation between the squares and the configuration of the vortex-core polarizations. Considering the excitation via a rotating in-plane magnetic field, it can be understood that only a weak response of the second vortex core is observed for equal core polarizations.

  9. Synchronization of period-doubling oscillations in vascular coupled nephrons.

    PubMed

    Laugesen, J L; Mosekilde, E; Holstein-Rathlou, N-H

    2011-09-01

    The mechanisms by which the individual functional unit (nephron) of the kidney regulates the incoming blood flow give rise to a number of nonlinear dynamic phenomena, including period-doubling bifurcations and intra-nephron synchronization between two different oscillatory modes. Interaction between the nephrons produces complicated and time-dependent inter-nephron synchronization patterns. In order to understand the processes by which a pair of vascular coupled nephrons synchronize, the paper presents a detailed analysis of the bifurcations that occur at the threshold of synchronization. We show that, besides infinite cascades of saddle-node bifurcations, these transitions involve mutually connected cascades of torus and homoclinic bifurcations. To illustrate the broader range of occurrence of this bifurcation structure for coupled period-doubling systems, we show that a similar structure arises in a system of two coupled, non-identical Rössler oscillators.

  10. Stochastic coupled oscillator model of EEG for Alzheimer's disease.

    PubMed

    Ghorbanian, P; Ramakrishnan, S; Ashrafiuon, H

    2014-01-01

    Coupled nonlinear oscillator models of EEG signals during resting eyes-closed and eyes-open conditions are presented based on Duffing-van der Pol oscillator dynamics. The frequency and information entropy contents of the output of the nonlinear model and the actual EEG signal is matched through an optimization algorithm. The framework is used to model and compare EEG signals recorded from Alzheimer's disease (AD) patients and age-matched healthy controls (CTL) subjects. The results show that 1) the generated model signal can capture the frequency and information entropy contents of the EEG signal with very similar power spectral distribution and non-periodic time history; 2) the EEG and the generated signal from the eyes-closed model are α band dominant for CTL subjects and θ band dominant for AD patients; and 3) statistically distinct models represent the EEG signals from AD patients and CTL subject during resting eyes-closed condition. PMID:25570056

  11. Emerging dynamics in neuronal networks of diffusively coupled hard oscillators.

    PubMed

    Ponta, L; Lanza, V; Bonnin, M; Corinto, F

    2011-06-01

    Oscillatory networks are a special class of neural networks where each neuron exhibits time periodic behavior. They represent bio-inspired architectures which can be exploited to model biological processes such as the binding problem and selective attention. In this paper we investigate the dynamics of networks whose neurons are hard oscillators, namely they exhibit the coexistence of different stable attractors. We consider a constant external stimulus applied to each neuron, which influences the neuron's own natural frequency. We show that, due to the interaction between different kinds of attractors, as well as between attractors and repellors, new interesting dynamics arises, in the form of synchronous oscillations of various amplitudes. We also show that neurons subject to different stimuli are able to synchronize if their couplings are strong enough.

  12. 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.

  13. Master equation for an oscillator coupled to the electromagnetic field

    SciTech Connect

    Ford, G.W. |; Lewis, J.T.; OConnell, R.F. |

    1996-12-01

    The macroscopic description of a quantum oscillator with linear passive dissipation is formulated in terms of a master equation for the reduced density matrix. The procedure used is based on the asymptotic methods of nonlinear dynamics, which enables one to obtain an expression for the general term in the weak coupling expansion. For the special example of a charged oscillator interacting with the electromagnetic field, an explicit form of the master equation through third order in this expansion is obtained. This form differs from that generally obtained using the rotating wave approximation in that there is no electromagnetic (Lamb) shift and that an explicit expression is given for the decay rate. Copyright {copyright} 1996 Academic Press, Inc.

  14. Cavity Optomechanics: Coherent Coupling of Light and Mechanical Oscillators

    NASA Astrophysics Data System (ADS)

    Kippenberg, Tobias J.

    2012-06-01

    The mutual coupling of optical and mechanical degrees of freedom via radiation pressure has been a subject of interest in the context of quantum limited displacements measurements for Gravity Wave Detection for many decades, however light forces have remained experimentally unexplored in such systems. Recent advances in nano- and micro-mechanical oscillators have for the first time allowed the observation of radiation pressure phenomena in an experimental setting and constitute the expanding research field of cavity optomechanics [1]. These advances have allowed achieving to enter the quantum regime of mechanical systems, which are now becoming a third quantum technology after atoms, ions and molecules in a first and electronic circuits in a second wave. In this talk I will review these advances. Using on-chip micro-cavities that combine both optical and mechanical degrees of freedom in one and the same device [2], radiation pressure back-action of photons is shown to lead to effective cooling [3-6]) of the mechanical oscillator mode using dynamical backaction, which has been predicted by Braginsky as early as 1969 [4]. This back-action cooling exhibits many close analogies to atomic laser cooling. With this novel technique the quantum mechanical ground state of a micromechanical oscillator has been prepared with high probability using both microwave and optical fields. In our research this is reached using cryogenic precooling to ca. 800 mK in conjunction with laser cooling, allowing cooling of micromechanical oscillator to only motional 1.7 quanta, implying that the mechanical oscillator spends about 40% of its time in the quantum ground state. Moreover it is possible in this regime to observe quantum coherent coupling in which the mechanical and optical mode hybridize and the coupling rate exceeds the mechanical and optical decoherence rate [7]. This accomplishment enables a range of quantum optical experiments, including state transfer from light to mechanics

  15. Coupled Pendulums: A Classical Depiction of Laser Oscillation, Phase Diffusion and Laser Line-width

    NASA Astrophysics Data System (ADS)

    Bordoloi, Rajib; Bordoloi, Ranjana Bora; Buruah, Gauranga Dhar

    2016-08-01

    In this work we have presented an analogy between the coupled vibrations of two classical oscillators and the oscillations that take place in a laser cavity. Our aim is to understand classically the causes that lead to the phase diffusion in a system of coupled classical oscillators and to explore possibilities of any relationship between phase fluctuation and the frequency difference. The equations of motion for the classical oscillators have been derived and solved, for different values of coupling coefficients, to obtain the expressions for the mode frequencies1.The solutions, while plotted graphically have led us to the conclusion that in classical oscillators the mode frequencies of the oscillators are far apart if their oscillation is heavily coupling dependent and consequently the phase relationship of the oscillators fluctuate vigorously and frequently, which is the converse of what happens in a laser cavity consisting atomic oscillators.

  16. Transient dynamics of pulse-coupled oscillators with nonlinear charging curves.

    PubMed

    O'Keeffe, Kevin P

    2016-03-01

    We consider the transient behavior of globally coupled systems of identical pulse-coupled oscillators. Synchrony develops through an aggregation phenomenon, with clusters of synchronized oscillators forming and growing larger in time. Previous work derived expressions for these time dependent clusters, when each oscillator obeyed a linear charging curve. We generalize these results to cases where the charging curves have nonlinearities.

  17. Quasi-BLOCH oscillations in curved coupled optical waveguides.

    PubMed

    Joushaghani, Arash; Iyer, Rajiv; Poon, Joyce K S; Aitchison, J Stewart; de Sterke, C Martijn; Wan, Jun; Dignam, Marc M

    2009-10-01

    We report the observation of quasi-Bloch oscillations, a recently proposed, new type of dynamic localization in the spatial evolution of light in a curved coupled optical waveguide array. By spatially resolving the optical intensity at various propagation distances, we show the delocalization and final relocalization of the beam in the waveguide array. Through comparisons with other structures, we show that this dynamic localization is robust beyond the nearest-neighbor tight-binding approximation and exhibits a wavelength dependence different from conventional dynamic localization.

  18. 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.

  19. Out-of-unison resonance in weakly nonlinear coupled oscillators

    PubMed Central

    Hill, T. L.; Cammarano, A.; Neild, S. A.; Wagg, D. J.

    2015-01-01

    Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems. PMID:25568619

  20. Analytical Insights on Theta-Gamma Coupled Neural Oscillators

    PubMed Central

    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

  1. Plastic bottle oscillator as an on-off-type oscillator: Experiments, modeling, and stability analyses of single and coupled systems

    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.

  2. Plastic bottle oscillator as an on-off-type oscillator: experiments, modeling, and stability analyses of single and coupled systems.

    PubMed

    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.

  3. Long distance coupling of a quantum mechanical oscillator to the internal states of an atomic ensemble

    NASA Astrophysics Data System (ADS)

    Vogell, B.; Kampschulte, T.; Rakher, M. T.; Faber, A.; Treutlein, P.; Hammerer, K.; Zoller, P.

    2015-04-01

    We propose and investigate a hybrid optomechanical system consisting of a micro-mechanical oscillator coupled to the internal states of a distant ensemble of atoms. The interaction between the systems is mediated by a light field which allows the coupling of the two systems in a modular way over long distances. Coupling to internal degrees of freedom of atoms opens up the possibility to employ high-frequency mechanical resonators in the MHz to GHz regime, such as optomechanical crystal structures, and to benefit from the rich toolbox of quantum control over internal atomic states. Previous schemes involving atomic motional states are rather limited in both of these aspects. We derive a full quantum model for the effective coupling including the main sources of decoherence. As an application we show that sympathetic ground-state cooling and strong coupling between the two systems is possible.

  4. On the (Frequency) Modulation of Coupled Oscillator Arrays in Phased Array Beam Control

    NASA Technical Reports Server (NTRS)

    Pogorzelski, R.; Acorn, J.; Zawadzki, M.

    2000-01-01

    It has been shown that arrays of voltage controlled oscillators coupled to nearest neighbors can be used to produce useful aperture phase distributions for phased array antennas. However, placing information of the transmitted signal requires that the oscillations be modulated.

  5. 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.

  6. Synchronization of pairwise-coupled, identical, relaxation oscillators based on metal-insulator phase transition devices: A model study

    NASA Astrophysics Data System (ADS)

    Parihar, Abhinav; Shukla, Nikhil; Datta, Suman; Raychowdhury, Arijit

    2015-02-01

    Computing with networks of synchronous oscillators has attracted wide-spread attention as novel materials and device topologies have enabled realization of compact, scalable and low-power coupled oscillatory systems. Of particular interest are compact and low-power relaxation oscillators that have been recently demonstrated using MIT (metal-insulator-transition) devices using properties of correlated oxides. Further the computational capability of pairwise coupled relaxation oscillators has also been shown to outperform traditional Boolean digital logic circuits. This paper presents an analysis of the dynamics and synchronization of a system of two such identical coupled relaxation oscillators implemented with MIT devices. We focus on two implementations of the oscillator: (a) a D-D configuration where complementary MIT devices (D) are connected in series to provide oscillations and (b) a D-R configuration where it is composed of a resistor (R) in series with a voltage-triggered state changing MIT device (D). The MIT device acts like a hysteresis resistor with different resistances in the two different states. The synchronization dynamics of such a system has been analyzed with purely charge based coupling using a resistive (RC) and a capacitive (CC) element in parallel. It is shown that in a D-D configuration symmetric, identical and capacitively coupled relaxation oscillator system synchronizes to an anti-phase locking state, whereas when coupled resistively the system locks in phase. Further, we demonstrate that for certain range of values of RC and CC, a bistable system is possible which can have potential applications in associative computing. In D-R configuration, we demonstrate the existence of rich dynamics including non-monotonic flows and complex phase relationship governed by the ratios of the coupling impedance. Finally, the developed theoretical formulations have been shown to explain experimentally measured waveforms of such pairwise coupled

  7. Link between truncated fractals and coupled oscillators in biological systems.

    PubMed

    Paar, V; Pavin, N; Rosandić, M

    2001-09-01

    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.

  8. Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling.

    PubMed

    Song, Yongli; Xu, Jian; Zhang, Tonghua

    2011-06-01

    In this paper, we study a system of three coupled van der Pol oscillators that are coupled through the damping terms. Hopf bifurcations and amplitude death induced by the coupling time delay are first investigated by analyzing the related characteristic equation. Then the oscillation patterns of these bifurcating periodic oscillations are determined and we find that there are two kinds of critical values of the coupling time delay: one is related to the synchronous periodic oscillations, the other is related to eight branches of asynchronous periodic solutions bifurcating simultaneously from the zero solution. The stability of these bifurcating periodic solutions are also explicitly determined by calculating the normal forms on center manifolds, and the stable synchronous and stable phase-locked periodic solutions are found. Finally, some numerical simulations are employed to illustrate and extend our obtained theoretical results and numerical studies also describe the switches of stable synchronous and phase-locked periodic oscillations.

  9. Spatiotemporal Symmetry in Rings of Coupled Biological Oscillators of Physarum Plasmodial Slime Mold

    NASA Astrophysics Data System (ADS)

    Takamatsu, Atsuko; Tanaka, Reiko; Yamada, Hiroyasu; Nakagaki, Toshiyuki; Fujii, Teruo; Endo, Isao

    2001-08-01

    Spatiotemporal patterns in rings of coupled biological oscillators of the plasmodial slime mold, Physarum polycephalum, were investigated by comparing with results analyzed by the symmetric Hopf bifurcation theory based on group theory. In three-, four-, and five-oscillator systems, all types of oscillation modes predicted by the theory were observed including a novel oscillation mode, a half period oscillation, which has not been reported anywhere in practical systems. Our results support the effectiveness of the symmetric Hopf bifurcation theory in practical systems.

  10. Spatiotemporal Symmetry in Rings of Coupled Biological Oscillators of Physarum Plasmodial Slime Mold

    SciTech Connect

    Takamatsu, Atsuko; Tanaka, Reiko; Yamada, Hiroyasu; Nakagaki, Toshiyuki; Fujii, Teruo; Endo, Isao

    2001-08-13

    Spatiotemporal patterns in rings of coupled biological oscillators of the plasmodial slime mold, Physarum polycephalum, were investigated by comparing with results analyzed by the symmetric Hopf bifurcation theory based on group theory. In three-, four-, and five-oscillator systems, all types of oscillation modes predicted by the theory were observed including a novel oscillation mode, a half period oscillation, which has not been reported anywhere in practical systems. Our results support the effectiveness of the symmetric Hopf bifurcation theory in practical systems.

  11. Observation of chaotic dynamics of coupled nonlinear oscillators

    SciTech Connect

    Van Buskirk, R.; Jeffries, C.

    1985-05-01

    The nonlinear charge storage property of driven Si p-n junction passive resonators gives rise to chaotic dynamics: period doubling, chaos, periodic windows, and an extended period-adding sequence corresponding to entrainment of the resonator by successive subharmonics of the driving frequency. The physical system is described; equations of motion and iterative maps are reviewed. Computed behavior is compared to data, with reasonable agreement for Poincare sections, bifurcation diagrams, and phase diagrams in parameter space (drive voltage, drive frequency). N = 2 symmetrically coupled resonators are found to display period doubling, Hopf bifurcations, entrainment horns (''Arnol'd tongues''), breakup of the torus, and chaos. This behavior is in reasonable agreement with theoretical models based on the characteristics of single-junction resonators. The breakup of the torus is studied in detail, by Poincare sections and by power spectra. Also studied are oscillations of the torus and cyclic crises. A phase diagram of the coupled resonators can be understood from the model. Poincare sections show self-similarity and fractal structure, with measured values of fractal dimension d = 2.03 and d = 2.23 for N = 1 and N = 2 resonators, respectively. Two line-coupled resonators display first a Hopf bifurcation as the drive parameter is increased, in agreement with the model. For N = 4 and N = 12 line-coupled resonators complex quasiperiodic behavior is observed with up to 3 and 4 incommensurate frequencies, respectively.

  12. Stimulus-locked responses of two phase oscillators coupled with delayed feedback

    NASA Astrophysics Data System (ADS)

    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.

  13. Theory of mode coupling in spin torque oscillators coupled to a thermal bath of magnons

    NASA Astrophysics Data System (ADS)

    Zhou, Yan; Zhang, Shulei; Li, Dong; Heinonen, Olle

    Recently, numerous experimental investigations have shown that the dynamics of a single spin torque oscillator (STO) exhibits complex behavior stemming from interactions between two or more modes of the oscillator. Examples are the observed mode-hopping and 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 this work, we rigorously derive such a theory starting with the generalized Landau-Lifshitz-Gilbert equation in the presence of the current-driven spin transfer torques. We will first show, in general, that how a linear mode coupling would arise through the coupling of the system to a thermal bath of magnons, which implies that the manifold of orbits and fixed points may shift with temperature. We then apply our theory to two experimentally interesting systems: 1) a STO patterned into nano-pillar with circular or elliptical cross-sections and 2) a nano-contact STO. For both cases, we found that in order to get mode coupling, it would be necessary to have either a finite in-plane component of the external field or an Oersted field. We will also discuss the temperature dependence of the linear mode coupling. Y. Zhou acknowledges the support by the Seed Funding Program for Basic Research from the University of Hong Kong, and University Grants Committee of Hong Kong (Contract No. AoE/P-04/08).

  14. Long-term fluctuations in globally coupled phase oscillators with general coupling: finite size effects.

    PubMed

    Nishikawa, Isao; Tanaka, Gouhei; Horita, Takehiko; Aihara, Kazuyuki

    2012-03-01

    We investigate the diffusion coefficient of the time integral of the Kuramoto order parameter in globally coupled nonidentical phase oscillators. This coefficient represents the deviation of the time integral of the order parameter from its mean value on the sample average. In other words, this coefficient characterizes long-term fluctuations of the order parameter. For a system of N coupled oscillators, we introduce a statistical quantity D, which denotes the product of N and the diffusion coefficient. We study the scaling law of D with respect to the system size N. In other well-known models such as the Ising model, the scaling property of D is D∼O(1) for both coherent and incoherent regimes except for the transition point. In contrast, in the globally coupled phase oscillators, the scaling law of D is different for the coherent and incoherent regimes: D∼O(1/N(a)) with a certain constant a>0 in the coherent regime and D∼O(1) in the incoherent regime. We demonstrate that these scaling laws hold for several representative coupling schemes.

  15. COUPLED ALFVEN AND KINK OSCILLATIONS IN CORONAL LOOPS

    SciTech Connect

    Pascoe, D. J.; Wright, A. N.; De Moortel, I.

    2010-03-10

    Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. However, there is ongoing discussion regarding their interpretation as kink or Alfven waves. To investigate the nature of transverse waves propagating in the solar corona and their potential for use as a coronal diagnostic in MHD seismology, we perform three-dimensional numerical simulations of footpoint-driven transverse waves propagating in a low beta plasma. We consider the cases of both a uniform medium and one with loop-like density structure and perform a parametric study for our structuring parameters. When density structuring is present, resonant absorption in inhomogeneous layers leads to the coupling of the kink mode to the Alfven mode. The decay of the propagating kink wave as energy is transferred to the local Alfven mode is in good agreement with a modified interpretation of the analysis of Ruderman and Roberts for standing kink modes. Numerical simulations support the most general interpretation of the observed loop oscillations as a coupling of the kink and Alfven modes. This coupling may account for the observed predominance of outward wave power in longer coronal loops since the observed damping length is comparable to our estimate based on an assumption of resonant absorption as the damping mechanism.

