Synchronization properties of coupled chaotic neurons: The role of random shared input

NASA Astrophysics Data System (ADS)

Kumar, Rupesh; Bilal, Shakir; Ramaswamy, Ram

2016-06-01

Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag-synchronous states, and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.

Synchronization properties of coupled chaotic neurons: The role of random shared input

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Rupesh; Bilal, Shakir; Ramaswamy, Ram

Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag–synchronous states,more » and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.« less

Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients

NASA Astrophysics Data System (ADS)

Mormann, Florian; Lehnertz, Klaus; David, Peter; E. Elger, Christian

2000-10-01

We apply the concept of phase synchronization of chaotic and/or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms (EEGs) recorded from patients with temporal lobe epilepsy. Using the mean phase coherence as a statistical measure for phase synchronization, we observe characteristic spatial and temporal shifts in synchronization that appear to be strongly related to pathological activity. In particular, we observe distinct differences in the degree of synchronization between recordings from seizure-free intervals and those before an impending seizure, indicating an altered state of brain dynamics prior to seizure activity.

Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.

PubMed

Mobayen, Saleh

2018-06-01

This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Quorum Sensing in Populations of Spatially Extended Chaotic Oscillators Coupled Indirectly via a Heterogeneous Environment

NASA Astrophysics Data System (ADS)

Li, Bing-Wei; Cao, Xiao-Zhi; Fu, Chenbo

2017-12-01

Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual element communicates with each other is heterogeneous. Nevertheless, most of previous works considered the homogeneous case only. Here we investigated the dynamical behaviors in a population of spatially distributed chaotic oscillators immersed in a heterogeneous environment. Various dynamical synchronization states (such as oscillation death, phase synchronization, and complete synchronized oscillation) as well as their transitions were explored. In particular, we uncovered a non-traditional quorum sensing transition: increasing the population density leaded to a transition from oscillation death to synchronized oscillation at first, but further increasing the density resulted in degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization. The underlying mechanism of this finding was attributed to the dual roles played by the population density. What's more, by treating the environment as another component of the oscillator, the full system was then effectively equivalent to a locally coupled system. This fact allowed us to utilize the master stability functions approach to predict the occurrence of complete synchronization oscillation, which agreed with that from the direct numerical integration of the system. The potential candidates for the experimental realization of our model were also discussed.

Synchronization of strange non-chaotic attractors via unidirectional coupling of quasiperiodically-forced systems

NASA Astrophysics Data System (ADS)

Sivaganesh, G.; Daniel Sweetlin, M.; Arulgnanam, A.

2016-07-01

In this paper, we present a numerical investigation on the robust synchronization phenomenon observed in a unidirectionally-coupled quasiperiodically-forced simple nonlinear electronic circuit system exhibiting strange non-chaotic attractors (SNAs) in its dynamics. The SNA obtained in the simple quasiperiodic system is characterized for its SNA behavior. Then, we studied the nature of the synchronized state in unidirectionally coupled SNAs by using the Master-Slave approach. The stability of the synchronized state is studied through the master stability functions (MSF) obtained for coupling different state variables of the drive and response system. The property of robust synchronization is analyzed for one type of coupling of the state variables through phase portraits, conditional lyapunov exponents and the Kaplan-Yorke dimension. The phenomenon of complete synchronization of SNAs via a unidirectional coupling scheme is reported for the first time.

Desynchronization of chaos in coupled logistic maps.

PubMed

Maistrenko, Y L; Maistrenko, V L; Popovych, O; Mosekilde, E

1999-09-01

When identical chaotic oscillators interact, a state of complete or partial synchronization may be attained in which the motion is restricted to an invariant manifold of lower dimension than the full phase space. Riddling of the basin of attraction arises when particular orbits embedded in the synchronized chaotic state become transversely unstable while the state remains attracting on the average. Considering a system of two coupled logistic maps, we show that the transition to riddling will be soft or hard, depending on whether the first orbit to lose its transverse stability undergoes a supercritical or subcritical bifurcation. A subcritical bifurcation can lead directly to global riddling of the basin of attraction for the synchronized chaotic state. A supercritical bifurcation, on the other hand, is associated with the formation of a so-called mixed absorbing area that stretches along the synchronized chaotic state, and from which trajectories cannot escape. This gives rise to locally riddled basins of attraction. We present three different scenarios for the onset of riddling and for the subsequent transformations of the basins of attraction. Each scenario is described by following the type and location of the relevant asynchronous cycles, and determining their stable and unstable invariant manifolds. One scenario involves a contact bifurcation between the boundary of the basin of attraction and the absorbing area. Another scenario involves a long and interesting series of bifurcations starting with the stabilization of the asynchronous cycle produced in the riddling bifurcation and ending in a boundary crisis where the stability of an asynchronous chaotic state is destroyed. Finally, a phase diagram is presented to illustrate the parameter values at which the various transitions occur.