  16. 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.

  17. Coupled-oscillator theory of dispersion and Casimir-Polder interactions

    SciTech Connect

    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.

  18. Decoherence in a system of strongly coupled quantum oscillators. I. Symmetric network

    SciTech Connect

    Ponte, M.A. de; Oliveira, M.C. de; Moussa, M.H.Y.

    2004-08-01

    In this work we analyze the coherence dynamics and estimate decoherence times of quantum states in a network composed of N coupled dissipative quantum oscillators. We assume a symmetric network where all oscillators are coupled to each other with the same coupling strength. Master equations are derived for regimes of both weak and strong coupling between the oscillators. The strong coupling regime is characterized by the coupling strength between the oscillators or by the number of oscillators in the network. The decoherence times of particular states of the network are computed and the results are clarified by analyzing the processes of state swap and recurrence of reduced states of the network together with the linear entropies of the joint and reduced systems.

  19. New type of excitatory pulse coupling of chemical oscillators via inhibitor.

    PubMed

    Proskurkin, Ivan S; Vanag, Vladimir K

    2015-07-21

    We introduce a new type of pulse coupling between chemical oscillators. A constant inflow of inhibitor in one reactor is interrupted shortly after a time delay after a sharp spike of activity in the other reactor. We proved experimentally and theoretically that this reversed inhibitory coupling is analogous to excitatory coupling. We did this by analyzing phase response curves, dependences of different synchronous regimes of the 1 : 1 resonance on time delay, and other resonances of two coupled chemical oscillators. Dynamical rhythms of two Belousov-Zhabotinsky oscillators coupled via "negative" inhibitory pulses were investigated.

  20. Quantifying phase-amplitude coupling in neuronal network oscillations.

    PubMed

    Onslow, Angela C E; Bogacz, Rafal; Jones, Matthew W

    2011-03-01

    Neuroscience time series data from a range of techniques and species reveal complex, non-linear interactions between different frequencies of neuronal network oscillations within and across brain regions. Here, we briefly review the evidence that these nested, cross-frequency interactions act in concert with linearly covariant (within-frequency) activity to dynamically coordinate functionally related neuronal ensembles during behaviour. Such studies depend upon reliable quantification of cross-frequency coordination, and we compare the properties of three techniques used to measure phase-amplitude coupling (PAC)--Envelope-to-Signal Correlation (ESC), the Modulation Index (MI) and Cross-Frequency Coherence (CFC)--by standardizing their filtering algorithms and systematically assessing their robustness to noise and signal amplitude using artificial signals. Importantly, we also introduce a freely-downloadable method for estimating statistical significance of PAC, a step overlooked in the majority of published studies. We find that varying data length and noise levels leads to the three measures differentially detecting false positives or correctly identifying frequency bands of interaction; these conditions should therefore be taken into careful consideration when selecting PAC analyses. Finally, we demonstrate the utility of the three measures in quantifying PAC in local field potential data simultaneously recorded from rat hippocampus and prefrontal cortex, revealing a novel finding of prefrontal cortical theta phase modulating hippocampal gamma power. Future adaptations that allow detection of time-variant PAC should prove essential in deciphering the roles of cross-frequency coupling in mediating or reflecting nervous system function.

  1. Delay-induced patterns in a two-dimensional lattice of coupled oscillators.

    PubMed

    Kantner, Markus; Schöll, Eckehard; Yanchuk, Serhiy

    2015-02-17

    We show how a variety of stable spatio-temporal periodic patterns can be created in 2D-lattices of coupled oscillators with non-homogeneous coupling delays. The results are illustrated using the FitzHugh-Nagumo coupled neurons as well as coupled limit cycle (Stuart-Landau) oscillators. A "hybrid dispersion relation" is introduced, which describes the stability of the patterns in spatially extended systems with large time-delay.

  2. Synchronous regimes in ensembles of coupled Bonhoeffer-van der Pol oscillators.

    PubMed

    Kryukov, Alexey K; Osipov, Grigory V; Polovinkin, Andrey V; Kurths, Jürgen

    2009-04-01

    We study synchronous behavior in ensembles of locally coupled nonidentical Bonhoeffer-van der Pol oscillators. We show that, in a chain of N elements not less than 2;{N-1}, different coexisting regimes of global synchronization are possible, and we investigate wave-induced synchronous regimes in a chain and in a lattice of coupled nonidentical Bonhoeffer-van der Pol oscillators.

  3. Restoration of distorted images, terahertz generation and terahertz interference based on multiple-coupled optical parametric oscillators

    NASA Astrophysics Data System (ADS)

    Ding, Yujie J.

    2015-03-01

    We review our progress made on applications of coupled optical parametric oscillators based on a composite consisting of adhesive-free-bonded KTiOPO4 stacks. By using the phase- conjugate output generated by the composite, we have demonstrated that the spatial profile after the beam propagates through the phase-distorted medium can be restored to the profile before the distortion. In addition, we have restored the images being blurred by the phase distortion. We have efficiently generated terahertz outputs by mixing the idler twins from the coupled optical parametric oscillators. By using the alternatively-rotated GaP plates as an output coupler for the coupled optical parametric oscillators, we have efficiently generated terahertz waves based on an intracavity configuration. By placing both the composite and a bulk KTiOPO4 crystal in the same cavity, we have demonstrated the interference effect of the THz waves generated by using different pairs of the optical beams.

  4. Energy eigenvalues and squeezing properties of general systems of coupled quantum anharmonic oscillators

    SciTech Connect

    Chung, N. N.; Chew, L. Y.

    2007-09-15

    We have generalized the two-step approach to the solution of systems of N coupled quantum anharmonic oscillators. By using the squeezed vacuum state of each individual oscillator, we construct the tensor product state, and obtain the optimal squeezed vacuum product state through energy minimization. We then employ this optimal state and its associated bosonic operators to define a basis set to construct the Heisenberg matrix. The diagonalization of the matrix enables us to obtain the energy eigenvalues of the coupled oscillators. In particular, we have applied our formalism to determine the eigenenergies of systems of two coupled quantum anharmonic oscillators perturbed by a general polynomial potential, as well as three and four coupled systems. Furthermore, by performing a first-order perturbation analysis about the optimal squeezed vacuum product state, we have also examined into the squeezing properties of two coupled oscillator systems.

  5. Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators.

    PubMed

    Senthilkumar, D V; Muruganandam, P; Lakshmanan, M; Kurths, J

    2010-06-01

    Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at (mN(c)+1)-th oscillators in the ring, where m is an integer and N(c) is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength ε(c) with a scaling exponent γ. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents of the coupled systems. We find that the same scaling relation exists for m couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength ε. In addition, we have found that ε(c) shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of Rössler and Lorenz oscillators.

  6. Controlling and synchronizing the spatiotemporal chaos of photorefractive ring oscillators with coupling

    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.

  7. Resonant Coupling of a Bose-Einstein Condensate to a Micromechanical Oscillator

    SciTech Connect

    Hunger, David; Camerer, Stephan; Haensch, Theodor W.; Treutlein, Philipp; Koenig, Daniel; Kotthaus, Joerg P.; Reichel, Jakob

    2010-04-09

    We report experiments in which the vibrations of a micromechanical oscillator are coupled to the motion of Bose-condensed atoms in a trap. The interaction relies on surface forces experienced by the atoms at about 1 {mu}m distance from the mechanical structure. We observe resonant coupling to several well-resolved mechanical modes of the condensate. Coupling via surface forces does not require magnets, electrodes, or mirrors on the oscillator and could thus be employed to couple atoms to molecular-scale oscillators such as carbon nanotubes.

  8. Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping

    NASA Astrophysics Data System (ADS)

    Raghavan, S.; Smerzi, A.; Fantoni, S.; Shenoy, S. R.

    1999-01-01

    We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to π (π-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of 3He-B and the internal Josephson effect in 3He-A are also discussed.

  9. An efficient method for simulation of noisy coupled multi-dimensional oscillators

    NASA Astrophysics Data System (ADS)

    Stinchcombe, Adam R.; Forger, Daniel B.

    2016-09-01

    We present an efficient computational method for the study of populations of noisy coupled oscillators. By taking a population density approach in which the probability density of observing an oscillator at a point of state space is the primary variable instead of the states of all of the oscillators, we are able to seamlessly account for intrinsic noise within the oscillators and global coupling within the population. The population is assumed to consist of a large number of oscillators so that the noise process is well sampled over the population. Our numerical method is able to solve the governing equation even in the challenging case of limit cycle oscillators with a large number of state variables. Instead of simulating a prohibitive number of oscillators, our particle method simulates relatively few particles allowing for the efficient solution of the governing equation.

  10. The influence of interchain coupling on intramolecular oscillation mobility in coupled macromolecular chains: The case of coplanar parallel chains

    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.

  11. Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure

    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.

  12. Pacemaking through Ca2+ stores interacting as coupled oscillators via membrane depolarization.

    PubMed

    Imtiaz, Mohammad S; Zhao, Jun; Hosaka, Kayoko; von der Weid, Pierre-Yves; Crowe, Melissa; van Helden, Dirk F

    2007-06-01

    This study presents an investigation of pacemaker mechanisms underlying lymphatic vasomotion. We tested the hypothesis that active inositol 1,4,5-trisphosphate receptor (IP(3)R)-operated Ca(2+) stores interact as coupled oscillators to produce near-synchronous Ca(2+) release events and associated pacemaker potentials, this driving action potentials and constrictions of lymphatic smooth muscle. Application of endothelin 1 (ET-1), an agonist known to enhance synthesis of IP(3), to quiescent lymphatic smooth muscle syncytia first enhanced spontaneous Ca(2+) transients and/or intracellular Ca(2+) waves. Larger near-synchronous Ca(2+) transients then occurred leading to global synchronous Ca(2+) transients associated with action potentials and resultant vasomotion. In contrast, blockade of L-type Ca(2+) channels with nifedipine prevented ET-1 from inducing near-synchronous Ca(2+) transients and resultant action potentials, leaving only asynchronous Ca(2+) transients and local Ca(2+) waves. These data were well simulated by a model of lymphatic smooth muscle with: 1), oscillatory Ca(2+) release from IP(3)R-operated Ca(2+) stores, which causes depolarization; 2), L-type Ca(2+) channels; and 3), gap junctions between cells. Stimulation of the stores caused global pacemaker activity through coupled oscillator-based entrainment of the stores. Membrane potential changes and positive feedback by L-type Ca(2+) channels to produce more store activity were fundamental to this process providing long-range electrochemical coupling between the Ca(2+) store oscillators. We conclude that lymphatic pacemaking is mediated by coupled oscillator-based interactions between active Ca(2+) stores. These are weakly coupled by inter- and intracellular diffusion of store activators and strongly coupled by membrane potential. Ca(2+) store-based pacemaking is predicted for cellular systems where: 1), oscillatory Ca(2+) release induces depolarization; 2), membrane depolarization provides positive

  13. Synchronization in an ensemble of spatially moving oscillators with linear and nonlinear coupling schemes

    NASA Astrophysics Data System (ADS)

    Janagal, Lavneet; Parmananda, P.

    2012-11-01

    We study synchronization in an ensemble of oscillators residing in a finite two-dimensional space. The interaction between the oscillators is governed by their spatial movement. The coupling is unidirectional and is of the intermediate kind, with the spatial vision of each oscillator deciding the number of oscillators to which it is coupled. We also analyze how the extent of synchronization, characterized by the order parameter, depends upon the system parameters, such as spatial vision, spatial motion, and strength of the coupling. The model systems employed here are the Van der Pol oscillator and the Brusselator. Furthermore, for the same spatial configuration, both linear and nonlinear coupling schemes are studied and their results compared.

  14. Synchronization in an ensemble of spatially moving oscillators with linear and nonlinear coupling schemes.

    PubMed

    Janagal, Lavneet; Parmananda, P

    2012-11-01

    We study synchronization in an ensemble of oscillators residing in a finite two-dimensional space. The interaction between the oscillators is governed by their spatial movement. The coupling is unidirectional and is of the intermediate kind, with the spatial vision of each oscillator deciding the number of oscillators to which it is coupled. We also analyze how the extent of synchronization, characterized by the order parameter, depends upon the system parameters, such as spatial vision, spatial motion, and strength of the coupling. The model systems employed here are the Van der Pol oscillator and the Brusselator. Furthermore, for the same spatial configuration, both linear and nonlinear coupling schemes are studied and their results compared. PMID:23214863

  15. The role of axonal delay in the synchronization of networks of coupled cortical oscillators.

    PubMed

    Crook, S M; Ermentrout, G B; Vanier, M C; Bower, J M

    1997-04-01

    Coupled oscillator models use a single phase variable to approximate the voltage oscillation of each neuron during repetitive firing where the behavior of the model depends on the connectivity and the interaction function chosen to describe the coupling. We introduce a network model consisting of a continuum of these oscillators that includes the effects of spatially decaying coupling and axonal delay. We derive equations for determining the stability of solutions and analyze the network behavior for two different interaction functions. The first is a sine function, and the second is derived from a compartmental model of a pyramidal cell. In both cases, the system of coupled neural oscillators can undergo a bifurcation from synchronous oscillations to waves. The change in qualitative behavior is due to the axonal delay, which causes distant connections to encourage a phase shift between cells. We suggest that this mechanism could contribute to the behavior observed in several neurobiological systems.

  16. Intense energy transfer and superharmonic resonance in a system of two coupled oscillators.

    PubMed

    Kovaleva, Agnessa; Manevitch, Leonid; Manevitch, Elina

    2010-05-01

    The paper presents the analytic study of energy exchange in a system of coupled nonlinear oscillators subject to superharmonic resonance. The attention is given to complete irreversible energy transfer that occurs in a system with definite initial conditions corresponding to a so-called limiting phase trajectory (LPT). We show that the energy imparted in the system is partitioned among the principal and superharmonic modes but energy exchange can be due to superharmonic oscillations. Using the LPT concept, we construct approximate analytic solutions describing intense irreversible energy transfer in a harmonically excited Duffing oscillator and a system of two nonlinearly coupled oscillators. Numerical simulations confirm the accuracy of the analytic approximations. PMID:20866315

  17. Phase-flip transition in nonlinear oscillators coupled by dynamic environment.

    PubMed

    Sharma, Amit; Shrimali, Manish Dev; Dana, Syamal Kumar

    2012-06-01

    We study the dynamics of nonlinear oscillators indirectly coupled through a dynamical environment or a common medium. We observed that this form of indirect coupling leads to synchronization and phase-flip transition in periodic as well as chaotic regime of oscillators. The phase-flip transition from in- to anti-phase synchronization or vise-versa is analyzed in the parameter plane with examples of Landau-Stuart and Rössler oscillators. The dynamical transitions are characterized using various indices such as average phase difference, frequency, and Lyapunov exponents. Experimental evidence of the phase-flip transition is shown using an electronic version of the van der Pol oscillators.

  18. Insights into collective cell behaviour from populations of coupled chemical oscillators.

    PubMed

    Taylor, Annette F; Tinsley, Mark R; Showalter, Kenneth

    2015-08-21

    Biological systems such as yeast show coordinated activity driven by chemical communication between cells. Here, we show how experiments with coupled chemical oscillators can provide insights into collective behaviour in cellular systems. Two methods of coupling the oscillators are described: exchange of chemical species with the surrounding solution and computer-controlled illumination of a light-sensitive catalyst. The collective behaviour observed includes synchronisation, dynamical quorum sensing (a density dependent transition to population-wide oscillations), and chimera states, where oscillators spontaneously split into coherent and incoherent groups. At the core of the different types of behaviour lies an intracellular autocatalytic signal and an intercellular communication mechanism that influences the autocatalytic growth.

  19. Synchronization and quorum sensing in an ensemble of indirectly coupled chaotic oscillators.

    PubMed

    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.

  20. 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.

  1. 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.

  2. Experimental and theoretical approach for the clustering of globally coupled density oscillators based on phase response.

    PubMed

    Horie, Masanobu; Sakurai, Tatsunari; Kitahata, Hiroyuki

    2016-01-01

    We investigated the phase-response curve of a coupled system of density oscillators with an analytical approach. The behaviors of two-, three-, and four-coupled systems seen in the experiments were reproduced by the model considering the phase-response curve. Especially in a four-coupled system, the clustering state and its incidence rate as functions of the coupling strength are well reproduced with this approach. Moreover, we confirmed that the shape of the phase-response curve we obtained analytically was close to that observed in the experiment where a perturbation is added to a single-density oscillator. We expect that this approach to obtaining the phase-response curve is general in the sense that it could be applied to coupled systems of other oscillators such as electrical-circuit oscillators, metronomes, and so on.

  3. Noise-induced synchronization, desynchronization, and clustering in globally coupled nonidentical oscillators.

    PubMed

    Lai, Yi Ming; Porter, Mason A

    2013-07-01

    We study ensembles of globally coupled, nonidentical phase oscillators subject to correlated noise, and we identify several important factors that cause noise and coupling to synchronize or desynchronize a system. By introducing noise in various ways, we find an estimate for the onset of synchrony of a system in terms of the coupling strength, noise strength, and width of the frequency distribution of its natural oscillations. We also demonstrate that noise alone can be sufficient to synchronize nonidentical oscillators. However, this synchrony depends on the first Fourier mode of a phase-sensitivity function, through which we introduce common noise into the system. We show that higher Fourier modes can cause desynchronization due to clustering effects, and that this can reinforce clustering caused by different forms of coupling. Finally, we discuss the effects of noise on an ensemble in which antiferromagnetic coupling causes oscillators to form two clusters in the absence of noise.

  4. Clustering in globally coupled oscillators near a Hopf bifurcation: Theory and experiments

    NASA Astrophysics Data System (ADS)

    Kori, Hiroshi; Kuramoto, Yoshiki; Jain, Swati; Kiss, István Z.; Hudson, John L.

    2014-06-01

    A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.

  5. Clustering in globally coupled oscillators near a Hopf bifurcation: theory and experiments.

    PubMed

    Kori, Hiroshi; Kuramoto, Yoshiki; Jain, Swati; Kiss, István Z; Hudson, John L

    2014-06-01

    A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators. PMID:25019850

  6. Clustering in globally coupled oscillators near a Hopf bifurcation: theory and experiments.

    PubMed

    Kori, Hiroshi; Kuramoto, Yoshiki; Jain, Swati; Kiss, István Z; Hudson, John L

    2014-06-01

    A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher-order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate analytically the phase coupling function from given limit-cycle oscillator models. Moreover, using the phase coupling function, the stability of phase clusters can be analyzed. We demonstrate our theory with the Brusselator model. Experiments are carried out to confirm the presence of phase clusters close to Hopf bifurcations with electrochemical oscillators.

  7. Revisiting an old concept: the coupled oscillator model for VCD. Part 1: the generalised coupled oscillator mechanism and its intrinsic connection to the strength of VCD signals.

    PubMed

    Nicu, Valentin Paul

    2016-08-01

    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.

  8. Clinical Application of the Forced Oscillation Technique.

    PubMed

    Shirai, Toshihiro; Kurosawa, Hajime

    2016-01-01

    The forced oscillation technique (FOT) is a noninvasive method with which to measure respiratory system resistance and reactance during tidal breathing. Recently, its clinical application has spread worldwide with the expansion of commercially available broadband frequency FOT devices, including MostGraph and Impulse Oscillometry. An increasing number of reports have supported the usefulness of the FOT in the management of asthma and chronic obstructive pulmonary disease (COPD). However, the FOT is not a surrogate test for spirometry, but should be used complementarily. Furthermore, reference values are not necessarily available and the interpretation of some measured data is controversial. There is a need to update the international statement for not only technical aspects but also the clinical use of the FOT. In this review, we summarize the previously published studies and discuss how to use the FOT in a clinical setting. PMID:26984069

  9. Planar dielectric resonator stabilized HEMT oscillator integrated with CPW/aperture coupled patch antenna

    NASA Technical Reports Server (NTRS)

    Simons, Rainee N.; Lee, Richard Q.

    1992-01-01

    A design of an active antenna with a dielectric resonator stabilized high-electron-mobility transistor (HEMT) oscillator (DRO) and an aperture-coupled patch antenna is reported. The circuit is fabricated using coplanar waveguide (CPW) with the oscillator and the antenna on opposite sides of the substrate. The active antenna was demonstrated at 7.6 GHz; however, the design can be scaled to higher frequencies. Excellent oscillator characteristics and radiation patterns were obtained.

  10. Planar dielectric resonator stabilized HEMT oscillator integrated with CPW/aperture coupled patch antenna

    NASA Technical Reports Server (NTRS)

    Simons, Rainee N.; Lee, Richard Q.

    1992-01-01

    A new design of an active antenna with a dielectric resonator stabilized high electron mobility transistor (HEMT) oscillator (DRO) and an aperture-coupled patch antenna is reported. The circuit is fabricated using coplanar waveguide (CPW) with the oscillator and the antenna on opposite sides of the substrate. The active antenna was demonstrated at 7.6 GHz; however, the design can be scaled to higher frequencies. Excellent oscillator characteristics and radiation patterns were obtained.

  11. Transverse mode coupling and supermode establishment in a free-electron laser oscillator

    SciTech Connect

    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.

  12. 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.

  13. 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.

  14. Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators

    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.

  15. Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling

    NASA Astrophysics Data System (ADS)

    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.

  16. Disorder-induced dynamics in a pair of coupled heterogeneous phase oscillator networks.

    PubMed

    Laing, Carlo R

    2012-12-01

    We consider a pair of coupled heterogeneous phase oscillator networks and investigate their dynamics in the continuum limit as the intrinsic frequencies of the oscillators are made more and more disparate. The Ott/Antonsen Ansatz is used to reduce the system to three ordinary differential equations. We find that most of the interesting dynamics, such as chaotic behaviour, can be understood by analysing a gluing bifurcation of periodic orbits; these orbits can be thought of as "breathing chimeras" in the limit of identical oscillators. We also add Gaussian white noise to the oscillators' dynamics and derive a pair of coupled Fokker-Planck equations describing the dynamics in this case. Comparison with simulations of finite networks of oscillators is used to confirm many of the results.

  17. Sequential nonideal measurements of quantum oscillators: Statistical characterization with and without environmental coupling

    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.

  18. Inhibitory and excitatory pulse coupling of two frequency-different chemical oscillators with time delay.

    PubMed

    Proskurkin, Ivan S; Lavrova, Anastasia I; Vanag, Vladimir K

    2015-06-01

    Dynamical regimes of two pulse coupled non-identical Belousov-Zhabotinsky oscillators have been studied experimentally as well as theoretically with the aid of ordinary differential equations and phase response curves both for pure inhibitory and pure excitatory coupling. Time delay τ between a spike in one oscillator and perturbing pulse in the other oscillator plays a significant role for the phase relations of synchronous regimes of the 1:1 and 1:2 resonances. Birhythmicity between anti-phase and in-phase oscillations for inhibitory pulse coupling as well as between 1:2 and 1:1 resonances for excitatory pulse coupling have also been found. Depending on the ratio of native periods of oscillations T2/T1, coupling strength, and time delay τ, such resonances as 1:1 (with different phase locking), 2:3, 1:2, 2:5, 1:3, 1:4, as well as complex oscillations and oscillatory death are observed.

  19. Amplitude and phase effects on the synchronization of delay-coupled oscillators

    SciTech Connect

    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.

  20. Transition from homogeneous to inhomogeneous steady states in oscillators under cyclic coupling

    NASA Astrophysics Data System (ADS)

    Bera, Bidesh K.; Hens, Chittaranjan; Bhowmick, Sourav K.; Pal, Pinaki; Ghosh, Dibakar

    2016-01-01

    We report a transition from homogeneous steady state to inhomogeneous steady state in coupled oscillators, both limit cycle and chaotic, under cyclic coupling and diffusive coupling as well when an asymmetry is introduced in terms of a negative parameter mismatch. Such a transition appears in limit cycle systems via pitchfork bifurcation as usual. Especially, when we focus on chaotic systems, the transition follows a transcritical bifurcation for cyclic coupling while it is a pitchfork bifurcation for the conventional diffusive coupling. We use the paradigmatic Van der Pol oscillator as the limit cycle system and a Sprott system as a chaotic system. We verified our results analytically for cyclic coupling and numerically check all results including diffusive coupling for both the limit cycle and chaotic systems.

  1. Pain Related Cortical Oscillations: Methodological Advances and Potential Applications

    PubMed Central

    Peng, Weiwei; Tang, Dandan

    2016-01-01

    Alongside the time-locked event-related potentials (ERPs), nociceptive somatosensory inputs can induce modulations of ongoing oscillations, appeared as event-related synchronization or desynchronization (ERS/ERD) in different frequency bands. These ERD/ERS activities are suggested to reflect various aspects of pain perception, including the representation, encoding, assessment, and integration of the nociceptive sensory inputs, as well as behavioral responses to pain, even the precise details of their roles remain unclear. Previous studies investigating the functional relevance of ERD/ERS activities in pain perception were normally done by assessing their latencies, frequencies, magnitudes, and scalp distributions, which would be then correlated with subjective pain perception or stimulus intensity. Nevertheless, these temporal, spectral, and spatial profiles of stimulus induced ERD/ERS could only partly reveal the dynamics of brain oscillatory activities. Indeed, additional parameters, including but not limited to, phase, neural generator, and cross frequency couplings, should be paid attention to comprehensively and systemically evaluate the dynamics of oscillatory activities associated with pain perception and behavior. This would be crucial in exploring the psychophysiological mechanisms of neural oscillation, and in understanding the neural functions of cortical oscillations involved in pain perception and behavior. Notably, some chronic pain (e.g., neurogenic pain and complex regional pain syndrome) patients are often associated with the occurrence of abnormal synchronized oscillatory brain activities, and selectively modulating cortical oscillatory activities has been showed to be a potential therapy strategy to relieve pain with the application of neurostimulation techniques, e.g., repeated transcranial magnetic stimulation (rTMS) and transcranial alternating current stimulation (tACS). Thus, the investigation of the oscillatory activities proceeding from

  2. Pain Related Cortical Oscillations: Methodological Advances and Potential Applications.

    PubMed

    Peng, Weiwei; Tang, Dandan

    2016-01-01

    Alongside the time-locked event-related potentials (ERPs), nociceptive somatosensory inputs can induce modulations of ongoing oscillations, appeared as event-related synchronization or desynchronization (ERS/ERD) in different frequency bands. These ERD/ERS activities are suggested to reflect various aspects of pain perception, including the representation, encoding, assessment, and integration of the nociceptive sensory inputs, as well as behavioral responses to pain, even the precise details of their roles remain unclear. Previous studies investigating the functional relevance of ERD/ERS activities in pain perception were normally done by assessing their latencies, frequencies, magnitudes, and scalp distributions, which would be then correlated with subjective pain perception or stimulus intensity. Nevertheless, these temporal, spectral, and spatial profiles of stimulus induced ERD/ERS could only partly reveal the dynamics of brain oscillatory activities. Indeed, additional parameters, including but not limited to, phase, neural generator, and cross frequency couplings, should be paid attention to comprehensively and systemically evaluate the dynamics of oscillatory activities associated with pain perception and behavior. This would be crucial in exploring the psychophysiological mechanisms of neural oscillation, and in understanding the neural functions of cortical oscillations involved in pain perception and behavior. Notably, some chronic pain (e.g., neurogenic pain and complex regional pain syndrome) patients are often associated with the occurrence of abnormal synchronized oscillatory brain activities, and selectively modulating cortical oscillatory activities has been showed to be a potential therapy strategy to relieve pain with the application of neurostimulation techniques, e.g., repeated transcranial magnetic stimulation (rTMS) and transcranial alternating current stimulation (tACS). Thus, the investigation of the oscillatory activities proceeding from

  3. Synchronization in slowly switching networks of coupled oscillators

    PubMed Central

    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

  4. Time-delay effects on the aging transition in a population of coupled oscillators.

    PubMed

    Thakur, Bhumika; Sharma, Devendra; Sen, Abhijit

    2014-10-01

    We investigate the influence of time-delayed coupling on the nature of the aging transition in a system of coupled oscillators that have a mix of active and inactive oscillators, where the aging transition is defined as the gradual loss of collective synchrony as the proportion of inactive oscillators is increased. We start from a simple model of two time-delay coupled Stuart-Landau oscillators that have identical frequencies but are located at different distances from the Hopf bifurcation point. A systematic numerical and analytic study delineates the dependence of the critical coupling strength (at which the system experiences total loss of synchrony) on time delay and the average distance of the system from the Hopf bifurcation point. We find that time delay can act to facilitate the aging transition by lowering the threshold coupling strength for amplitude death in the system. We then extend our study to larger systems of globally coupled active and inactive oscillators including an infinite system in the thermodynamic limit. Our model system and results can provide a useful paradigm for understanding the functional robustness of diverse physical and biological systems that are prone to aging transitions.

  5. Two pulse-coupled non-identical, frequency-different BZ oscillators with time delay.

    PubMed

    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.

  6. Self-sustained oscillation and harmonic generation in optomechanical systems with quadratic couplings

    NASA Astrophysics Data System (ADS)

    Zhang, Lin; Kong, Hong-Yan

    2014-02-01

    Many works are based on the steady-state analysis of mean-value dynamics in electro- or optomechanical systems to explore vibration cooling, squeezing, and quantum-state controlling of massive objects. These studies are always conducted in a red-detuned pumping field under a lower power to maintain a stable situation. In this paper we consider self-sustained oscillations of a cavity-field-driven oscillator combined with quadratic coupling in a blue-detuned regime above a pumping threshold. Our study finds that the oscillator will be far away from its steady-state behavior by conducting a self-sustained oscillation with a discrete amplitude locking effect producing a rich energy-balanced structure. The dynamical backaction of this self-oscillation on the field mode induces a multipeak field spectrum, which implies an efficient harmonic generation with its intensity modified not only by the displacement x0 but also by the amplitude A of the mechanical oscillation. The corresponding nonlinear field spectrum and its magnitude are analytically analyzed with quadratic coupling when the mechanical oscillator is dynamically locked to a self-sustained oscillation.

  7. Enhanced interaction between a mechanical oscillator and two coupled resonant electrical circuits

    PubMed Central

    Dmitriev, A. V.; Mitrofanov, V. P.

    2014-01-01

    This paper reports result of calculation and experimental realization of an electromechanical system that consists of a high-Q mechanical oscillator parametrically coupled in the manner of a capacitive transducer with a radio frequency (RF) circuit, which is in turn inductively coupled with another RF circuit. The system operates in the resolved sideband regime when the mechanical oscillator's frequency is larger than the electrical circuits' bandwidths. Using two coupled RF circuits allowed one to enhance the interaction between them and the mechanical oscillator which is one of flexural vibrational modes of a free-edge circular silicon wafer. Such a coupled electromechanical system can be used as a high-sensitive capacitive vibration sensor. PMID:25173304

  8. Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators.

    PubMed

    Selivanov, Anton A; Lehnert, Judith; Dahms, Thomas; Hövel, Philipp; Fradkov, Alexander L; Schöll, Eckehard

    2012-01-01

    We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime. We propose goal functions based on both the difference of the oscillators and a generalized order parameter and demonstrate that the speed-gradient method allows one to find appropriate coupling phases with which different states of synchronization, e.g., in-phase oscillation, splay, or various cluster states, can be selected.

  9. Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrödinger equations

    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.

  10. Nonreciprocal wave scattering on nonlinear string-coupled oscillators

    SciTech Connect

    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.

  11. Using Coupled Harmonic Oscillators to Model Some Greenhouse Gas Molecules

    SciTech Connect

    Go, Clark Kendrick C.; Maquiling, Joel T.

    2010-07-28

    Common greenhouse gas molecules SF{sub 6}, NO{sub 2}, CH{sub 4}, and CO{sub 2} are modeled as harmonic oscillators whose potential and kinetic energies are derived. Using the Euler-Lagrange equation, their equations of motion are derived and their phase portraits are plotted. The authors use these data to attempt to explain the lifespan of these gases in the atmosphere.

  12. Ultracold atoms coupled to micro- and nanomechanical oscillators: towards hybrid quantum systems

    NASA Astrophysics Data System (ADS)

    Treutlein, Philipp

    2009-05-01

    Micro- and nanomechanical oscillators are presently approaching the quantum regime, driven by the continuous improvement of techniques to read out and cool mechanical motion. For trapped ultracold atoms, a rich toolbox of quantum control techniques already exists. By coupling mechanical oscillators to ultracold atoms, hybrid quantum systems could be formed, in which the atoms are used to cool, read out, and coherently manipulate the oscillators' state. In our work, we investigate different coupling mechanisms between ultracold atoms and mechanical oscillators. In a first experiment, we use atom-surface forces to couple the vibrations of a mechanical cantilever to the motion of a Bose-Einstein condensate in a magnetic microtrap on a chip. The atoms are trapped at sub-micrometer distance from the cantilever surface. We make use of the coupling to read out the cantilever vibrations with the atoms. Coupling via surface forces could be employed to couple atoms to molecular-scale oscillators such as carbon nanotubes. In a second experiment, we investigate coupling via a 1D optical lattice that is formed by a laser beam retroreflected from the cantilever tip. The optical lattice serves as a transfer rod which couples vibrations of the cantilever to the atoms and vice versa. Finally, we investigate magnetic coupling between the spin of ultracold atoms and the vibrations of a nanoscale cantilever with a magnetic tip. Theoretical investigations show that at low temperatures, the backaction of the atoms onto the cantilever is significant and the system represents a mechanical analog of cavity quantum electrodynamics in the strong coupling regime.

  13. How to induce multiple delays in coupled chaotic oscillators?

    SciTech Connect

    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.

  14. Double resonance surface enhanced Raman scattering substrates: an intuitive coupled oscillator model.

    PubMed

    Chu, Yizhuo; Wang, Dongxing; Zhu, Wenqi; Crozier, Kenneth B

    2011-08-01

    The strong coupling between localized surface plasmons and surface plasmon polaritons in a double resonance surface enhanced Raman scattering (SERS) substrate is described by a classical coupled oscillator model. The effects of the particle density, the particle size and the SiO2 spacer thickness on the coupling strength are experimentally investigated. We demonstrate that by tuning the geometrical parameters of the double resonance substrate, we can readily control the resonance frequencies and tailor the SERS enhancement spectrum. PMID:21934853

  15. Variational study of a two-level system coupled to a harmonic oscillator in an ultrastrong-coupling regime

    SciTech Connect

    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.

  16. Coupling cellular oscillators: a mechanism that maintains synchrony against developmental noise in the segmentation clock.

    PubMed

    Ishimatsu, Kana; Horikawa, Kazuki; Takeda, Hiroyuki

    2007-06-01

    A unique feature of vertebrate segmentation is its strict periodicity, which is governed by the segmentation clock consisting of numerous cellular oscillators. These cellular oscillators, driven by a negative-feedback loop of Hairy transcription factor, are linked through Notch-dependent intercellular coupling and display the synchronous expression of clock genes. Combining our transplantation experiments in zebrafish with mathematical simulations, we review how the cellular oscillators maintain synchrony and form a robust system that is resistant to the effects of developmental noise such as stochastic gene expression and active cell proliferation. The accumulated evidence indicates that the segmentation clock behaves as a "coupled oscillators," a mechanism that also underlies the synchronous flashing seen in fireflies.

  17. Periodically forced ensemble of nonlinearly coupled oscillators: from partial to full synchrony.

    PubMed

    Baibolatov, Yernur; Rosenblum, Michael; Zhanabaev, Zeinulla Zh; Kyzgarina, Meyramgul; Pikovsky, Arkady

    2009-10-01

    We analyze the dynamics of a periodically forced oscillator ensemble with global nonlinear coupling. Without forcing, the system exhibits complicated collective dynamics, even for the simplest case of identical phase oscillators: due to nonlinearity, the synchronous state becomes unstable for certain values of the coupling parameter, and the system settles at the border between synchrony and asynchrony, what can be denoted as partial synchrony. We find that an external common forcing can result in two synchronous states: (i) a weak forcing entrains only the mean field, whereas the individual oscillators remain unlocked to the force and, correspondingly, to the mean field; (ii) a strong forcing fully synchronizes the system, making the phases of all oscillators identical. Analytical results are confirmed by numerics.

  18. 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.

  19. Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators.

    PubMed

    Lauter, Roland; Brendel, Christian; Habraken, Steven J M; Marquardt, Florian

    2015-07-01

    Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. We find that the full dynamical equations for the phase dynamics of a limit-cycle oscillator array go beyond previously studied Kuramoto-type equations. We analyze the evolution of the phase field in a two-dimensional array and obtain a "phase diagram" for the resulting stationary and nonstationary patterns. Our results are of direct relevance in the context of currently emerging experiments on nano- and optomechanical oscillator arrays, as well as for any array of coupled limit-cycle oscillators that have undergone a Hopf bifurcation. The possible observation in optomechanical arrays is discussed briefly. PMID:26274242

  20. Transonic shock oscillations calculated with a new interactive boundary layer coupling method

    NASA Technical Reports Server (NTRS)

    Edwards, John W.