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.

Quantum-chaotic cryptography

NASA Astrophysics Data System (ADS)

de Oliveira, G. L.; Ramos, R. V.

2018-03-01

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

Phase locking route behind complex periodic windows in a forced oscillator

NASA Astrophysics Data System (ADS)

Jan, Hengtai; Tsai, Kuo-Ting; Kuo, Li-wei

2013-09-01

Chaotic systems have complex reactions against an external driving force; even in cases with low-dimension oscillators, the routes to synchronization are diverse. We proposed a stroboscope-based method for analyzing driven chaotic systems in their phase space. According to two statistic quantities generated from time series, we could realize the system state and the driving behavior simultaneously. We demonstrated our method in a driven bi-stable system, which showed complex period windows under a proper driving force. With increasing periodic driving force, a route from interior periodic oscillation to phase synchronization through the chaos state could be found. Periodic windows could also be identified and the circumstances under which they occurred distinguished. Statistical results were supported by conditional Lyapunov exponent analysis to show the power in analyzing the unknown time series.

A novel double-convection chaotic attractor, its adaptive control and circuit simulation

NASA Astrophysics Data System (ADS)

Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

Synchronization of chaotic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pecora, Louis M.; Carroll, Thomas L.

2015-09-15

We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years tomore » a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.« less

Hybrid electronic/optical synchronized chaos communication system.

PubMed

Toomey, J P; Kane, D M; Davidović, A; Huntington, E H

2009-04-27

A hybrid electronic/optical system for synchronizing a chaotic receiver to a chaotic transmitter has been demonstrated. The chaotic signal is generated electronically and injected, in addition to a constant bias current, to a semiconductor laser to produce an optical carrier for transmission. The optical chaotic carrier is photodetected to regenerate an electronic signal for synchronization in a matched electronic receiver The system has been successfully used for the transmission and recovery of a chaos masked message that is added to the chaotic optical carrier. Past demonstrations of synchronized chaos based, secure communication systems have used either an electronic chaotic carrier or an optical chaotic carrier (such as the chaotic output of various nonlinear laser systems). This is the first electronic/optical hybrid system to be demonstrated. We call this generation of a chaotic optical carrier by electronic injection.

Phase definition to assess synchronization quality of nonlinear oscillators

NASA Astrophysics Data System (ADS)

Freitas, Leandro; Torres, Leonardo A. B.; Aguirre, Luis A.

2018-05-01

This paper proposes a phase definition, named the vector field phase, which can be defined for systems with arbitrary finite dimension and is a monotonically increasing function of time. The proposed definition can properly quantify the dynamics in the flow direction, often associated with the null Lyapunov exponent. Numerical examples that use benchmark periodic and chaotic oscillators are discussed to illustrate some of the main features of the definition, which are that (i) phase information can be obtained either from the vector field or from a time series, (ii) it permits not only detection of phase synchronization but also quantification of it, and (iii) it can be used in the phase synchronization of very different oscillators.

Phase definition to assess synchronization quality of nonlinear oscillators.

PubMed

Freitas, Leandro; Torres, Leonardo A B; Aguirre, Luis A

2018-05-01

This paper proposes a phase definition, named the vector field phase, which can be defined for systems with arbitrary finite dimension and is a monotonically increasing function of time. The proposed definition can properly quantify the dynamics in the flow direction, often associated with the null Lyapunov exponent. Numerical examples that use benchmark periodic and chaotic oscillators are discussed to illustrate some of the main features of the definition, which are that (i) phase information can be obtained either from the vector field or from a time series, (ii) it permits not only detection of phase synchronization but also quantification of it, and (iii) it can be used in the phase synchronization of very different oscillators.

Transition from complete synchronization to spatio-temporal chaos in coupled chaotic systems with nonhyperbolic and hyperbolic attractors

NASA Astrophysics Data System (ADS)

Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim

2017-06-01

We study the transition from coherence (complete synchronization) to incoherence (spatio-temporal chaos) in ensembles of nonlocally coupled chaotic maps with nonhyperbolic and hyperbolic attractors. As basic models of a partial element we use the Henon map and the Lozi map. We show that the transition to incoherence in a ring of coupled Henon maps occurs through the appearance of phase and amplitude chimera states. An ensemble of coupled Lozi maps demonstrates the coherence-incoherence transition via solitary states and no chimera states are observed in this case.

Synchronization of Chaotic Systems without Direct Connections Using Reinforcement Learning

NASA Astrophysics Data System (ADS)

Sato, Norihisa; Adachi, Masaharu

In this paper, we propose a control method for the synchronization of chaotic systems that does not require the systems to be connected, unlike existing methods such as that proposed by Pecora and Carroll in 1990. The method is based on the reinforcement learning algorithm. We apply our method to two discrete-time chaotic systems with mismatched parameters and achieve M step delay synchronization. Moreover, we extend the proposed method to the synchronization of continuous-time chaotic systems.

Synchronization in node of complex networks consist of complex chaotic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wei, Qiang, E-mail: qiangweibeihua@163.com; Digital Images Processing Institute of Beihua University, BeiHua University, Jilin, 132011, Jilin; Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024

2014-07-15

A new synchronization method is investigated for node of complex networks consists of complex chaotic system. When complex networks realize synchronization, different component of complex state variable synchronize up to different scaling complex function by a designed complex feedback controller. This paper change synchronization scaling function from real field to complex field for synchronization in node of complex networks with complex chaotic system. Synchronization in constant delay and time-varying coupling delay complex networks are investigated, respectively. Numerical simulations are provided to show the effectiveness of the proposed method.

Synchronization of networked chaotic oscillators under external periodic driving.

PubMed

Yang, Wenchao; Lin, Weijie; Wang, Xingang; Huang, Liang

2015-03-01

The dynamical responses of a complex system to external perturbations are of both fundamental interest and practical significance. Here, by the model of networked chaotic oscillators, we investigate how the synchronization behavior of a complex network is influenced by an externally added periodic driving. Interestingly, it is found that by a slight change of the properties of the external driving, e.g., the frequency or phase lag between its intrinsic oscillation and external driving, the network synchronizability could be significantly modified. We demonstrate this phenomenon by different network models and, based on the method of master stability function, give an analysis on the underlying mechanisms. Our studies highlight the importance of external perturbations on the collective behaviors of complex networks, and also provide an alternate approach for controlling network synchronization.

The equal combination synchronization of a class of chaotic systems with discontinuous output

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Runzi; Zeng, Yanhui

This paper investigates the equal combination synchronization of a class of chaotic systems. The chaotic systems are assumed that only the output state variable is available and the output may be discontinuous state variable. By constructing proper observers, some novel criteria for the equal combination synchronization are proposed. The Lorenz chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.

Synchronization and an application of a novel fractional order King Cobra chaotic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muthukumar, P., E-mail: muthukumardgl@gmail.com; Balasubramaniam, P., E-mail: balugru@gmail.com; Ratnavelu, K., E-mail: kuru052001@gmail.com

2014-09-01

In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness ofmore » the proposed theoretical results.« less

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks.

PubMed

Feng, Cun-Fang; Xu, Xin-Jian; Wang, Sheng-Jun; Wang, Ying-Hai

2008-06-01

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks, and we find both its existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.

Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity

NASA Astrophysics Data System (ADS)

Pittorino, Fabrizio; Ibáñez-Berganza, Miguel; di Volo, Matteo; Vezzani, Alessandro; Burioni, Raffaella

2017-03-01

A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasisynchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.

A new chaotic communication scheme based on adaptive synchronization.

PubMed

Xiang-Jun, Wu

2006-12-01

A new chaotic communication scheme using adaptive synchronization technique of two unified chaotic systems is proposed. Different from the existing secure communication methods, the transmitted signal is modulated into the parameter of chaotic systems. The adaptive synchronization technique is used to synchronize two identical chaotic systems embedded in the transmitter and the receiver. It is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical unified chaotic systems with unknown system parameters asymptotically synchronized; thus the parameter of the receiver system is identified. Then the recovery of the original information signal in the receiver is successfully achieved on the basis of the estimated parameter. It is noticed that the time required for recovering the information signal and the accuracy of the recovered signal very sensitively depends on the frequency of the information signal. Numerical results have verified the effectiveness of the proposed scheme.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2018-03-01

Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Adaptive feedback synchronization of a unified chaotic system

NASA Astrophysics Data System (ADS)

Lu, Junan; Wu, Xiaoqun; Han, Xiuping; Lü, Jinhu

2004-08-01

This Letter further improves and extends the work of Wang et al. [Phys. Lett. A 312 (2003) 34]. In detailed, the linear feedback synchronization and adaptive feedback synchronization with only one controller for a unified chaotic system are discussed here. It is noticed that this unified system contains the noted Lorenz and Chen systems. Two chaotic synchronization theorems are attained. Also, numerical simulations are given to show the effectiveness of these methods.