    1993-01-01

    A new viscous-inviscid interactive coupling method is described with the aim of allowing time-accurate computation of unsteady transonic flows involving separation and reattachment. A lag-entrainment integral boundary layer method is used in conjunction with a transonic small disturbance potential code. The solutions are coupled with a novel variable gain, integral control method for the boundary layer displacement thickness. 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 thick 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.

  1. Tight Coupling of Metabolic Oscillations and Intracellular Water Dynamics in Saccharomyces cerevisiae

    PubMed Central

    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

  2. Power-rate synchronization of coupled genetic oscillators with unbounded time-varying delay.

    PubMed

    Alofi, Abdulaziz; Ren, Fengli; Al-Mazrooei, Abdullah; Elaiw, Ahmed; Cao, Jinde

    2015-10-01

    In this paper, a new synchronization problem for the collective dynamics among genetic oscillators with unbounded time-varying delay is investigated. The dynamical system under consideration consists of an array of linearly coupled identical genetic oscillators with each oscillators having unbounded time-delays. A new concept called power-rate synchronization, which is different from both the asymptotical synchronization and the exponential synchronization, is put forward to facilitate handling the unbounded time-varying delays. By using a combination of the Lyapunov functional method, matrix inequality techniques and properties of Kronecker product, we derive several sufficient conditions that ensure the coupled genetic oscillators to be power-rate synchronized. The criteria obtained in this paper are in the form of matrix inequalities. Illustrative example is presented to show the effectiveness of the obtained results.

  3. Coupled harmonic oscillators for the measurement of a weak classical force at the standard quantum limit

    SciTech Connect

    Leaci, Paola; Ortolan, Antonello

    2007-12-15

    We discuss limitations in precision measurements of a weak classical force coupled to quantum mechanical systems, the so-called standard quantum limit (SQL). Among the several contexts exploiting the measurement of classical signals, gravitational wave (GW) detection is of paramount importance. In this framework, we analyze the quantum limited sensitivity of a free test mass, a quantum mechanical harmonic oscillator, two harmonic oscillators with equal masses and different resonance frequencies, and finally two mechanical oscillators with different masses and resonating at the same frequency. The sensitivity analysis of the latter two cases illustrates the potentialities of back-action reduction and classical impedance matching schemes, respectively. By examining coupled quantum oscillators as detectors of classical signals, we found a viable path to approach the SQL for planned or operating GW detectors, such as DUAL and AURIGA.

  4. Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators.

    PubMed

    Lauter, Roland; Brendel, Christian; Habraken, Steven J M; Marquardt, Florian

    2015-07-01

    Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. We find that the full dynamical equations for the phase dynamics of a limit-cycle oscillator array go beyond previously studied Kuramoto-type equations. We analyze the evolution of the phase field in a two-dimensional array and obtain a "phase diagram" for the resulting stationary and nonstationary patterns. Our results are of direct relevance in the context of currently emerging experiments on nano- and optomechanical oscillator arrays, as well as for any array of coupled limit-cycle oscillators that have undergone a Hopf bifurcation. The possible observation in optomechanical arrays is discussed briefly.

  5. Evolution of a quantum harmonic oscillator coupled to a minimal thermal environment

    NASA Astrophysics Data System (ADS)

    Vidiella-Barranco, A.

    2016-10-01

    In this paper it is studied the influence of a minimal thermal environment on the dynamics of a quantum harmonic oscillator (labelled A), prepared in a coherent state. The environment itself consists of a second oscillator (labelled B), initially in a thermal state. Two types of interaction Hamiltonians are considered, and the time-evolution of the reduced density operator of oscillator A is compared to the one obtained from the usual master equation approach, i.e., assuming that oscillator A is coupled to a large reservoir. An analysis of the linear entropy evolution of oscillator A shows that simplified models may be able to describe important features related to the phenomenon of decoherence, such as the rapid growth of the linear entropy, as well as its dependence on the effective temperature of the environment.

  6. Two-Dimensional Array Beam Scanning Via Externally and Mutually Injection Locked Coupled Oscillators

    NASA Technical Reports Server (NTRS)

    Pogorzelski, Ronald J.

    2000-01-01

    Some years ago, Stephan proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage-controlled electronic oscillators coupled to nearest neighbors. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately. Stephan's approach consists of deriving two signals from a master oscillator, one signal phase shifted with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals.The beam direction is therefore controlled by adjusting this phase difference. Recently, Pogorzelski and York presented a formulation which facilitates theoretical analysis of the above beam steering technique. This was subsequently applied by Pogorzelski in analysis of two dimensional beam steering using perimeter detuning of a coupled oscillator array. The formulation is based on a continuum model in which the oscillator phases are represented by a continuous function satisfying a partial differential equation of diffusion type. This equation can be solved via the Laplace transform and the resulting solution exhibits the dynamic behavior of the array as the beam is steered. Stephan's beam steering technique can be similarly generalized to two-dimensional arrays in which the beam control signals are applied to the oscillators on the perimeter of the array. In this paper the continuum model for this two-dimensional case is developed and the dynamic solution for the corresponding aperture phase function is obtained. The corresponding behavior of the

  7. Gβ Regulates Coupling between Actin Oscillators for Cell Polarity and Directional Migration.

    PubMed

    Hoeller, Oliver; Toettcher, Jared E; Cai, Huaqing; Sun, Yaohui; Huang, Chuan-Hsiang; Freyre, Mariel; Zhao, Min; Devreotes, Peter N; Weiner, Orion D

    2016-02-01

    For directional movement, eukaryotic cells depend on the proper organization of their actin cytoskeleton. This engine of motility is made up of highly dynamic nonequilibrium actin structures such as flashes, oscillations, and traveling waves. In Dictyostelium, oscillatory actin foci interact with signals such as Ras and phosphatidylinositol 3,4,5-trisphosphate (PIP3) to form protrusions. However, how signaling cues tame actin dynamics to produce a pseudopod and guide cellular motility is a critical open question in eukaryotic chemotaxis. Here, we demonstrate that the strength of coupling between individual actin oscillators controls cell polarization and directional movement. We implement an inducible sequestration system to inactivate the heterotrimeric G protein subunit Gβ and find that this acute perturbation triggers persistent, high-amplitude cortical oscillations of F-actin. Actin oscillators that are normally weakly coupled to one another in wild-type cells become strongly synchronized following acute inactivation of Gβ. This global coupling impairs sensing of internal cues during spontaneous polarization and sensing of external cues during directional motility. A simple mathematical model of coupled actin oscillators reveals the importance of appropriate coupling strength for chemotaxis: moderate coupling can increase sensitivity to noisy inputs. Taken together, our data suggest that Gβ regulates the strength of coupling between actin oscillators for efficient polarity and directional migration. As these observations are only possible following acute inhibition of Gβ and are masked by slow compensation in genetic knockouts, our work also shows that acute loss-of-function approaches can complement and extend the reach of classical genetics in Dictyostelium and likely other systems as well. PMID:26890004

  8. Gβ Regulates Coupling between Actin Oscillators for Cell Polarity and Directional Migration

    PubMed Central

    Cai, Huaqing; Sun, Yaohui; Huang, Chuan-Hsiang; Freyre, Mariel; Zhao, Min; Devreotes, Peter N.; Weiner, Orion D.

    2016-01-01

    For directional movement, eukaryotic cells depend on the proper organization of their actin cytoskeleton. This engine of motility is made up of highly dynamic nonequilibrium actin structures such as flashes, oscillations, and traveling waves. In Dictyostelium, oscillatory actin foci interact with signals such as Ras and phosphatidylinositol 3,4,5-trisphosphate (PIP3) to form protrusions. However, how signaling cues tame actin dynamics to produce a pseudopod and guide cellular motility is a critical open question in eukaryotic chemotaxis. Here, we demonstrate that the strength of coupling between individual actin oscillators controls cell polarization and directional movement. We implement an inducible sequestration system to inactivate the heterotrimeric G protein subunit Gβ and find that this acute perturbation triggers persistent, high-amplitude cortical oscillations of F-actin. Actin oscillators that are normally weakly coupled to one another in wild-type cells become strongly synchronized following acute inactivation of Gβ. This global coupling impairs sensing of internal cues during spontaneous polarization and sensing of external cues during directional motility. A simple mathematical model of coupled actin oscillators reveals the importance of appropriate coupling strength for chemotaxis: moderate coupling can increase sensitivity to noisy inputs. Taken together, our data suggest that Gβ regulates the strength of coupling between actin oscillators for efficient polarity and directional migration. As these observations are only possible following acute inhibition of Gβ and are masked by slow compensation in genetic knockouts, our work also shows that acute loss-of-function approaches can complement and extend the reach of classical genetics in Dictyostelium and likely other systems as well. PMID:26890004

  9. Does hyperbolicity impede emergence of chimera states in networks of nonlocally coupled chaotic oscillators?

    NASA Astrophysics Data System (ADS)

    Semenova, N.; Zakharova, A.; Schöll, E.; Anishchenko, V.

    2015-11-01

    We analyze nonlocally coupled networks of identical chaotic oscillators with either time-discrete or time-continuous dynamics (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 oscillators with nonhyperbolic chaotic attractors and cannot be found in networks of systems with hyperbolic chaotic attractors. This hypothesis is supported by analytical results and numerical simulations for hyperbolic and nonhyperbolic cases.

  10. Chimera and chimera-like states in populations of nonlocally coupled homogeneous and heterogeneous chemical oscillators

    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.

  11. Strain Coupling of a Nitrogen-Vacancy Center Spin to a Diamond Mechanical Oscillator

    NASA Astrophysics Data System (ADS)

    Teissier, J.; Barfuss, A.; Appel, P.; Neu, E.; Maletinsky, P.

    2014-07-01

    We report on single electronic spins coupled to the motion of mechanical resonators by a novel mechanism based on crystal strain. Our device consists of single-crystal diamond cantilevers with embedded nitrogen-vacancy center spins. Using optically detected electron spin resonance, we determine the unknown spin-strain coupling constants and demonstrate that our system resides well within the resolved sideband regime. We realize coupling strengths exceeding 10 MHz under mechanical driving and show that our system has the potential to reach strong coupling. Our novel hybrid system forms a resource for future experiments on spin-based cantilever cooling and coherent spin-oscillator coupling.

  12. Generalized synchronization in mutually coupled oscillators and complex networks.

    PubMed

    Moskalenko, Olga I; Koronovskii, Alexey A; Hramov, Alexander E; Boccaletti, Stefano

    2012-09-01

    We introduce a concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset of the synchronous regime is confirmed by the dependence of the system's Lyapunov exponents on the coupling parameter. The presence of a generalized synchronization regime is verified by means of the nearest neighbor method.

  13. Average dynamics of a finite set of coupled phase oscillators

    SciTech Connect

    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.

  14. Coulomb Blockade Oscillations in Coupled Single-Electron Transistors

    NASA Astrophysics Data System (ADS)

    Shin, Mincheol; Lee, Seongjae; Park, Kyoung Wan

    2000-03-01

    The system we consider in this work is parallel coupled single-electron transistors (SETs) at strong coupling. For weak coupling, the transport characteristics of our coupled SETs are the same as those of the single SET, with the stability diagram exhibiting usual Coulomb diamonds. When the coupling becomes sufficiently strong, however, electron-hole binding and transport become important. In contrast to the previous works carried out in the cotunneling-dominating Coulomb blockade regime [1,2], we study e-h binding in the sequential-tunneling-dominating conducting regime. The major findings in this work are that the Coulomb diamonds in the conducting regime break up into fine internal structures at strong coupling, and that, although the cotunneling processes are much less frequent, they nonetheless play a crucial role. [1] D. V. Averin, A. N. Korotkov, and Yu. V. Nazarov, Phys. Rev. Lett. 66, 2818 (1991). [2] M. Matters, J. J. Versluys, and J. E. Mooij, Phys. Rev. Lett. 78, 2469 (1997).

  15. Achieving synchronization with active hybrid materials: Coupling self-oscillating gels and piezoelectric films.

    PubMed

    Yashin, Victor V; Levitan, Steven P; Balazs, Anna C

    2015-06-24

    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".

  16. Achieving synchronization with active hybrid materials: Coupling self-oscillating gels and piezoelectric films

    NASA Astrophysics Data System (ADS)

    Yashin, Victor V.; Levitan, Steven P.; Balazs, Anna C.

    2015-06-01

    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”.

  17. Achieving synchronization with active hybrid materials: Coupling self-oscillating gels and piezoelectric films.

    PubMed

    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

  18. Achieving synchronization with active hybrid materials: Coupling self-oscillating gels and piezoelectric films

    PubMed Central

    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

  19. Order parameter analysis for low-dimensional behaviors of coupled phase-oscillators

    PubMed Central

    Gao, Jian; Xu, Can; Sun, Yuting; Zheng, Zhigang

    2016-01-01

    Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple and concise approach based on equations of order parameters, namely, order parameter analysis, with which we point out that OA ansatz is rooted in the dynamical symmetry of order parameters. With our approach the scope of OA ansatz is identified as two conditions, i.e., the limit of infinitely many oscillators and only three nonzero Fourier coefficients of the coupling function. Coinciding with each of the conditions, a distinctive system out of the scope is taken into account and discussed with the order parameter analysis. Two approximation methods are introduced respectively, namely the expectation assumption and the dominating-term assumption. PMID:27443639

  20. Effect of node-degree correlation on synchronization of identical pulse-coupled oscillators.

    PubMed

    LaMar, M Drew; Smith, Gregory D

    2010-04-01

    We explore the effect of correlations between the in and out degrees of random directed networks on the synchronization of identical pulse-coupled oscillators. Numerical experiments demonstrate that the proportion of initial conditions resulting in a globally synchronous state (prior to a large but finite time) is an increasing function of node-degree correlation. For those networks observed to globally synchronize, both the mean and standard deviation of time to synchronization are decreasing functions of node-degree correlation. Pulse-coupled oscillator networks with negatively correlated node degree often exhibit multiple coherent attracting states, with trajectories performing fast transitions between them. These effects of node-degree correlation on dynamics of pulse-coupled oscillators are consistent with aspects of network topology (e.g., the effect of node-degree correlation on the eigenvalues of the Laplacian matrix) that have been shown to affect synchronization in other contexts.

  1. Order parameter analysis for low-dimensional behaviors of coupled phase-oscillators

    NASA Astrophysics Data System (ADS)

    Gao, Jian; Xu, Can; Sun, Yuting; Zheng, Zhigang

    2016-07-01

    Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple and concise approach based on equations of order parameters, namely, order parameter analysis, with which we point out that OA ansatz is rooted in the dynamical symmetry of order parameters. With our approach the scope of OA ansatz is identified as two conditions, i.e., the limit of infinitely many oscillators and only three nonzero Fourier coefficients of the coupling function. Coinciding with each of the conditions, a distinctive system out of the scope is taken into account and discussed with the order parameter analysis. Two approximation methods are introduced respectively, namely the expectation assumption and the dominating-term assumption.

  2. Coherent dynamics of a flux qubit coupled to a harmonic oscillator.

    PubMed

    Chiorescu, I; Bertet, P; Semba, K; Nakamura, Y; Harmans, C J P M; Mooij, J E

    2004-09-01

    In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits (qubits). Single-qubit operations, direct coupling between two qubits and the realization of a quantum gate have been reported. However, complex manipulation of entangled states-such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments and cavity quantum electrodynamics-has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system. PMID:15356624

  3. Order parameter analysis for low-dimensional behaviors of coupled phase-oscillators.

    PubMed

    Gao, Jian; Xu, Can; Sun, Yuting; Zheng, Zhigang

    2016-07-22

    Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple and concise approach based on equations of order parameters, namely, order parameter analysis, with which we point out that OA ansatz is rooted in the dynamical symmetry of order parameters. With our approach the scope of OA ansatz is identified as two conditions, i.e., the limit of infinitely many oscillators and only three nonzero Fourier coefficients of the coupling function. Coinciding with each of the conditions, a distinctive system out of the scope is taken into account and discussed with the order parameter analysis. Two approximation methods are introduced respectively, namely the expectation assumption and the dominating-term assumption.

  4. 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

  5. Adaptive oscillator networks with conserved overall coupling: Sequential firing and near-synchronized states

    NASA Astrophysics Data System (ADS)

    Picallo, Clara B.; Riecke, Hermann

    2011-03-01

    Motivated by recent observations in neuronal systems we investigate all-to-all networks of nonidentical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all incoming links is conserved. We find multiple phase-locked states that fall into two classes: near-synchronized states and splay states. Among the near-synchronized states are states that oscillate with a frequency that depends only very weakly on the coupling strength and is essentially given by the frequency of one of the oscillators, which is, however, neither the fastest nor the slowest oscillator. In sufficiently large networks the adaptive coupling is found to develop effective network topologies dominated by one or two loops. This results in a multitude of stable splay states, which differ in their firing sequences. With increasing coupling strength their frequency increases linearly and the oscillators become less synchronized. The essential features of the two classes of states are captured analytically in perturbation analyses of the extended Kuramoto model used in the simulations.

  6. Experimental study of synchronization of coupled electrical self-oscillators and comparison to the Sakaguchi-Kuramoto model.

    PubMed

    English, L Q; Zeng, Zhuwei; Mertens, David

    2015-11-01

    We explore the collective phase dynamics of Wien-bridge oscillators coupled resistively. We carefully analyze the behavior of two coupled oscillators, obtaining a transformation from voltage to effective phase. From the phase dynamics we show that the coupling can be quantitatively described by Sakaguchi's modification to the Kuramoto model. We also examine an ensemble of oscillators whose frequencies are taken from a flat distribution within a fixed frequency interval. We characterize in detail the synchronized cluster, its initial formation, as well as its effect on unsynchronized oscillators, all as a function of a global coupling strength.

  7. Amplitude death through a Hopf bifurcation in coupled electrochemical oscillators: experiments and simulations.

    PubMed

    Zhai, Yumei; Kiss, István Z; Hudson, John L

    2004-02-01

    Amplitude death was observed in experiments with two coupled periodic electrochemical oscillators without time delay. Simulation results confirmed that the observed amplitude death was obtained via a Hopf bifurcation. The two oscillators must have a minimum discrepancy and both be near their individual Hopf bifurcations for amplitude death to occur. Phase drift (coexisting with unstable asymmetric phase-locked solutions), amplitude death, and in-phase synchronization were observed in both the experiments and simulations as coupling strength was increased. In addition, the simulations showed that a stable asymmetric phase-locked solution exists between the phase drift and amplitude death regions.