Multivariate singular spectrum analysis and the road to phase synchronization

NASA Astrophysics Data System (ADS)

Groth, Andreas; Ghil, Michael

2010-05-01

Singular spectrum analysis (SSA) and multivariate SSA (M-SSA) are based on the classical work of Kosambi (1943), Loeve (1945) and Karhunen (1946) and are closely related to principal component analysis. They have been introduced into information theory by Bertero, Pike and co-workers (1982, 1984) and into dynamical systems analysis by Broomhead and King (1986a,b). Ghil, Vautard and associates have applied SSA and M-SSA to the temporal and spatio-temporal analysis of short and noisy time series in climate dynamics and other fields in the geosciences since the late 1980s. M-SSA provides insight into the unknown or partially known dynamics of the underlying system by decomposing the delay-coordinate phase space of a given multivariate time series into a set of data-adaptive orthonormal components. These components can be classified essentially into trends, oscillatory patterns and noise, and allow one to reconstruct a robust "skeleton" of the dynamical system's structure. For an overview we refer to Ghil et al. (Rev. Geophys., 2002). In this talk, we present M-SSA in the context of synchronization analysis and illustrate its ability to unveil information about the mechanisms behind the adjustment of rhythms in coupled dynamical systems. The focus of the talk is on the special case of phase synchronization between coupled chaotic oscillators (Rosenblum et al., PRL, 1996). Several ways of measuring phase synchronization are in use, and the robust definition of a reasonable phase for each oscillator is critical in each of them. We illustrate here the advantages of M-SSA in the automatic identification of oscillatory modes and in drawing conclusions about the transition to phase synchronization. Without using any a priori definition of a suitable phase, we show that M-SSA is able to detect phase synchronization in a chain of coupled chaotic oscillators (Osipov et al., PRE, 1996). Recently, Muller et al. (PRE, 2005) and Allefeld et al. (Intl. J. Bif. Chaos, 2007) have demonstrated the usefulness of principal component analysis in detecting phase synchronization from multivariate time series. The present talk provides a generalization of this idea and presents a robust implementation thereof via M-SSA.

Dynamical inference: where phase synchronization and generalized synchronization meet.

PubMed

Stankovski, Tomislav; McClintock, Peter V E; Stefanovska, Aneta

2014-06-01

Synchronization is a widespread phenomenon that occurs among interacting oscillatory systems. It facilitates their temporal coordination and can lead to the emergence of spontaneous order. The detection of synchronization from the time series of such systems is of great importance for the understanding and prediction of their dynamics, and several methods for doing so have been introduced. However, the common case where the interacting systems have time-variable characteristic frequencies and coupling parameters, and may also be subject to continuous external perturbation and noise, still presents a major challenge. Here we apply recent developments in dynamical Bayesian inference to tackle these problems. In particular, we discuss how to detect phase slips and the existence of deterministic coupling from measured data, and we unify the concepts of phase synchronization and general synchronization. Starting from phase or state observables, we present methods for the detection of both phase and generalized synchronization. The consistency and equivalence of phase and generalized synchronization are further demonstrated, by the analysis of time series from analog electronic simulations of coupled nonautonomous van der Pol oscillators. We demonstrate that the detection methods work equally well on numerically simulated chaotic systems. In all the cases considered, we show that dynamical Bayesian inference can clearly identify noise-induced phase slips and distinguish coherence from intrinsic coupling-induced synchronization.

Synchronization of chaotic systems involving fractional operators of Liouville-Caputo type with variable-order

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.

2017-12-01

In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.

A discrete-time chaos synchronization system for electronic locking devices

NASA Astrophysics Data System (ADS)

Minero-Ramales, G.; López-Mancilla, D.; Castañeda, Carlos E.; Huerta Cuellar, G.; Chiu Z., R.; Hugo García López, J.; Jaimes Reátegui, R.; Villafaña Rauda, E.; Posadas-Castillo, C.

2016-11-01

This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.

General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameter identification in several chaotic and hyperchaotic systems

NASA Astrophysics Data System (ADS)

Sun, Jun-Wei; Shen, Yi; Zhang, Guo-Dong; Wang, Yan-Feng; Cui, Guang-Zhao

2013-04-01

According to the Lyapunov stability theorem, a new general hybrid projective complete dislocated synchronization scheme with non-derivative and derivative coupling based on parameter identification is proposed under the framework of drive-response systems. Every state variable of the response system equals the summation of the hybrid drive systems in the previous hybrid synchronization. However, every state variable of the drive system equals the summation of the hybrid response systems while evolving with time in our method. Complete synchronization, hybrid dislocated synchronization, projective synchronization, non-derivative and derivative coupling, and parameter identification are included as its special item. The Lorenz chaotic system, Rössler chaotic system, memristor chaotic oscillator system, and hyperchaotic Lü system are discussed to show the effectiveness of the proposed methods.

Hidden imperfect synchronization of wall turbulence.

PubMed

Tardu, Sedat F

2010-03-01

Instantaneous amplitude and phase concept emerging from analytical signal formulation is applied to the wavelet coefficients of streamwise velocity fluctuations in the buffer layer of a near wall turbulent flow. Experiments and direct numerical simulations show both the existence of long periods of inert zones wherein the local phase is constant. These regions are separated by random phase jumps. The local amplitude is globally highly intermittent, but not in the phase locked regions wherein it varies smoothly. These behaviors are reminiscent of phase synchronization phenomena observed in stochastic chaotic systems. The lengths of the constant phase inert (laminar) zones reveal a type I intermittency behavior, in concordance with saddle-node bifurcation, and the periodic orbits of saddle nature recently identified in Couette turbulence. The imperfect synchronization is related to the footprint of coherent Reynolds shear stress producing eddies convecting in the low buffer.

Design and Hardware Implementation of a New Chaotic Secure Communication Technique

PubMed Central

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness. PMID:27548385

Design and Hardware Implementation of a New Chaotic Secure Communication Technique.

PubMed

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness.

Analysis of the time structure of synchronization in multidimensional chaotic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makarenko, A. V., E-mail: avm.science@mail.ru

2015-05-15

A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.

Chaos M-ary modulation and demodulation method based on Hamilton oscillator and its application in communication.

PubMed

Fu, Yongqing; Li, Xingyuan; Li, Yanan; Yang, Wei; Song, Hailiang

2013-03-01

Chaotic communication has aroused general interests in recent years, but its communication effect is not ideal with the restriction of chaos synchronization. In this paper a new chaos M-ary digital modulation and demodulation method is proposed. By using region controllable characteristics of spatiotemporal chaos Hamilton map in phase plane and chaos unique characteristic, which is sensitive to initial value, zone mapping method is proposed. It establishes the map relationship between M-ary digital information and the region of Hamilton map phase plane, thus the M-ary information chaos modulation is realized. In addition, zone partition demodulation method is proposed based on the structure characteristic of Hamilton modulated information, which separates M-ary information from phase trajectory of chaotic Hamilton map, and the theory analysis of zone partition demodulator's boundary range is given. Finally, the communication system based on the two methods is constructed on the personal computer. The simulation shows that in high speed transmission communications and with no chaos synchronization circumstance, the proposed chaotic M-ary modulation and demodulation method has outperformed some conventional M-ary modulation methods, such as quadrature phase shift keying and M-ary pulse amplitude modulation in bit error rate. Besides, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-noise performance, and the system complexity is low and chaos signal is easy to generate.

Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators.

PubMed

Xu, Kesheng; Maidana, Jean Paul; Castro, Samy; Orio, Patricio

2018-05-30

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that - when isolated - can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Synchronous behaviour of two interacting oscillatory systems undergoing quasiperiodic route to chaos.

PubMed

Mondal, S; Pawar, S A; Sujith, R I

2017-10-01

Thermoacoustic instability, caused by a positive feedback between the unsteady heat release and the acoustic field in a combustor, is a major challenge faced in most practical combustors such as those used in rockets and gas turbines. We employ the synchronization theory for understanding the coupling between the unsteady heat release and the acoustic field of a thermoacoustic system. Interactions between coupled subsystems exhibiting different collective dynamics such as periodic, quasiperiodic, and chaotic oscillations are addressed. Even though synchronization studies have focused on different dynamical states separately, synchronous behaviour of two coupled systems exhibiting a quasiperiodic route to chaos has not been studied. In this study, we report the first experimental observation of different synchronous behaviours between two subsystems of a thermoacoustic system exhibiting such a transition as reported in Kabiraj et al. [Chaos 22, 023129 (2012)]. A rich variety of synchronous behaviours such as phase locking, intermittent phase locking, and phase drifting are observed as the dynamics of such subsystem change. The observed synchronization behaviour is further characterized using phase locking value, correlation coefficient, and relative mean frequency. These measures clearly reveal the boundaries between different states of synchronization.

Amplification through chaotic synchronization in spatially extended beam-plasma systems

NASA Astrophysics Data System (ADS)

Moskalenko, Olga I.; Frolov, Nikita S.; Koronovskii, Alexey A.; Hramov, Alexander E.

2017-12-01

In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.

Automated quantification of the synchrogram by recurrence plot analysis.