  8. 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.

  9. Variety of alternative stable phase-locking in networks of electrically coupled relaxation oscillators.

    PubMed

    Meyrand, Pierre; Bem, Tiaza

    2014-01-01

    We studied the dynamics of a large-scale model network comprised of oscillating electrically coupled neurons. Cells are modeled as relaxation oscillators with short duty cycle, so they can be considered either as models of pacemaker cells, spiking cells with fast regenerative and slow recovery variables or firing rate models of excitatory cells with synaptic depression or cellular adaptation. It was already shown that electrically coupled relaxation oscillators exhibit not only synchrony but also anti-phase behavior if electrical coupling is weak. We show that a much wider spectrum of spatiotemporal patterns of activity can emerge in a network of electrically coupled cells as a result of switching from synchrony, produced by short external signals of different spatial profiles. The variety of patterns increases with decreasing rate of neuronal firing (or duty cycle) and with decreasing strength of electrical coupling. We study also the effect of network topology--from all-to-all--to pure ring connectivity, where only the closest neighbors are coupled. We show that the ring topology promotes anti-phase behavior as compared to all-to-all coupling. It also gives rise to a hierarchical organization of activity: during each of the main phases of a given pattern cells fire in a particular sequence determined by the local connectivity. We have analyzed the behavior of the network using geometric phase plane methods and we give heuristic explanations of our findings. Our results show that complex spatiotemporal activity patterns can emerge due to the action of stochastic or sensory stimuli in neural networks without chemical synapses, where each cell is equally coupled to others via gap junctions. This suggests that in developing nervous systems where only electrical coupling is present such a mechanism can lead to the establishment of proto-networks generating premature multiphase oscillations whereas the subsequent emergence of chemical synapses would later stabilize

  10. Variety of alternative stable phase-locking in networks of electrically coupled relaxation oscillators.

    PubMed

    Meyrand, Pierre; Bem, Tiaza

    2014-01-01

    We studied the dynamics of a large-scale model network comprised of oscillating electrically coupled neurons. Cells are modeled as relaxation oscillators with short duty cycle, so they can be considered either as models of pacemaker cells, spiking cells with fast regenerative and slow recovery variables or firing rate models of excitatory cells with synaptic depression or cellular adaptation. It was already shown that electrically coupled relaxation oscillators exhibit not only synchrony but also anti-phase behavior if electrical coupling is weak. We show that a much wider spectrum of spatiotemporal patterns of activity can emerge in a network of electrically coupled cells as a result of switching from synchrony, produced by short external signals of different spatial profiles. The variety of patterns increases with decreasing rate of neuronal firing (or duty cycle) and with decreasing strength of electrical coupling. We study also the effect of network topology--from all-to-all--to pure ring connectivity, where only the closest neighbors are coupled. We show that the ring topology promotes anti-phase behavior as compared to all-to-all coupling. It also gives rise to a hierarchical organization of activity: during each of the main phases of a given pattern cells fire in a particular sequence determined by the local connectivity. We have analyzed the behavior of the network using geometric phase plane methods and we give heuristic explanations of our findings. Our results show that complex spatiotemporal activity patterns can emerge due to the action of stochastic or sensory stimuli in neural networks without chemical synapses, where each cell is equally coupled to others via gap junctions. This suggests that in developing nervous systems where only electrical coupling is present such a mechanism can lead to the establishment of proto-networks generating premature multiphase oscillations whereas the subsequent emergence of chemical synapses would later stabilize

  11. Two-dimensional Array Beam Scanning via Externally and Mutually Injection Locked Coupled Oscillators

    NASA Technical Reports Server (NTRS)

    Pogorzelski, Ronald J.

    1999-01-01

    Some years ago, Stephan proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage-controlled electronic oscillators coupled to nearest neighbors. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately.Stephan's approach consists of deriving two signals from a master oscillator, one signal phase shined with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array as shown in Figure 1. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals. The beam direction is therefore controlled by adjusting this phase difference.

  12. Self-organized network of phase oscillators coupled by activity-dependent interactions.

    PubMed

    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.

  13. Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators

    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.

  14. Collective dipole oscillations of a spin-orbit coupled Bose-Einstein condensate.

    PubMed

    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

    2012-09-14

    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.

  15. Stochastic phase resetting of two coupled phase oscillators stimulated at different times

    NASA Astrophysics Data System (ADS)

    Tass, Peter A.

    2003-05-01

    A model of two coupled phase oscillators is presented, where the oscillators are subject to random forces and are stimulated at different times. Transient phase dynamics, synchronization, and desynchronization, which are stimulus locked (i.e., tightly time locked to a repetitively administered stimulus), are investigated. Complex coordinated responses, in terms of a noise-induced switching across trials between qualitatively different responses, may occur when the two oscillators are reset close to an unstable fixed point of their relative phases. This can be achieved with an appropriately chosen delay between the two stimuli. The switching of the responses shows up as a coordinated cross-trial (CT) response clustering of the oscillators, where the two oscillators produce two different pairs of responses. By varying noise amplitude and coupling strength we observe a stochastic resonance and a coupling-mediated resonance of the CT response clustering, respectively. The presented data analysis method makes it possible to detect such processes in numerical and experimental signals. Its time resolution is enormous, since it is only restricted by the time resolution of the preprocessing necessary for extracting the phases from experimental data. In contrast, standard data analysis tools applied across trials relative to stimulus onset, such as CT averaging (where an ensemble of poststimulus responses is simply averaged), CT standard deviation, and CT cross correlation, fail in detecting complex coordinated responses and lead to severe misinterpretations and artifacts. The consequences for the analysis of evoked responses in medicine and neuroscience are significant and are discussed in detail.

  16. Robustness of chimera states for coupled FitzHugh-Nagumo oscillators.

    PubMed

    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.

  17. Permanent Rabi oscillations in coupled exciton-photon systems with PT-symmetry.

    PubMed

    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.

  18. Permanent Rabi oscillations in coupled exciton-photon systems with PT -symmetry

    PubMed Central

    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

  19. Frequency stabilization of spin-torque-driven oscillations by coupling with a magnetic nonlinear resonator

    SciTech Connect

    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.

  20. Dynamics of Freely Oscillating and Coupled Hair Cell Bundles under Mechanical Deflection

    PubMed Central

    Fredrickson-Hemsing, Lea; Strimbu, C. Elliott; Roongthumskul, Yuttana; Bozovic, Dolores

    2012-01-01

    In vitro, attachment to the overlying membrane was found to affect the resting position of the hair cell bundles of the bullfrog sacculus. To assess the effects of such a deflection on mechanically decoupled hair bundles, comparable offsets were imposed on decoupled spontaneously oscillating bundles. Strong modulation was observed in their dynamic state under deflection, with qualitative changes in the oscillation profile, amplitude, and characteristic frequency of oscillation seen in response to stimulus. Large offsets were found to arrest spontaneous oscillation, with subsequent recovery upon reversal of the stimulus. The dynamic state of the hair bundle displayed hysteresis and a dependence on the direction of the imposed offset. The coupled system of hair bundles, with the overlying membrane left on top of the preparation, also exhibited a dependence on offset position, with an increase in the linear response function observed under deflections in the inhibitory direction. PMID:22768934

  1. Dynamics of freely oscillating and coupled hair cell bundles under mechanical deflection.

    PubMed

    Fredrickson-Hemsing, Lea; Strimbu, C Elliott; Roongthumskul, Yuttana; Bozovic, Dolores

    2012-04-18

    In vitro, attachment to the overlying membrane was found to affect the resting position of the hair cell bundles of the bullfrog sacculus. To assess the effects of such a deflection on mechanically decoupled hair bundles, comparable offsets were imposed on decoupled spontaneously oscillating bundles. Strong modulation was observed in their dynamic state under deflection, with qualitative changes in the oscillation profile, amplitude, and characteristic frequency of oscillation seen in response to stimulus. Large offsets were found to arrest spontaneous oscillation, with subsequent recovery upon reversal of the stimulus. The dynamic state of the hair bundle displayed hysteresis and a dependence on the direction of the imposed offset. The coupled system of hair bundles, with the overlying membrane left on top of the preparation, also exhibited a dependence on offset position, with an increase in the linear response function observed under deflections in the inhibitory direction. PMID:22768934

  2. Achieving synchronization with active hybrid materials: Coupling self-oscillating gels and piezoelectric films

    NASA Astrophysics Data System (ADS)

    Yashin, Victor V.; Levitan, Steven P.; Balazs, Anna C.

    Our goal is to develop materials that compute by using non-linear oscillating chemical reactions to perform spatio-temporal recognition tasks. The material of choice is a polymer gel undergoing the oscillatory Belousov-Zhabotinsky reaction. The novelty of our approach is in employing hybrid gel-piezoelectric micro-electro-mechanical systems (MEMS) to couple local chemo-mechanical oscillations over long distances by electrical connection. Our modeling revealed that (1) interaction between the MEMS units is sufficiently strong for synchronization; (2) the mode of synchronization depends on the number of units, type of circuit connection (serial of parallel), and polarity of the units; (3) each mode has a distinctive pattern in phase of oscillations and generated voltage. The results indicate feasibility of using the hybrid gel-piezoelectric MEMS for oscillator based unconventional computing.

  3. Permanent Rabi oscillations in coupled exciton-photon systems with PT -symmetry

    NASA Astrophysics Data System (ADS)

    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.

  4. Addressing Two-Level Systems Variably Coupled to an Oscillating Field

    NASA Astrophysics Data System (ADS)

    Navon, Nir; Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Almog, Ido; Ozeri, Roee

    2013-08-01

    We propose a simple method to spectrally resolve an array of identical two-level systems coupled to an inhomogeneous oscillating field. The addressing protocol uses a dressing field with a spatially dependent coupling to the atoms. We validate this scheme experimentally by realizing single-spin addressing of a linear chain of trapped ions that are separated by ˜3μm, dressed by a laser field that is resonant with the micromotion sideband of a narrow optical transition.

  5. Synchronization and spatiotemporal patterns in coupled phase oscillators on a weighted planar network

    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.

  6. Phase multistability and phase synchronization in an array of locally coupled period-doubling oscillators.

    PubMed

    Shabunin, A; Feudel, U; Astakhov, V

    2009-08-01

    We consider phase multistability and phase synchronization phenomena in a chain of period-doubling oscillators. The synchronization in arrays of diffusively coupled self-sustained oscillators manifests itself as rotating wave regimes, which are characterized by equal amplitudes and phases in every site which are shifted by a constant value. The value of the phase shift is preserved while the shape of motion becomes more complex through a period-doubling cascade. The number of coexisting attractors increases drastically after the transition from period-one to period-two oscillations and then after every following period-doubling bifurcation. In the chaotic region, we observe a number of phase-synchronized modes with instantaneous phases locked in different values. The loss of phase synchronization with decreasing coupling is accompanied by intermittency between several synchronous regimes.

  7. Correlations, fluctuations, and stability of a finite-size network of coupled oscillators.

    PubMed

    Buice, Michael A; Chow, Carson C

    2007-09-01

    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 nonequilibrium 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.

  8. Decoherence and dissipation of a quantum harmonic oscillator coupled to two-level systems

    SciTech Connect

    Schlosshauer, Maximilian; Hines, A. P.; Milburn, G. J.

    2008-02-15

    We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four 'canonical' system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum-electromechanical systems and micron-scale ion traps. Decoherence and dissipation rates are found to exhibit temperature dependencies significantly different from those in quantum Brownian motion. In particular, the systematic dissipation rate for the central oscillator decreases with increasing temperature and goes to zero at zero temperature, but there also exists a temperature-independent momentum-diffusion (heating) rate.

  9. Thermodynamics of trajectories of a quantum harmonic oscillator coupled to N baths

    NASA Astrophysics Data System (ADS)

    Pigeon, Simon; Fusco, Lorenzo; Xuereb, André; De Chiara, Gabriele; Paternostro, Mauro

    2015-07-01

    We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to N dissipative baths by using an approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyze the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.

  10. 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

  11. Mobility and density induced amplitude death in metapopulation networks of coupled oscillators.

    PubMed

    Shen, Chuansheng; Chen, Hanshuang; Hou, Zhonghuai

    2014-12-01

    We investigate the effects of mobility and density on the amplitude death of coupled Landau-Stuart oscillators and Brusselators in metapopulation networks, wherein each node represents a subpopulation occupied any number of mobile individuals. By numerical simulations in scale-free topology, we find that the systems undergo phase transitions from incoherent state to amplitude death, and then to frequency synchronization with increasing the mobility rate or density of oscillators. Especially, there exists an extent of intermediate mobility rate and density that can lead to global oscillator death. Furthermore, we show that such nontrivial phenomena are robust to diverse network topologies. Our findings may invoke further efforts and attentions to explore the underlying mechanism of collective behaviors in coupled metapopulation systems.

  12. Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators

    NASA Astrophysics Data System (ADS)

    Jiang, Haibo; Liu, Yang; Zhang, Liping; Yu, Jianjiang

    2016-10-01

    This paper studies the synchronization in two mechanical oscillators coupled by impacts which can be considered as a class of state-dependent impulsively coupled oscillators. The two identical oscillators are harmonically excited in a counter phase, and the synchronous (anti-phase synchronization) and the asynchronous motions are considered. One- and two-parameter bifurcations of the system have been studied by varying the amplitude and the frequency of external excitation. Numerical simulations show that the system could exhibit complex phenomena, including symmetry and asymmetry periodic solutions, quasi-periodic solutions and chaotic solutions. In particular, the regimes in anti-phase synchronization are identified, and it is found that the symmetry-breaking bifurcation plays an important role in the transition from synchronous to asynchronous motion.

  13. Correlations, fluctuations, and stability of a finite-size network of coupled oscillators

    SciTech Connect

    Buice, Michael A.; Chow, Carson C.

    2007-09-15

    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 nonequilibrium 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{yields}{infinity} limit of this theory is what is traditionally called mean field theory for the Kuramoto model.

  14. 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.…

  15. Demonstrating Energy Migration in Coupled Oscillators: A Central Concept in the Theory of Unimolecular Reactions

    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…

  16. Towards a proper estimation of phase-amplitude coupling in neural oscillations

    PubMed Central

    Dvorak, Dino; Fenton, André A.

    2014-01-01

    Background The phase-amplitude coupling (PAC) between distinct neural oscillations is critical to brain functions that include cross-scale organization, selection of attention, routing the flow of information through neural circuits, memory processing and information coding. Several methods for PAC estimation have been proposed but the limitations of PAC estimation as well as the assumptions about the data for accurate PAC estimation are unclear. New Method We define boundary conditions for standard PAC algorithms and propose “oscillation-triggered coupling” (OTC), a parameter-free, data-driven algorithm for unbiased estimation of PAC. OTC establishes a unified framework that treats individual oscillations as discrete events for estimating PAC from a set of oscillations and for characterizing events from time windows as short as a single modulating oscillation. Results For accurate PAC estimation, standard PAC algorithms require amplitude filters with a bandwidth at least twice the modulatory frequency. The phase filters must be moderately narrow-band, especially when the modulatory rhythm is non-sinusoidal. The minimally appropriate analysis window is ~10 seconds. We then demonstrate that OTC can characterize PAC by treating neural oscillations as discrete events rather than continuous phase and amplitude time series. Comparison with existing methods These findings show that in addition to providing the same information about PAC as the standard approach, OTC facilitates characterization of single oscillations and their sequences, in addition to explaining the role of individual oscillations in generating PAC patterns. Conclusions OTC allows PAC analysis at the level of individual oscillations and therefore enables investigation of PAC at the time scales of cognitive phenomena. PMID:24447842

  17. Effect of bidirectional mechanoelectrical coupling on spontaneous oscillations and sensitivity in a model of hair cells

    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.

  18. Vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to harmonic bath.

    PubMed

    Joutsuka, Tatsuya; Ando, Koji

    2011-05-28

    The vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to a harmonic bath are examined to assess the applicability of the time correlation function (TCF), the response function, and the semiclassical frequency modulation (SFM) model to the calculation of infrared (IR) spectra. These three approaches are often used in connection with the molecular dynamics simulations but have not been compared in detail. We also analyze the vibrational energy relaxation (VER), which determines the line shape and is itself a pivotal process in energy transport. The IR spectra and VER are calculated using the generalized Langevin equation (GLE), the Gaussian wavepacket (GWP) method, and the quantum master equation (QME). By calculating the vibrational frequency TCF, a detailed analysis of the frequency fluctuation and correlation time of the model is provided. The peak amplitude and width in the IR spectra calculated by the GLE with the harmonic quantum correction are shown to agree well with those by the QME though the vibrational frequency is generally overestimated. The GWP method improves the peak position by considering the zero-point energy and the anharmonicity although the red-shift slightly overshoots the QME reference. The GWP also yields an extra peak in the higher-frequency region than the fundamental transition arising from the difference frequency of the center and width oscillations of a wavepacket. The SFM approach underestimates the peak amplitude of the IR spectra but well reproduces the peak width. Further, the dependence of the VER rate on the strength of an excitation pulse is discussed. PMID:21639460

  19. The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators.

    PubMed

    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. PMID:26931583

  20. The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators

    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.

  1. Typical trajectories of coupled degrade-and-fire oscillators: from dispersed populations to massive clustering.

    PubMed

    Fernandez, Bastien; Tsimring, Lev S

    2014-06-01

    We consider the dynamics of a piecewise affine system of degrade-and-fire oscillators with global repressive interaction, inspired by experiments on synchronization in colonies of bacteria-embedded genetic circuits. Due to global coupling, if any two oscillators happen to be in the same state at some time, they remain in sync at all subsequent times; thus clusters of synchronized oscillators cannot shrink as a result of the dynamics. Assuming that the system is initiated from random initial configurations of fully dispersed populations (no clusters), we estimate asymptotic cluster sizes as a function of the coupling strength. A sharp transition is proved to exist that separates a weak coupling regime of unclustered populations from a strong coupling phase where clusters of extensive size are formed. Each phenomena occurs with full probability in the thermodynamics limit. Moreover, the maximum number of asymptotic clusters is known to diverge linearly in this limit. In contrast, we show that with positive probability, the number of asymptotic clusters remains bounded, provided that the coupling strength is sufficiently large.

  2. Time delay induced different synchronization patterns in repulsively coupled chaotic oscillators.

    PubMed

    Yao, Chenggui; Yi, Ming; Shuai, Jianwei

    2013-09-01

    Time delayed coupling plays a crucial role in determining the system's dynamics. We here report that the time delay induces transition from the asynchronous state to the complete synchronization (CS) state in the repulsively coupled chaotic oscillators. In particular, by changing the coupling strength or time delay, various types of synchronous patterns, including CS, antiphase CS, antiphase synchronization (ANS), and phase synchronization, can be generated. In the transition regions between different synchronous patterns, bistable synchronous oscillators can be observed. Furthermore, we show that the time-delay-induced phase flip bifurcation is of key importance for the emergence of CS. All these findings may light on our understanding of neuronal synchronization and information processing in the brain.

  3. Time delay induced different synchronization patterns in repulsively coupled chaotic oscillators

    NASA Astrophysics Data System (ADS)

    Yao, Chenggui; Yi, Ming; Shuai, Jianwei

    2013-09-01

    Time delayed coupling plays a crucial role in determining the system's dynamics. We here report that the time delay induces transition from the asynchronous state to the complete synchronization (CS) state in the repulsively coupled chaotic oscillators. In particular, by changing the coupling strength or time delay, various types of synchronous patterns, including CS, antiphase CS, antiphase synchronization (ANS), and phase synchronization, can be generated. In the transition regions between different synchronous patterns, bistable synchronous oscillators can be observed. Furthermore, we show that the time-delay-induced phase flip bifurcation is of key importance for the emergence of CS. All these findings may light on our understanding of neuronal synchronization and information processing in the brain.

  4. Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

    NASA Astrophysics Data System (ADS)

    Sadurní, E.; Torres, J. M.; Seligman, T. H.

    2010-07-01

    The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of a solution is given by recasting the known solution of the Dirac oscillator into matrix form; there one notes that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two dimensional. Choosing couplings that do not affect the block structure, these blow up the 2 × 2 matrices to 4 × 4 matrices, thus conserving solvability. The result can be cast again in covariant form. By way of an example we apply this exact solution to calculate the evolution of entanglement.

  5. Synchronization and plateau splitting of coupled oscillators with long-range power-law interactions.

    PubMed

    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. PMID:26764785

  6. Synchronization and plateau splitting of coupled oscillators with long-range power-law interactions.

    PubMed

    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.

  7. Multiplicity of singular synchronous states in the Kuramoto model of coupled oscillators.

    PubMed

    Komarov, Maxim; Pikovsky, Arkady

    2013-11-15

    We study the Kuramoto model of globally coupled oscillators with a biharmonic coupling function. We develop an analytic self-consistency approach to find stationary synchronous states in the thermodynamic limit and demonstrate that there is a huge multiplicity of such states, which differ microscopically in the distributions of locked phases. These synchronous regimes already exist prior to the linear instability transition of the fully asynchronous state. In the presence of white Gaussian noise, the multiplicity is lifted, but the dependence of the order parameters on coupling constants remains nontrivial.

  8. Synchronization states and multistability in a ring of periodic oscillators: Experimentally variable coupling delays

    SciTech Connect

    Williams, Caitlin R. S.; Sorrentino, Francesco; Murphy, Thomas E.; Roy, Rajarshi

    2013-12-15

    We experimentally study the complex dynamics of a unidirectionally coupled ring of four identical optoelectronic oscillators. The coupling between these systems is time-delayed in the experiment and can be varied over a wide range of delays. We observe that as the coupling delay is varied, the system may show different synchronization states, including complete isochronal synchrony, cluster synchrony, and two splay-phase states. We analyze the stability of these solutions through a master stability function approach, which we show can be effectively applied to all the different states observed in the experiment. Our analysis supports the experimentally observed multistability in the system.

  9. 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.

  10. Chimera states in coupled Kuramoto oscillators with inertia.

    PubMed

    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.

  11. Chimera states in coupled Kuramoto oscillators with inertia

    SciTech Connect

    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.

  12. Chimera states in coupled Kuramoto oscillators with inertia.

    PubMed

    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. PMID:26723164

  13. Spatiotemporal variation of metabolism in a plant circadian rhythm: the biological clock as an assembly of coupled individual oscillators.

    PubMed

    Rascher, U; Hütt, M T; Siebke, K; Osmond, B; Beck, F; Lüttge, U

    2001-09-25

    The complex dynamic properties of biological timing in organisms remain a central enigma in biology despite the increasingly precise genetic characterization of oscillating units and their components. Although attempts to obtain the time constants from oscillations of gene activity and biochemical units have led to substantial progress, we are still far from a full molecular understanding of endogenous rhythmicity and the physiological manifestations of biological clocks. Applications of nonlinear dynamics have revolutionized thinking in physics and in biomedical and life sciences research, and spatiotemporal considerations are now advancing our understanding of development and rhythmicity. Here we show that the well known circadian rhythm of a metabolic cycle in a higher plant, namely the crassulacean acid metabolism mode of photosynthesis, is expressed as dynamic patterns of independently initiated variations in photosynthetic efficiency (phi(PSII)) over a single leaf. Noninvasive highly sensitive chlorophyll fluorescence imaging reveals randomly initiated patches of varying phi(PSII) that are propagated within minutes to hours in wave fronts, forming dynamically expanding and contracting clusters and clearly dephased regions of phi(PSII). Thus, this biological clock is a spatiotemporal product of many weakly coupled individual oscillators, defined by the metabolic constraints of crassulacean acid metabolism. The oscillators operate independently in space and time as a consequence of the dynamics of metabolic pools and limitations of CO(2) diffusion between tightly packed cells.

  14. The fundamental organization of cardiac mitochondria as a network of coupled oscillators.

    PubMed

    Aon, Miguel Antonio; Cortassa, Sonia; O'Rourke, Brian

    2006-12-01

    Mitochondria can behave as individual oscillators whose dynamics may obey collective, network properties. We have shown that cardiomyocytes exhibit high-amplitude, self-sustained, and synchronous oscillations of bioenergetic parameters when the mitochondrial network is stressed to a critical state. Computational studies suggested that additional low-amplitude, high-frequency oscillations were also possible. Herein, employing power spectral analysis, we show that the temporal behavior of mitochondrial membrane potential (DeltaPsi(m)) in cardiomyocytes under physiological conditions is oscillatory and characterized by a broad frequency distribution that obeys a homogeneous power law (1/f(beta)) with a spectral exponent, beta = 1.74. Additionally, relative dispersional analysis shows that mitochondrial oscillatory dynamics exhibits long-term memory, characterized by an inverse power law that scales with a fractal dimension (D(f)) of 1.008, distinct from random behavior (D(f) = 1.5), over at least three orders of magnitude. Analysis of a computational model of the mitochondrial oscillator suggests that the mechanistic origin of the power law behavior is based on the inverse dependence of amplitude versus frequency of oscillation related to the balance between reactive oxygen species production and scavenging. The results demonstrate that cardiac mitochondria behave as a network of coupled oscillators under both physiological and pathophysiological conditions.

  15. Nontrivial Bloch oscillations in waveguide arrays with second-order coupling.

    PubMed

    Wang, Gang; Huang, Ji Ping; Yu, Kin Wah

    2010-06-01

    Under the influence of the next-nearest-neighbor interaction, we theoretically investigate the occurrence of Bloch oscillations in zigzag waveguide arrays. Because of the special topological configuration of the lattice itself, the second-order coupling (SOC) can be enhanced significantly and leads to the band alteration beyond the nearest-neighbor model, i.e., the offset of minimum value from the band edge. Contrary to the behavior in the vanishing SOC, the oscillation patterns exhibit new features, namely, a double turning-back occurs when the beam approaches the band edge. Our results can be applied to some ordered-lattice systems.

  16. Relation of the entanglement entropy and uncertainty product in ground states of coupled anharmonic oscillators

    SciTech Connect

    Chung, N. N.; Er, C. H.; Teo, Y. S.; Chew, L. Y.

    2010-07-15

    We explore quantitatively the fundamental connection between the entropy and local uncertainty product as an entanglement measure within the lowest energy eigenstate of a class of two-coupled anharmonic oscillator systems. We find that these two quantum aspects approach a unique relation as the entanglement between the oscillators becomes large if the potential of the first collective mode displays a generic single-well potential structure. This implies that the uncertainty product can be a good choice for the characterization of entanglement when the entropy is sufficiently large. Interestingly, although this relation is robust against the anharmonic perturbation, we find that it can be altered effectively by a quantum catastrophe.

  17. The effect of stiffness and mass on coupled oscillations in a phononic crystal

    SciTech Connect

    Baboly, M. Ghasemi; Su, M. F.; Alaie, S.; Goettler, D. F.; Leseman, Z. C.; Reinke, C. M.; El-Kady, I.

    2013-11-15

    Insight into phononic bandgap formation is presented using a first principles-type approach where phononic lattices are treated as coupled oscillators connected via massless tethers. The stiffness of the tethers and the mass of the oscillator are varied and their influences on the bandgap formation are deduced. This analysis is reinforced by conducting numerical simulations to examine the modes bounding the bandgap and highlighting the effect of the above parameters. The analysis presented here not only sheds light on the origins of gap formation, but also allows one to define design rules for wide phononic gaps and maximum gap-to-midgap ratios.

  18. Quantum entanglement in coupled harmonic oscillator systems: from micro to macro

    NASA Astrophysics Data System (ADS)

    Kao, Jhih-Yuan; Chou, Chung-Hsien

    2016-07-01

    We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number.

  19. Revisiting an old concept: the coupled oscillator model for VCD. Part 2: implications of the generalised coupled oscillator mechanism for the VCD robustness concept.

    PubMed

    Nicu, Valentin Paul

    2016-08-01

    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.

  20. Computer simulation of spatial coupling in chemical oscillations of CO oxidation on two Pd(110) single crystals

    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.

  1. Glassy states and super-relaxation in populations of coupled phase oscillators.

    PubMed

    Iatsenko, D; McClintock, P V E; Stefanovska, A

    2014-01-01

    Large networks of coupled oscillators appear in many branches of science, so that the kinds of phenomena they exhibit are not only of intrinsic interest but also of very wide importance. In 1975, Kuramoto proposed an analytically tractable model to describe these systems, which has since been successfully applied in many contexts and remains a subject of intensive research. Some related problems, however, remain unclarified for decades, such as the existence and properties of the oscillator glass state. Here we present a detailed analysis of a very general form of the Kuramoto model. In particular, we find the conditions when it can exhibit glassy behaviour, which represents a kind of synchronous disorder in the present case. Furthermore, we discover a new and intriguing phenomenon that we refer to as super-relaxation where the oscillators feel no interaction at all while relaxing to incoherence. Our findings offer the possibility of creating glassy states and observing super-relaxation in real systems.

  2. Coupled oscillators utilised as gait rhythm generators of a two-legged walking machine.

    PubMed

    Zielińska, T

    1996-03-01

    The gait of current two-legged walking machines differs from that of humans, although the kinematic structures of these machines' legs frequently imitate human limbs. This paper presents a method of generating the trajectories of hip and knee joint angles resulting in a gait pattern similar to that of a human. For this purpose the solutions of coupled van der Pol oscillator equations are utilised. There is much evidence that these equations can be treated as a good model of the central pattern generator generating functional (also locomotional) rhythms in living creatures. The oscillator equations are solved by numerical integration. The method of changing the type of gait by changing appropriate parameter values in the oscillator equations is presented (change of velocity and trajectory of leg-ends). The results obtained enable enhanced control of two-legged walking systems by including gait pattern generators which will assume a similar role to that of biological generators.

  3. 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.

  4. Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators.

    PubMed

    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.

  5. Two-step approach to the dynamics of coupled anharmonic oscillators

    SciTech Connect

    Chung, N. N.; Chew, L. Y.

    2009-07-15

    We have further extended the two-step approach developed by Chung and Chew [N. N. Chung and L. Y. Chew, Phys. Rev. A 76, 032113 (2007)] to the solution of the quantum dynamics of general systems of N-coupled anharmonic oscillators. The idea is to employ an optimized basis set to represent the dynamical quantum states of these oscillator systems. The set is generated via the action of the optimized Bogoliubov transformed bosonic operators on the optimal squeezed vacuum product state. The procedure requires (i) applying the two-step approach to the eigendecomposition of the time evolution operator and (ii) transforming the representation of the initial state from the original to the optimal bases. We have applied the formalism to examine the dynamics of squeezing and entanglement of several anharmonic oscillator systems.

  6. Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators

    SciTech Connect

    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.

  7. 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.

  8. Antiresonant ring output-coupled continuous-wave optical parametric oscillator.

    PubMed

    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.

  9. Transonic Shock Oscillations and Wing Flutter Calculated with an Interactive Boundary Layer Coupling Method

    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.

  10. Bursting phenomena as well as the bifurcation mechanism in a coupled BVP oscillator with periodic excitation

    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).

  11. Grouping synchronization in a pulse-coupled network of chaotic spiking oscillators.

    PubMed

    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.

  12. Experimental investigation of chimera states with quiescent and synchronous domains in coupled electronic oscillators.

    PubMed

    Gambuzza, Lucia Valentina; Buscarino, Arturo; Chessari, Sergio; Fortuna, Luigi; Meucci, Riccardo; Frasca, Mattia

    2014-09-01

    Chimera states, that is, dynamical regimes characterized by the existence of a symmetry-broken solution where a coherent domain and an incoherent one coexist, have been theoretically demonstrated and numerically found in networks of homogeneously coupled identical oscillators. In this work we experimentally investigate the behavior of a closed and an open chain of electronic circuits with neuron-like spiking dynamics and first neighbor connections. Experimental results show the onset of a regime that we call chimera states with quiescent and synchronous domains, where synchronization coexists with spatially patterned oscillation death. The whole experimental bifurcation scenario, showing how disordered states, synchronization, chimera states with quiescent and synchronous domains, and oscillatory death states emerge as coupling is varied, is presented.

  13. Analysis on Patterns of Globally Coupled Phase Oscillators with Attractive and Repulsive Interactions

    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

  14. 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.

  15. 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.

  16. Synchronization of Stochastically Coupled Oscillators: Dynamical Phase Transitions and Large Deviations Theory (or Birds and Frogs)

    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.

  17. Synchronization in interacting populations of heterogeneous oscillators with time-varying coupling.

    PubMed

    So, Paul; Cotton, Bernard C; Barreto, Ernest

    2008-09-01

    In many networks of interest (including technological, biological, and social networks), the connectivity between the interacting elements is not static, but changes in time. Furthermore, the elements themselves are often not identical, but rather display a variety of behaviors, and may come in different classes. Here, we investigate the dynamics of such systems. Specifically, we study a network of two large interacting heterogeneous populations of limit-cycle oscillators whose connectivity switches between two fixed arrangements at a particular frequency. We show that for sufficiently high switching frequency, this system behaves as if the connectivity were static and equal to the time average of the switching connectivity. We also examine the mechanisms by which this fast-switching limit is approached in several nonintuitive cases. The results illuminate novel mechanisms by which synchronization can arise or be thwarted in large populations of coupled oscillators with nonstatic coupling.

  18. Current driven spin–orbit torque oscillator: ferromagnetic and antiferromagnetic coupling

    NASA Astrophysics Data System (ADS)

    Johansen, Øyvind; Linder, Jacob

    2016-09-01

    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.

  19. Current driven spin–orbit torque oscillator: ferromagnetic and antiferromagnetic coupling

    PubMed Central

    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

  20. 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.

  1. Experimental observation of three-frequency quasiperiodic solution in a ring of unidirectionally coupled oscillators.

    PubMed

    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. PMID:26172771

  2. When does noise destroy or enhance synchronous behavior in two mutually coupled light-controlled oscillators?

    PubMed

    Ramírez Ávila, G M; Kurths, J; Guisset, J L; Deneubourg, J L

    2010-11-01

    We study the influence of white gaussian noise in a system of two mutually coupled light-controlled oscillators (LCOs). We show that under certain noise intensity conditions, noise can destroy or enhance synchronization. We build some Arnold tonguelike structures in order to explain the effects due to noise. It is remarkable that noise-enhanced synchronization is possible only when the variances of the noise acting on each of the LCOs are different.

  3. Energy level formula for the Morse oscillator with an additional kinetic coupling potential

    NASA Astrophysics Data System (ADS)

    Fan, Hong-yi; Chen, Bo-zhan; Fan, Yue

    1996-02-01

    Based on the <η| representation which is the common eigenstate of the relative position x1 - x2 and the total momentum P1 + P2 of two particles we derive the energy level formula for a Morse oscillator with an additional kinetic coupling potential. The <η| representation seems to provide a direct and convenient approach for solving certain dynamical problems for two-body systems.

  4. Driven Dynamics and Rotary Echo of a Qubit Tunably Coupled to a Harmonic Oscillator

    NASA Astrophysics Data System (ADS)

    Gustavsson, S.; Bylander, J.; Yan, F.; Forn-Díaz, P.; Bolkhovsky, V.; Braje, D.; Fitch, G.; Harrabi, K.; Lennon, D.; Miloshi, J.; Murphy, P.; Slattery, R.; Spector, S.; Turek, B.; Weir, T.; Welander, P. B.; Yoshihara, F.; Cory, D. G.; Nakamura, Y.; Orlando, T. P.; Oliver, W. D.

    2012-04-01

    We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an oscillating field mediated by off-resonant driving of the resonator, leading to strong modifications of the qubit Rabi frequency. This opens an additional noise channel, and we find that low-frequency noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.

  5. Driven Dynamics and Rotary Echo of a Qubit Tunably Coupled to a Harmonic Oscillator

    NASA Astrophysics Data System (ADS)

    Oliver, William; Gustavsson, Simon; Bylander, Jonas; Yan, Fei; Forn-Diaz, Pol; Bolkhovsky, Vlad; Braje, Danielle; Fitch, George; Harrabi, Khalil; Lennon, Donna; Miloshi, Jovi; Murphy, Peter; Slattery, Rick; Spector, Steven; Turek, Ben; Weir, Terry; Welander, Paul; Yoshihara, Fumiki; Cory, David; Nakamura, Yasunobu; Orlando, Terry

    2013-03-01

    We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an oscillating field mediated by off-resonant driving of the resonator, leading to strong modifications of the qubit Rabi frequency. This opens an additional noise channel, and we find that low-frequency noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.

  6. Emergence of a super-synchronized mobbing state in a large population of coupled chemical oscillators.

    PubMed

    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

  7. Chimeralike states in a network of oscillators under attractive and repulsive global coupling.

    PubMed

    Mishra, Arindam; Hens, Chittaranjan; Bose, Mridul; Roy, Prodyot K; Dana, Syamal K

    2015-12-01

    We report chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify the existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (which we refer to as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. We find a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrate in time from one to another subpopulation. The relative size of the incoherent subpopulation, in the chimeralike states, remains almost stable with increasing size of the network. The generality of the coupling configuration in the origin of the chimeralike states is tested, using a second example of bistable system, the van der Pol-Duffing oscillator where the chimeralike states emerge as weakly chaotic in the coherent subpopulation and chaotic in the incoherent subpopulation. Furthermore, we apply the coupling, in a simplified form, to form a network of the chaotic Rössler system where both the noncoherent and the coherent subpopulations show chaotic dynamics. PMID:26764787

  8. Chimeralike states in a network of oscillators under attractive and repulsive global coupling

    NASA Astrophysics Data System (ADS)

    Mishra, Arindam; Hens, Chittaranjan; Bose, Mridul; Roy, Prodyot K.; Dana, Syamal K.