PubMed

Nguyen, Chinh Duc; Wilson, Stephen James; Crozier, Stuart

2012-04-01

Recently, the concept of phase synchronization of two weakly coupled oscillators has raised a great research interest and has been applied to characterize synchronization phenomenon in physiological data. Phase synchronization of cardiorespiratory coupling is often studied by a synchrogram analysis, a graphical tool investigating the relationship between instantaneous phases of two signals. Although several techniques have been proposed to automatically quantify the synchrogram, most of them require a preselection of a phase-locking ratio by trial and error. One technique does not require this information; however, it is based on the power spectrum of phase's distribution in the synchrogram, which is vulnerable to noise. This study aims to introduce a new technique to automatically quantify the synchrogram by studying its dynamic structure. Our technique exploits recurrence plot analysis, which is a well-established tool for characterizing recurring patterns and nonstationarities in experiments. We applied our technique to detect synchronization in simulated and measured infants' cardiorespiratory data. Our results suggest that the proposed technique is able to systematically detect synchronization in noisy and chaotic data without preselecting the phase-locking ratio. By embedding phase information of the synchrogram into phase space, the phase-locking ratio is automatically unveiled as the number of attractors.

Synchronization and anti-synchronization of a fractional order delayed memristor-based chaotic system using active control

NASA Astrophysics Data System (ADS)

Ding, Dawei; Qian, Xin; Wang, Nian; Liang, Dong

2018-05-01

In this paper, the issue of synchronization and anti-synchronization for fractional-delayed memristor-based chaotic system is studied by using active control strategy. Firstly, some explicit conditions are proposed to guarantee the synchronization and anti-synchronization of the proposed system. Secondly, the influence of order and time delay on the synchronization (anti-synchronization) is discussed. It reveals that synchronization (anti-synchronization) is faster as the order increases or the time delay decreases. Finally, some numerical simulations are presented to verify the validity of our theoretical analysis.

Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system

NASA Astrophysics Data System (ADS)

Huang, Chengdai; Cao, Jinde

2017-05-01

This paper is concerned with the issues of synchronization and anti-synchronization for fractional chaotic financial system with market confidence by taking advantage of active control approach. Some sufficient conditions are derived to guarantee the synchronization and anti-synchronization for the proposed fractional system. Moreover, the relationship between the order and synchronization(anti-synchronization) is demonstrated numerically. It reveals that synchronization(anti-synchronization) is faster as the order increases. Finally, two illustrative examples are exploited to verify the efficiency of the obtained theoretical results.

Regional business cycle synchronization through expectations

NASA Astrophysics Data System (ADS)

Onozaki, Tamotsu; Yanagita, Tatsuo; Kaizoji, Taisei; Toyabe, Kazutaka

2007-09-01

This paper provides an example in which regional business cycles may synchronize via producers’ expectations, even though there is no interregional trade, by means of a system of globally coupled, noninvertible maps. We concentrate on the dependence of the dynamics on a parameter η which denotes the inverse of price elasticity of demand. Simulation results show that several phases (the short transient, the complete asynchronous, the long transient and the intermediate transient) appear one after another as η increases. In the long transient phase, the intermittent clustering process with a long chaotic transient appears repeatedly.

Quantifying phase synchronization using instances of Hilbert phase slips

NASA Astrophysics Data System (ADS)

Govindan, R. B.

2018-07-01

We propose to quantify phase synchronization between two signals, x(t) and y(t), by calculating variance in the Hilbert phase of y(t) at instances of phase slips exhibited by x(t). The proposed approach is tested on numerically simulated coupled chaotic Roessler systems and second order autoregressive processes. Furthermore we compare the performance of the proposed and original approaches using uterine electromyogram signals and show that both approaches yield consistent results A standard phase synchronization approach, which involves unwrapping the Hilbert phases (ϕ1(t) and ϕ2(t)) of the two signals and analyzing the variance in the | n ṡϕ1(t) - m ṡϕ2(t) | , mod 2 π, (n and m are integers), was used for comparison. The synchronization indexes obtained from the proposed approach and the standard approach agree reasonably well in all of the systems studied in this work. Our results indicate that the proposed approach, unlike the traditional approach, does not require the non-invertible transformations - unwrapping of the phases and calculation of mod 2 π and it can be used to reliably to quantify phase synchrony between two signals.

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system.

PubMed

Wang, Rong; Gao, Jin-Yue

2005-09-01

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.

Compound synchronization of four memristor chaotic oscillator systems and secure communication.

PubMed

Sun, Junwei; Shen, Yi; Yin, Quan; Xu, Chengjie

2013-03-01

In this paper, a novel kind of compound synchronization among four chaotic systems is investigated, where the drive systems have been conceptually divided into two categories: scaling drive systems and base drive systems. Firstly, a sufficient condition is obtained to ensure compound synchronization among four memristor chaotic oscillator systems based on the adaptive technique. Secondly, a secure communication scheme via adaptive compound synchronization of four memristor chaotic oscillator systems is presented. The corresponding theoretical proofs and numerical simulations are given to demonstrate the validity and feasibility of the proposed control technique. The unpredictability of scaling drive systems can additionally enhance the security of communication. The transmitted signals can be split into several parts loaded in the drive systems to improve the reliability of communication.

Real-time multi-target ranging based on chaotic polarization laser radars in the drive-response VCSELs.