    2015-12-01

    We report chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify the existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (which we refer to as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. We find a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrate in time from one to another subpopulation. The relative size of the incoherent subpopulation, in the chimeralike states, remains almost stable with increasing size of the network. The generality of the coupling configuration in the origin of the chimeralike states is tested, using a second example of bistable system, the van der Pol-Duffing oscillator where the chimeralike states emerge as weakly chaotic in the coherent subpopulation and chaotic in the incoherent subpopulation. Furthermore, we apply the coupling, in a simplified form, to form a network of the chaotic Rössler system where both the noncoherent and the coherent subpopulations show chaotic dynamics.

  9. Emergence of a super-synchronized mobbing state in a large population of coupled chemical oscillators

    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.

  10. Emergence of a super-synchronized mobbing state in a large population of coupled chemical oscillators

    PubMed Central

    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

  11. Robust synchronization of coupled circadian and cell cycle oscillators in single mammalian cells.

    PubMed

    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.

  12. Emergence of a super-synchronized mobbing state in a large population of coupled chemical oscillators.

    PubMed

    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.

  13. 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.

  14. 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).

  15. El Nino-southern oscillation: A coupled response to the greenhouse effect?

    SciTech Connect

    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.

  16. Enzyme oscillation can enhance the thermodynamic efficiency of cellular metabolism: consequence of anti-phase coupling between reaction flux and affinity

    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.

  17. The Intercellular Synchronization of Ca2+ Oscillations Evaluates Cx36-Dependent Coupling

    PubMed Central

    Bavamian, Sabine; Pontes, Helena; Cancela, José; Charollais, Anne; Startchik, Sergei; Van De Ville, Dimitri; Meda, Paolo

    2012-01-01

    Connexin36 (Cx36) plays an important role in insulin secretion by controlling the intercellular synchronization of Ca2+ transients induced during stimulation. The lack of drugs acting on Cx36 channels is a major limitation in further unraveling the molecular mechanism underlying this effect. To screen for such drugs, we have developed an assay allowing for a semi-automatic, fluorimetric quantification of Ca2+ transients in large populations of MIN6 cells. Here, we show that (1) compared to control cells, MIN6 cells with reduced Cx36 expression or function showed decreased synchrony of glucose-induced Ca2+ oscillations; (2) glibenclamide, a sulphonylurea which promotes Cx36 junctions and coupling, increased the number of synchronous MIN6 cells, whereas quinine, an antimalarial drug which inhibits Cx36-dependent coupling, decreased this proportion; (3) several drugs were identified that altered the intercellular Ca2+ synchronization, cell coupling and distribution of Cx36; (4) some of them also affected insulin content. The data indicate that the intercellular synchronization of Ca2+ oscillations provides a reliable and non-invasive measurement of Cx36-dependent coupling, which is useful to identify novel drugs affecting the function of β-cells, neurons, and neuron-related cells that express Cx36. PMID:22848521

  18. Coupling between intrinsic prefrontal HbO2 and central EEG beta power oscillations in the resting brain.

    PubMed

    Pfurtscheller, Gert; Daly, Ian; Bauernfeind, Günther; Müller-Putz, Gernot R

    2012-01-01

    There is increasing interest in the intrinsic activity in the resting brain, especially that of ultraslow and slow oscillations. Using near-infrared spectroscopy (NIRS), electroencephalography (EEG), blood pressure (BP), respiration and heart rate recordings during 5 minutes of rest, combined with cross spectral and sliding cross correlation calculations, we identified a short-lasting coupling (duration [Formula: see text] s) between prefrontal oxyhemoglobin (HbO2) in the frequency band between 0.07 and 0.13 Hz and central EEG alpha and/or beta power oscillations in 8 of the 9 subjects investigated. The HbO2 peaks preceded the EEG band power peaks by 3.7 s in 6 subjects, with moderate or no coupling between BP and HbO2 oscillations. HbO2 and EEG band power oscillations were approximately in phase with BP oscillations in the 2 subjects with an extremely high coupling (squared coherence [Formula: see text]) between BP and HbO2 oscillation. No coupling was identified in one subject. These results indicate that slow precentral (de)oxyhemoglobin concentration oscillations during awake rest can be temporarily coupled with EEG fluctuations in sensorimotor areas and modulate the excitability level in the brains' motor areas, respectively. Therefore, this provides support for the idea that resting state networks fluctuate with frequencies of between 0.01 and 0.1 Hz (Mantini et.al. PNAS 2007).

  19. Driving Potential and Noise Level Determine the Synchronization State of Hydrodynamically Coupled Oscillators

    NASA Astrophysics Data System (ADS)

    Bruot, Nicolas; Kotar, Jurij; de Lillo, Filippo; Cosentino Lagomarsino, Marco; Cicuta, Pietro

    2012-10-01

    Motile cilia are highly conserved structures in the evolution of organisms, generating the transport of fluid by periodic beating, through remarkably organized behavior in space and time. It is not known how these spatiotemporal patterns emerge and what sets their properties. Individual cilia are nonequilibrium systems with many degrees of freedom. However, their description can be represented by simpler effective force laws that drive oscillations, and paralleled with nonlinear phase oscillators studied in physics. Here a synthetic model of two phase oscillators, where colloidal particles are driven by optical traps, proves the role of the average force profile in establishing the type and strength of synchronization. We find that highly curved potentials are required for synchronization in the presence of noise. The applicability of this approach to biological data is also illustrated by successfully mapping the behavior of cilia in the alga Chlamydomonas onto the coarse-grained model.

  20. 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.

  1. Two generalized algorithms measuring phase-amplitude cross-frequency coupling in neuronal oscillations network.

    PubMed

    Li, Qun; Zheng, Chen-Guang; Cheng, Ning; Wang, Yi-Yi; Yin, Tao; Zhang, Tao

    2016-06-01

    An increasing number of studies pays attention to cross-frequency coupling in neuronal oscillations network, as it is considered to play an important role in exchanging and integrating of information. In this study, two generalized algorithms, phase-amplitude coupling-evolution map approach and phase-amplitude coupling-conditional mutual information which have been developed and applied originally in an identical rhythm, are generalized to measure cross-frequency coupling. The effectiveness of quantitatively distinguishing the changes of coupling strength from the measurement of phase-amplitude coupling (PAC) is demonstrated based on simulation data. The data suggest that the generalized algorithms are able to effectively evaluate the strength of PAC, which are consistent with those traditional approaches, such as PAC-PLV and PAC-MI. Experimental data, which are local field potentials obtained from anaesthetized SD rats, have also been analyzed by these two generalized approaches. The data show that the theta-low gamma PAC in the hippocampal CA3-CA1 network is significantly decreased in the glioma group compared to that in the control group. The results, obtained from either simulation data or real experimental signals, are consistent with that of those traditional approaches PAC-MI and PAC-PLV. It may be considered as a proper indicator for the cross frequency coupling in sub-network, such as the hippocampal CA3 and CA1. PMID:27275379

  2. Two generalized algorithms measuring phase-amplitude cross-frequency coupling in neuronal oscillations network.

    PubMed

    Li, Qun; Zheng, Chen-Guang; Cheng, Ning; Wang, Yi-Yi; Yin, Tao; Zhang, Tao

    2016-06-01

    An increasing number of studies pays attention to cross-frequency coupling in neuronal oscillations network, as it is considered to play an important role in exchanging and integrating of information. In this study, two generalized algorithms, phase-amplitude coupling-evolution map approach and phase-amplitude coupling-conditional mutual information which have been developed and applied originally in an identical rhythm, are generalized to measure cross-frequency coupling. The effectiveness of quantitatively distinguishing the changes of coupling strength from the measurement of phase-amplitude coupling (PAC) is demonstrated based on simulation data. The data suggest that the generalized algorithms are able to effectively evaluate the strength of PAC, which are consistent with those traditional approaches, such as PAC-PLV and PAC-MI. Experimental data, which are local field potentials obtained from anaesthetized SD rats, have also been analyzed by these two generalized approaches. The data show that the theta-low gamma PAC in the hippocampal CA3-CA1 network is significantly decreased in the glioma group compared to that in the control group. The results, obtained from either simulation data or real experimental signals, are consistent with that of those traditional approaches PAC-MI and PAC-PLV. It may be considered as a proper indicator for the cross frequency coupling in sub-network, such as the hippocampal CA3 and CA1.

  3. Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle.

    PubMed

    Feillet, Céline; Krusche, Peter; Tamanini, Filippo; Janssens, Roel C; Downey, Mike J; Martin, Patrick; Teboul, Michèle; Saito, Shoko; Lévi, Francis A; Bretschneider, Till; van der Horst, Gijsbertus T J; Delaunay, Franck; Rand, David A

    2014-07-01

    Daily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle progression, and hence its biological relevance, is not understood. In particular, we do not know how the temporal organization of cell division at the single-cell level produces this daily rhythm at the tissue level. Here we use multispectral imaging of single live cells, computational methods, and mathematical modeling to address this question in proliferating mouse fibroblasts. We show that in unsynchronized cells the cell cycle and circadian clock robustly phase lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronized way with a common frequency. Dexamethasone-induced synchronization reveals additional clock states. As well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock. Cells transition to these states after dexamethasone synchronization. The temporal coordination of cell division by phase locking to the clock at a single-cell level has significant implications because disordered circadian function is increasingly being linked to the pathogenesis of many diseases, including cancer.

  4. Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model.

    PubMed

    Freitas, Celso; Macau, Elbert; Pikovsky, Arkady

    2015-04-01

    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.

  5. Partial synchronization dynamics of coupled ultradian oscillators comprising an insect neurosecretory cell system.

    PubMed

    Ichikawa, Toshio

    2009-12-01

    An insulin-related peptide, bombyxin, in the silkmoth Bombyx mori is secreted by four pairs of cerebral neurosecretory cells that form a weakly coupled oscillator system to produce a pulsatile pattern of hormone secretion. The activity of individual bombyxin-producing (BP) cells oscillated with different periods (20-70 min). The population of BP cells exhibited complex phase dynamics, including spontaneous synchronization and desynchronization of different combinations of cells. Statistical cross-correlation analyses of oscillation patterns between BP cells revealed that one cell usually correlated closely with a few particular cells of similar periodicity. Close investigation of the phase differences between individual active phases of the related cell pairs revealed that an inphase synchronous state was usually maintained for many cycles, whereas an antiphase state was transient, lasting for a few cycles. In contrast, antiphase synchronous states often occurred between several cell pairs when the brain containing the cerebral neurosecretory cell system was disconnected from the ventral nerve cord containing the neuronal mechanism that induced periodic heartbeat reversals at intervals of 80-110 min and exerted a periodic suppressive or phase-resetting effect on individual BP cells. These results suggest that the internal coupling mechanism in the BP cell system is not sufficient to maintain an in-phase synchronous state in the heterogeneous cell population, and that the external phase resetting mechanism may assist in-phase synchronization of many neurosecretory cells to generate an overall pulsatile pattern of bombyxin secretion.

  6. Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle

    PubMed Central

    Feillet, Céline; Krusche, Peter; Tamanini, Filippo; Janssens, Roel C.; Downey, Mike J.; Martin, Patrick; Teboul, Michèle; Saito, Shoko; Lévi, Francis A.; Bretschneider, Till; van der Horst, Gijsbertus T. J.; Delaunay, Franck; Rand, David A.

    2014-01-01

    Daily synchronous rhythms of cell division at the tissue or organism level are observed in many species and suggest that the circadian clock and cell cycle oscillators are coupled. For mammals, despite known mechanistic interactions, the effect of such coupling on clock and cell cycle progression, and hence its biological relevance, is not understood. In particular, we do not know how the temporal organization of cell division at the single-cell level produces this daily rhythm at the tissue level. Here we use multispectral imaging of single live cells, computational methods, and mathematical modeling to address this question in proliferating mouse fibroblasts. We show that in unsynchronized cells the cell cycle and circadian clock robustly phase lock each other in a 1:1 fashion so that in an expanding cell population the two oscillators oscillate in a synchronized way with a common frequency. Dexamethasone-induced synchronization reveals additional clock states. As well as the low-period phase-locked state there are distinct coexisting states with a significantly higher period clock. Cells transition to these states after dexamethasone synchronization. The temporal coordination of cell division by phase locking to the clock at a single-cell level has significant implications because disordered circadian function is increasingly being linked to the pathogenesis of many diseases, including cancer. PMID:24958884

  7. Coupled slow and fast surface dynamics in an electrocatalytic oscillator: Model and simulations

    SciTech Connect

    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.

  8. Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis.

    PubMed

    Tirabassi, Giulio; Sevilla-Escoboza, Ricardo; Buldú, Javier M; Masoller, Cristina

    2015-06-04

    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.

  9. Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model

    SciTech Connect

    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.

  10. Neuronal Oscillations with Non-sinusoidal Morphology Produce Spurious Phase-to-Amplitude Coupling and Directionality

    PubMed Central

    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

  11. Neuronal Oscillations with Non-sinusoidal Morphology Produce Spurious Phase-to-Amplitude Coupling and Directionality.

    PubMed

    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 showed

  12. Neuronal Oscillations with Non-sinusoidal Morphology Produce Spurious Phase-to-Amplitude Coupling and Directionality

    PubMed Central

    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

  13. 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.

  14. Experimental synchronization of chaos in a large ring of mutually coupled single-transistor oscillators: phase, amplitude, and clustering effects.

    PubMed

    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. PMID:25554028

  15. Experimental synchronization of chaos in a large ring of mutually coupled single-transistor oscillators: Phase, amplitude, and clustering effects

    SciTech Connect

    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.

  16. Effect of periodic parametric excitation on an ensemble of force-coupled self-oscillators.

    PubMed

    Shchekinova, E Y

    2010-06-01

    We report the synchronization behavior in an ensemble of identical limit cycle oscillators coupled to a mass-spring load via a force relation. We consider the effect of periodic parametric modulation on the final states of the system. Two types of external parametric excitations are investigated numerically: periodic modulation of the stiffness of the inertial oscillator and periodic excitation of the frequency of the self-oscillatory element. We show that the synchronization scenarios are not only ruled by the choice of parameters of the excitation force but also depend on the initial collective state in the ensemble. We give detailed analysis of entrainment behavior for initially synchronous or antiphase synchronous states as well as for disorganized states.

  17. The universe dominated by oscillating scalar with non-minimal derivative coupling to gravity

    SciTech Connect

    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.

  18. Consecutive transitions from localized to delocalized transport states in the anharmonic chain of three coupled oscillators.

    PubMed

    Kislovsky, V; Kovaleva, M; Jayaprakash, K R; Starosvetsky, Y

    2016-07-01

    In the present paper, we study the mechanism of formation and bifurcations of highly nonstationary regimes manifested by different energy transport intensities, emerging in an anharmonic trimer model. The basic model under investigation comprises a chain of three coupled anharmonic oscillators subject to localized excitation, where the initial energy is imparted to the first oscillator only. We report the formation of three basic nonstationary transport states traversed by locally excited regimes. These states differ by spatial energy distribution, as well as by the intensity of energy transport along the chain. In the current study, we focus on numerical and analytical investigation of the intricate resonant mechanism governing the inter-state transitions of locally excited regimes. Results of the analytical study are in good agreement with the numerical simulations of the trimer model.

  19. Consecutive transitions from localized to delocalized transport states in the anharmonic chain of three coupled oscillators

    NASA Astrophysics Data System (ADS)

    Kislovsky, V.; Kovaleva, M.; Jayaprakash, K. R.; Starosvetsky, Y.

    2016-07-01

    In the present paper, we study the mechanism of formation and bifurcations of highly nonstationary regimes manifested by different energy transport intensities, emerging in an anharmonic trimer model. The basic model under investigation comprises a chain of three coupled anharmonic oscillators subject to localized excitation, where the initial energy is imparted to the first oscillator only. We report the formation of three basic nonstationary transport states traversed by locally excited regimes. These states differ by spatial energy distribution, as well as by the intensity of energy transport along the chain. In the current study, we focus on numerical and analytical investigation of the intricate resonant mechanism governing the inter-state transitions of locally excited regimes. Results of the analytical study are in good agreement with the numerical simulations of the trimer model.

  20. Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli.

    PubMed

    Ly, Cheng; Ermentrout, G Bard

    2009-06-01

    The response of neurons to external stimuli greatly depends on the intrinsic dynamics of the network. Here, the intrinsic dynamics are modeled as coupling and the external input is modeled as shared and unshared noise. We assume the neurons are repetitively firing action potentials (i.e., neural oscillators), are weakly and identically coupled, and the external noise is weak. Shared noise can induce bistability between the synchronous and anti-phase states even though the anti-phase state is the only stable state in the absence of noise. We study the Fokker-Planck equation of the system and perform an asymptotic reduction rho(0). The rho(0) solution is more computationally efficient than both the Monte Carlo simulations and the 2D Fokker-Planck solver, and agrees remarkably well with the full system with weak noise and weak coupling. With moderate noise and coupling, rho(0) is still qualitatively correct despite the small noise and coupling assumption in the asymptotic reduction. Our phase model accurately predicts the behavior of a realistic synaptically coupled Morris-Lecar system.

  1. Master stability islands for amplitude death in networks of delay-coupled oscillators.

    PubMed

    Huddy, Stanley R; Sun, Jie

    2016-05-01

    This paper presents a master stability function (MSF) approach for analyzing the stability of amplitude death (AD) in networks of delay-coupled oscillators. Unlike the familiar MSFs for instantaneously coupled networks, which typically have a single input encoding for the effects of the eigenvalues of the network Laplacian matrix, for delay-coupled networks we show that such MSFs generally require two additional inputs: the time delay and the coupling strength. To utilize the MSF for determining the stability of AD of general networks for a chosen nonlinear system (node dynamics) and coupling function, we introduce the concept of master stability islands (MSIs), which are two-dimensional stability islands of the delay-coupling parameter space together with a third dimension ("altitude") encoding for eigenvalues that result in stable AD. We numerically compute the MSFs and visualize the corresponding MSIs for several common chaotic systems including the Rössler, the Lorenz, and Chen's system and find that it is generally possible to achieve AD and that a nonzero time delay is necessary for the stabilization of the AD states.