PubMed

Zhong, Dongzhou; Xu, Geliang; Luo, Wei; Xiao, Zhenzhen

2017-09-04

According to the principle of complete chaos synchronization and the theory of Hilbert phase transformation, we propose a novel real-time multi-target ranging scheme by using chaotic polarization laser radar in the drive-response vertical-cavity surface-emitting lasers (VCSELs). In the scheme, to ensure each polarization component (PC) of the master VCSEL (MVCSEL) to be synchronized steadily with that of the slave VCSEL, the output x-PC and y-PC from the MVCSEL in the drive system and those in the response system are modulated by the linear electro-optic effect simultaneously. Under this condition, by simulating the influences of some key parameters of the system on the synchronization quality and the relative errors of the two-target ranging, related operating parameters can be optimized. The x-PC and the y-PC, as two chaotic radar sources, are used to implement the real-time ranging for two targets. It is found that the measured distances of the two targets at arbitrary position exhibit strong real-time stability and only slight jitter. Their resolutions are up to millimeters, and their relative errors are very small and less than 2.7%.

Nonlinear optimal control for the synchronization of chaotic and hyperchaotic finance systems

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Loia, V.; Ademi, S.; Ghosh, T.

2017-11-01

It is possible to make specific finance systems get synchronized to other finance systems exhibiting chaotic and hyperchaotic dynamics, by applying nonlinear optimal (H-infinity) control. This signifies that chaotic behavior can be generated in finance systems by exerting a suitable control input. Actually, a lead financial system is considered which exhibits inherently chaotic dynamics. Moreover, a follower finance system is introduced having parameters in its model that inherently prohibit the appearance of chaotic dynamics. Through the application of a suitable nonlinear optimal (H-infinity) control input it is proven that the follower finance system can replicate the chaotic dynamics of the lead finance system. By applying Lyapunov analysis it is proven that asymptotically the follower finance system gets synchronized with the lead system and that the tracking error between the state variables of the two systems vanishes.

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method.

PubMed

Wang, Yu; Li, Feng-Ming; Wang, Yi-Ze

2015-06-01

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two buckling cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Yu; Wang, Yi-Ze; Li, Feng-Ming, E-mail: fmli@bjut.edu.cn

2015-06-15

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two bucklingmore » cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.« less

Trajectory-probed instability and statistics of desynchronization events in coupled chaotic systems

NASA Astrophysics Data System (ADS)

de Oliveira, Gilson F.; Chevrollier, Martine; Passerat de Silans, Thierry; Oriá, Marcos; de Souza Cavalcante, Hugo L. D.

2015-11-01

Complex systems, such as financial markets, earthquakes, and neurological networks, exhibit extreme events whose mechanisms of formation are not still completely understood. These mechanisms may be identified and better studied in simpler systems with dynamical features similar to the ones encountered in the complex system of interest. For instance, sudden and brief departures from the synchronized state observed in coupled chaotic systems were shown to display non-normal statistical distributions similar to events observed in the complex systems cited above. The current hypothesis accepted is that these desynchronization events are influenced by the presence of unstable object(s) in the phase space of the system. Here, we present further evidence that the occurrence of large events is triggered by the visitation of the system's phase-space trajectory to the vicinity of these unstable objects. In the system studied here, this visitation is controlled by a single parameter, and we exploit this feature to observe the effect of the visitation rate in the overall instability of the synchronized state. We find that the probability of escapes from the synchronized state and the size of those desynchronization events are enhanced in attractors whose shapes permit the chaotic trajectories to approach the region of strong instability. This result shows that the occurrence of large events requires not only a large local instability to amplify noise, or to amplify the effect of parameter mismatch between the coupled subsystems, but also that the trajectories of the system wander close to this local instability.

Analysis of Synchronization Phenomena in Broadband Signals with Nonlinear Excitable Media

NASA Astrophysics Data System (ADS)

Chernihovskyi, Anton; Elger, Christian E.; Lehnertz, Klaus

2009-12-01

We apply the method of frequency-selective excitation waves in excitable media to characterize synchronization phenomena in interacting complex dynamical systems by measuring coincidence rates of induced excitations. We relax the frequency-selectivity of excitable media and demonstrate two applications of the method to signals with broadband spectra. Findings obtained from analyzing time series of coupled chaotic oscillators as well as electroencephalographic (EEG) recordings from an epilepsy patient indicate that this method can provide an alternative and complementary way to estimate the degree of phase synchronization in noisy signals.