  2. Master stability islands for amplitude death in networks of delay-coupled oscillators

    NASA Astrophysics Data System (ADS)

    Huddy, Stanley R.; Sun, Jie

    2016-05-01

    This paper presents a master stability function (MSF) approach for analyzing the stability of amplitude death (AD) in networks of delay-coupled oscillators. Unlike the familiar MSFs for instantaneously coupled networks, which typically have a single input encoding for the effects of the eigenvalues of the network Laplacian matrix, for delay-coupled networks we show that such MSFs generally require two additional inputs: the time delay and the coupling strength. To utilize the MSF for determining the stability of AD of general networks for a chosen nonlinear system (node dynamics) and coupling function, we introduce the concept of master stability islands (MSIs), which are two-dimensional stability islands of the delay-coupling parameter space together with a third dimension ("altitude") encoding for eigenvalues that result in stable AD. We numerically compute the MSFs and visualize the corresponding MSIs for several common chaotic systems including the Rössler, the Lorenz, and Chen's system and find that it is generally possible to achieve AD and that a nonzero time delay is necessary for the stabilization of the AD states.

  3. Robust synchronization of coupled neural oscillators using the derivative-free nonlinear Kalman Filter.

    PubMed

    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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses.

    PubMed

    Bressloff, P C

    1999-08-01

    We analyze the effects of synaptic depression or facilitation on the existence and stability of the splay or asynchronous state in a population of all-to-all, pulse-coupled neural oscillators. We use mean-field techniques to derive conditions for the local stability of the splay state and determine how stability depends on the degree of synaptic depression or facilitation. We also consider the effects of noise. Extensions of the mean-field results to finite networks are developed in terms of the nonlinear firing time map.

  10. Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators.

    PubMed

    Timme, Marc; Wolf, Fred; Geisel, Theo

    2002-12-16

    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.

  11. Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays.

    PubMed

    Sethia, Gautam C; Sen, Abhijit; Atay, Fatihcan M

    2010-05-01

    We study the existence and stability of synchronous solutions in a continuum field of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. We present a comprehensive stability diagram in the parameter space of the system. From the numerical results, a heuristic synchronization condition is suggested and an analytic relation for the marginal stability curve is obtained. We also provide an expression in the form of a scaling relation that closely follows the marginal stability curve over the complete range of the nonlocality parameter.

  12. The Dirac-Moshinsky oscillator coupled to an external field and its connection to quantum optics

    NASA Astrophysics Data System (ADS)

    Torres, Juan Mauricio; Sadurní, Emerson; Seligman, Thomas H.

    2010-12-01

    The Dirac-Moshinsky oscillator is an elegant example of an exactly solvable quantum relativistic model that under certain circumstances can be mapped onto the Jaynes-Cummings model in quantum optics. In this work we show, how to do this in detail. Then we extend it by considering its coupling with an external (isospin) field and find the conditions that maintain solvability. We use this extended system to explore entanglement in relativistic systems and then identify its quantum optical analog: two different atoms interacting with an electromagnetic mode. We show different aspects of entanglement which gain relevance in this last system, which can be used to emulate the former.

  13. Robust autoassociative memory with coupled networks of Kuramoto-type oscillators.

    PubMed

    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. PMID:27627319

  14. Robust autoassociative memory with coupled networks of Kuramoto-type oscillators.

    PubMed

    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.

  15. Geometry of classical periodic orbits and quantum coherent states in coupled oscillators with SU(2) transformations

    SciTech Connect

    Chen, Y. F.

    2011-03-15

    The geometry of classical dynamics in coupled oscillators with SU(2) transformations is explored and found to be relevant to a family of continuous-transformation orbits between Lissajous and trochoidal curves. The quantum wave-packet coherent states are derived analytically to correspond exactly to the transformation geometry of classical dynamics. By using the quantum wave-packet coherent states derived herein, stationary coherent states are constructed and are shown to possess spatial patterns identical to the transformation geometry between Lissajous and trochoidal orbits.

  16. Linearly coupled oscillations in fully degenerate pair and warm pair-ion astrophysical plasmas

    NASA Astrophysics Data System (ADS)

    Khan, S. A.; Ilyas, M.; Wazir, Z.; Ehsan, Zahida

    2014-08-01

    In this paper we study the coexisting low frequency oscillations in strongly degenerate, magnetized, (electron-positron) pair and warm pair-ion plasma. The dispersion relations are obtained for both the cases in macroscopic quantum hydrodynamics approximation. In pair-ion case, the dispersion equation shows coupling of electrostatic and (shear) electromagnetic modes under certain circumstances with important role of ion temperature. Domain of existence of such waves and their relevance to dense degenerate astrophysical plasmas is pointed out. Results are analyzed numerically for typical systems with variation of ion concentration and ion temperature.

  17. Coordination of spinal locomotor activity in the lamprey: long-distance coupling of spinal oscillators.

    PubMed

    McClellan, A D; Hagevik, A

    1999-05-01

    The extent and strength of long-distance coupling between locomotor networks in the rostral and caudal spinal cord of larval lamprey were examined with in vitro brain/spinal cord preparations, in which spinal locomotor activity was initiated by chemical microstimulation in the brain, as well as with computer modeling. When locomotor activity and short-distance coupling were blocked in the middle spinal cord for at least 40 segments, burst activity in the rostral and caudal spinal cord was still coupled 1:1, indicating that long-distance coupling is extensive. However, in the absence of short-distance coupling, intersegmental phase lags were not constant but decreased significantly with increasing cycle times, suggesting that long-distance coupling maintains a relatively constant delay rather than a constant phase lag between rostral and caudal bursts. In addition, under these conditions, intersegmental phase lags, measured between rostral and caudal burst activity, were significantly less than normal, and the decrease was greater for longer distances between rostral and caudal locomotor networks. The above result could be mimicked by a computer model consisting of pairs of oscillators in the rostral, middle, and caudal spinal cord that were connected by short- and long-distance coupling. With short-distance coupling blocked in the middle spinal cord, strychnine was applied to either the rostral or caudal spinal cord to convert the pattern locally from right-left alternation to synchronous burst activity. Synchronous burst activity in the rostral spinal cord resulted in a reduction in right-left phase values for burst activity in the caudal cord. These results also could be mimicked by the computer model. Strychnine-induced synchronous burst activity in the caudal spinal cord did not appear to alter the right-left phase values of rostral burst activity. Taken together, the experimental and modeling results suggest that the descending and ascending components of long

  18. Atmosphere-ocean coupled processes in the Madden-Julian oscillation

    NASA Astrophysics Data System (ADS)

    DeMott, Charlotte A.; Klingaman, Nicholas P.; Woolnough, Steven J.

    2015-12-01

    The Madden-Julian oscillation (MJO) is a convectively coupled 30-70 day (intraseasonal) tropical atmospheric mode that drives variations in global weather but which is poorly simulated in most atmospheric general circulation models. Over the past two decades, field campaigns and modeling experiments have suggested that tropical atmosphere-ocean interactions may sustain or amplify the pattern of enhanced and suppressed atmospheric convection that defines the MJO and encourage its eastward propagation through the Indian and Pacific Oceans. New observations collected during the past decade have advanced our understanding of the ocean response to atmospheric MJO forcing and the resulting intraseasonal sea surface temperature fluctuations. Numerous modeling studies have revealed a considerable impact of the mean state on MJO ocean-atmosphere coupled processes, as well as the importance of resolving the diurnal cycle of atmosphere-upper ocean interactions. New diagnostic methods provide insight to atmospheric variability and physical processes associated with the MJO but offer limited insight on the role of ocean feedbacks. Consequently, uncertainty remains concerning the role of the ocean in MJO theory. Our understanding of how atmosphere-ocean coupled processes affect the MJO can be improved by collecting observations in poorly sampled regions of MJO activity, assessing oceanic and atmospheric drivers of surface fluxes, improving the representation of upper ocean mixing in coupled model simulations, designing model experiments that minimize mean state differences, and developing diagnostic tools to evaluate the nature and role of coupled ocean-atmosphere processes over the MJO cycle.

  19. State diagram of magnetostatic coupling phase-locked spin-torque oscillators

    SciTech Connect

    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.

  20. Phase locking of spin-torque nano-oscillator pairs with magnetic dipolar coupling

    NASA Astrophysics Data System (ADS)

    Chen, Hao-Hsuan; Lee, Ching-Ming; Zhang, Zongzhi; Liu, Yaowen; Wu, Jong-Ching; Horng, Lance; Chang, Ching-Ray

    2016-06-01

    A spin-torque nanopillar oscillator (STNO) that combines a perpendicular-to-plane polarizer (PERP) with an in-plane magnetized free layer is a good candidate for phase locking, which opens a potential approach to enhancement of the output power of STNOs. In this paper, the magnetic dipolar coupling effect is used as the driving force to synchronize two STNOs. We develop an approximation theory for synchronizing two identical and nonidentical pairs of PERP STNOs, by which the critical current of synchronization, dipolar coupling strength, phase-locking transient time, and frequency can be analytically predicted. These predictions are further confirmed by macrospin and micromagnetic simulations. Finally, we show the phase diagrams of the phase locking as a function of applied current and separation between two STNOs.

  1. Periodic Forcing of a 555-IC Based Electronic Oscillator in the Strong Coupling Limit

    NASA Astrophysics Data System (ADS)

    Santillán, Moisés

    We designed and developed a master-slave electronic oscillatory system (based on the 555-timer IC working in the astable mode), and investigated its dynamic behavior regarding synchronization. For that purpose, we measured the rotation numbers corresponding to the phase-locking rhythms achieved in a large set of values of the normalized forcing frequency (NFF) and of the coupling strength between the master and the slave oscillators. In particular, we were interested in the system behavior in the strong-coupling limit, because such problem has not been extensively studied from an experimental perspective. Our results indicate that, in such a limit, a degenerate codimension-2 bifurcation point at NFF = 2 exists, in which all the phase-locking regions converge. These findings were corroborated by means of a mathematical model developed to that end, as well as by ad hoc further experiments.

  2. Simultaneous cooling of coupled mechanical oscillators using whispering gallery mode resonances.

    PubMed

    Li, Ying Lia; Millen, James; Barker, P F

    2016-01-25

    We demonstrate simultaneous center-of-mass cooling of two coupled oscillators, consisting of a microsphere-cantilever and a tapered optical fiber. Excitation of a whispering gallery mode (WGM) of the microsphere, via the evanescent field of the taper, provides a transduction signal that continuously monitors the relative motion between these two microgram objects with a sensitivity of 3 pm. The cavity enhanced optical dipole force is used to provide feedback damping on the motion of the micron-diameter taper, whereas a piezo stack is used to damp the motion of the much larger (up to 180 μm in diameter), heavier (up to 1.5 × 10(-7) kg) and stiffer microsphere-cantilever. In each feedback scheme multiple mechanical modes of each oscillator can be cooled, and mode temperatures below 10 K are reached for the dominant mode, consistent with limits determined by the measurement noise of our system. This represents stabilization on the picometer level and is the first demonstration of using WGM resonances to cool the mechanical modes of both the WGM resonator and its coupling waveguide. PMID:26832520

  3. Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators.

    PubMed

    Dodla, Ramana; Wilson, Charles J

    2013-10-01

    We investigate why electrically coupled neuronal oscillators synchronize or fail to synchronize using the theory of weakly coupled oscillators. Stability of synchrony and antisynchrony is predicted analytically and verified using numerical bifurcation diagrams. The shape of the phase response curve (PRC), the shape of the voltage time course, and the frequency of spiking are freely varied to map out regions of parameter spaces that hold stable solutions. We find that type 1 and type 2 PRCs can hold both synchronous and antisynchronous solutions, but the shape of the PRC and the voltage determine the extent of their stability. This is achieved by introducing a five-piecewise linear model to the PRC and a three-piecewise linear model to the voltage time course, and then analyzing the resultant eigenvalue equations that determine the stability of the phase-locked solutions. A single time parameter defines the skewness of the PRC, and another single time parameter defines the spike width and frequency. Our approach gives a comprehensive picture of the relation of the PRC shape, voltage time course, and stability of the resultant synchronous and antisynchronous solutions.

  4. Spin-orbit coupling and the production of misaligned hot Jupiters via Lidov-Kozai oscillations

    NASA Astrophysics Data System (ADS)

    Storch, Natalia I.; Anderson, Kassandra R.; Lai, Dong

    2015-12-01

    Many hot Jupiter systems exhibit misalignment between the orbital axis of the planet and the spin axis of its host star. While this misalignment could be primordial in nature, a large fraction of hot Jupiters are found in systems with distant stellar companions, and thus could have undergone Lidov-Kozai (LK) oscillations and acquired their misalignment dynamically. Here we present a study of the effect of spin-orbit coupling during LK oscillations, and the resulting spin-orbit misalignment angle distributions. We show that spin-orbit coupling induces complex, often chaotic, behavior in the spin axis of the host star, and that this behavior depends significantly on the mass of the planet and the properties of the host star (mass and spin history). We develop a semi-analytical framework that successfully explains most of the possible stellar spin behaviors. We then present a comprehensive population synthesis of hot Jupiters created via the LK mechanism, and discuss their possible observable signatures.

  5. Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators.

    PubMed

    Driben, R; Konotop, V V; Malomed, B A; Meier, T

    2016-07-01

    The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1. PMID:27575123

  6. Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators

    NASA Astrophysics Data System (ADS)

    Driben, R.; Konotop, V. V.; Malomed, B. A.; Meier, T.

    2016-07-01

    The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3 +3 harmonic-oscillator p -wave eigenfunctions with orbital and magnetic quantum numbers l =1 and m =1 , 0, -1 . The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p -wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l =1 .

  7. Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators.

    PubMed

    Driben, R; Konotop, V V; Malomed, B A; Meier, T

    2016-07-01

    The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1.

  8. Efficiency at maximum power of a quantum heat engine based on two coupled oscillators.

    PubMed

    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)(

  9. 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(

  10. Hormone-induced calcium oscillations depend on cross-coupling with inositol 1,4,5-trisphosphate oscillations.

    PubMed

    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.

  11. Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory

    SciTech Connect

    Schroeder, Markus; Schreiber, Michael; Kleinekathoefer, Ulrich

    2007-03-21

    Several techniques to solve a hierarchical set of equations of motion for propagating a reduced density matrix coupled to a thermal bath have been developed in recent years. This is either done using the path integral technique as in the original proposal by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1998)] or by the use of stochastic fields as done by Yan et al. [Chem. Phys. Lett. 395, 216 (2004)]. Based on the latter ansatz a compact derivation of the hierarchy using a decomposition of the spectral density function is given in the present contribution. The method is applied to calculate the time evolution of the reduced density matrix describing the motion in a harmonic, an anharmonic, and two coupled oscillators where each system is coupled to a thermal bath. Calculations to several orders in the system-bath coupling with two different truncations of the hierarchy are performed. The respective density matrices are used to calculate the time evolution of various system properties and the results are compared and discussed with a special focus on the convergence with respect to the truncation scheme applied.

  12. Entrainment and synchronization in networks of Rayleigh-van der Pol oscillators with diffusive and Haken-Kelso-Bunz couplings.

    PubMed

    Alderisio, Francesco; Bardy, Benoît G; di Bernardo, Mario

    2016-06-01

    We analyze a network of non-identical Rayleigh-van der Pol (RvdP) oscillators interconnected through either diffusive or nonlinear coupling functions. The work presented here extends existing results on the case of two nonlinearly coupled RvdP oscillators to the problem of considering a network of three or more of them. Specifically, we study synchronization and entrainment in networks of heterogeneous RvdP oscillators and contrast the effects of diffusive linear coupling strategies with the nonlinear Haken-Kelso-Bunz coupling, originally introduced to study human bimanual experiments. We show how convergence of the error among the nodes' trajectories toward a bounded region is possible with both linear and nonlinear coupling functions. Under the assumption that the network is connected, simple, and undirected, analytical results are obtained to prove boundedness of the error when the oscillators are coupled diffusively. All results are illustrated by way of numerical examples and compared with the experimental findings available in the literature on synchronization of people rocking chairs, confirming the effectiveness of the model we propose to capture some of the features of human group synchronization observed experimentally in the previous literature. PMID:27108135

  13. Effect of sharp jumps at the edges of phase response curves on synchronization of electrically coupled neuronal oscillators.

    PubMed

    Dodla, Ramana; Wilson, Charles J

    2013-01-01

    We study synchronization phenomenon of coupled neuronal oscillators using the theory of weakly coupled oscillators. The role of sudden jumps in the phase response curve profiles found in some experimental recordings and models on the ability of coupled neurons to exhibit synchronous and antisynchronous behavior is investigated, when the coupling between the neurons is electrical. The level of jumps in the phase response curve at either end, spike width and frequency of voltage time course of the coupled neurons are parameterized using piecewise linear functional forms, and the conditions for stable synchrony and stable antisynchrony in terms of those parameters are computed analytically. The role of the peak position of the phase response curve on phase-locking is also investigated.

  14. Magnetic nanoparticles for applications in oscillating magnetic field

    SciTech Connect

    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

  15. How synaptic weights determine stability of synchrony in networks of pulse-coupled excitatory and inhibitory oscillators.

    PubMed

    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.

  16. How synaptic weights determine stability of synchrony in networks of pulse-coupled excitatory and inhibitory oscillators

    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.

  17. Cell-cycle-coupled structural oscillation of centromeric nucleosomes in yeast.

    PubMed

    Shivaraju, Manjunatha; Unruh, Jay R; Slaughter, Brian D; Mattingly, Mark; Berman, Judith; Gerton, Jennifer L

    2012-07-20

    The centromere is a specialized chromosomal structure that regulates chromosome segregation. Centromeres are marked by a histone H3 variant. In budding yeast, the histone H3 variant Cse4 is present in a single centromeric nucleosome. Experimental evidence supports several different models for the structure of centromeric nucleosomes. To investigate Cse4 copy number in live yeast, we developed a method coupling fluorescence correlation spectroscopy and calibrated imaging. We find that centromeric nucleosomes have one copy of Cse4 during most of the cell cycle, whereas two copies are detected at anaphase. The proposal of an anaphase-coupled structural change is supported by Cse4-Cse4 interactions, incorporation of Cse4, and the absence of Scm3 in anaphase. Nucleosome reconstitution and ChIP suggests both Cse4 structures contain H2A/H2B. The increase in Cse4 intensity and deposition at anaphase are also observed in Candida albicans. Our experimental evidence supports a cell-cycle-coupled oscillation of centromeric nucleosome structure in yeast. PMID:22817893

  18. 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.

  19. Collective dynamics of identical phase oscillators with high-order coupling.

    PubMed

    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

  20. Beat Keeping in a Sea Lion As Coupled Oscillation: Implications for Comparative Understanding of Human Rhythm

    PubMed Central

    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