On adaptive modified projective synchronization of a supply chain management system

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2017-12-01

In this paper, the synchronization problem of a chaotic supply chain management system is studied. A novel adaptive modified projective synchronization method is introduced to control the behaviour of the leader supply chain system by a follower chaotic system and to adjust the leader system parameters until the measurable errors of the system parameters converge to zero. The stability evaluation and convergence analysis are carried out by the Lyapanov stability theorem. The proposed synchronization and antisynchronization techniques are studied for identical supply chain chaotic systems. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical discussions.

Exponential H(infinity) synchronization of general discrete-time chaotic neural networks with or without time delays.

PubMed

Qi, Donglian; Liu, Meiqin; Qiu, Meikang; Zhang, Senlin

2010-08-01

This brief studies exponential H(infinity) synchronization of a class of general discrete-time chaotic neural networks with external disturbance. On the basis of the drive-response concept and H(infinity) control theory, and using Lyapunov-Krasovskii (or Lyapunov) functional, state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays, but also reduce the effect of external disturbance on the synchronization error to a minimal H(infinity) norm constraint. The proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities. Most discrete-time chaotic systems with or without time delays, such as Hopfield neural networks, cellular neural networks, bidirectional associative memory networks, recurrent multilayer perceptrons, Cohen-Grossberg neural networks, Chua's circuits, etc., can be transformed into this general chaotic neural network to be H(infinity) synchronization controller designed in a unified way. Finally, some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods.

Correlations in electrically coupled chaotic lasers.

PubMed

Rosero, E J; Barbosa, W A S; Martinez Avila, J F; Khoury, A Z; Rios Leite, J R

2016-09-01

We show how two electrically coupled semiconductor lasers having optical feedback can present simultaneous antiphase correlated fast power fluctuations, and strong in-phase synchronized spikes of chaotic power drops. This quite counterintuitive phenomenon is demonstrated experimentally and confirmed by numerical solutions of a deterministic dynamical system of rate equations. The occurrence of negative and positive cross correlation between parts of a complex system according to time scales, as proved in our simple arrangement, is relevant for the understanding and characterization of collective properties in complex networks.

Generating Spatiotemporal Joint Torque Patterns from Dynamical Synchronization of Distributed Pattern Generators

PubMed Central

Pitti, Alexandre; Lungarella, Max; Kuniyoshi, Yasuo

2009-01-01

Pattern generators found in the spinal cord are no more seen as simple rhythmic oscillators for motion control. Indeed, they achieve flexible and dynamical coordination in interaction with the body and the environment dynamics giving to rise motor synergies. Discovering the mechanisms underlying the control of motor synergies constitutes an important research question not only for neuroscience but also for robotics: the motors coordination of high dimensional robotic systems is still a drawback and new control methods based on biological solutions may reduce their overall complexity. We propose to model the flexible combination of motor synergies in embodied systems via partial phase synchronization of distributed chaotic systems; for specific coupling strength, chaotic systems are able to phase synchronize their dynamics to the resonant frequencies of one external force. We take advantage of this property to explore and exploit the intrinsic dynamics of one specified embodied system. In two experiments with bipedal walkers, we show how motor synergies emerge when the controllers phase synchronize to the body's dynamics, entraining it to its intrinsic behavioral patterns. This stage is characterized by directed information flow from the sensors to the motors exhibiting the optimal situation when the body dynamics drive the controllers (mutual entrainment). Based on our results, we discuss the relevance of our findings for modeling the modular control of distributed pattern generators exhibited in the spinal cord, and for exploring the motor synergies in robots. PMID:20011216

Detecting unstable periodic orbits in chaotic time series using synchronization

NASA Astrophysics Data System (ADS)

Olyaei, Ali Azimi; Wu, Christine; Kinsner, Witold

2017-07-01

An alternative approach of detecting unstable periodic orbits in chaotic time series is proposed using synchronization techniques. A master-slave synchronization scheme is developed, in which the chaotic system drives a system of harmonic oscillators through a proper coupling condition. The proposed scheme is designed so that the power of the coupling signal exhibits notches that drop to zero once the system approaches an unstable orbit yielding an explicit indication of the presence of a periodic motion. The results shows that the proposed approach is particularly suitable in practical situations, where the time series is short and noisy, or it is obtained from high-dimensional chaotic systems.

Synchronizing noisy nonidentical oscillators by transient uncoupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tandon, Aditya, E-mail: adityat@iitk.ac.in; Mannattil, Manu, E-mail: mmanu@iitk.ac.in; Schröder, Malte, E-mail: malte@nld.ds.mpg.de

2016-09-15

Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them—a phenomenon termed “generalized synchronization.” Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the unitsmore » stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.« less

Amplitude-Phase Modulation, Topological Horseshoe and Scaling Attractor of a Dynamical System

NASA Astrophysics Data System (ADS)

Li, Chun-Lai; Li, Wen; Zhang, Jing; Xie, Yuan-Xi; Zhao, Yi-Bo

2016-09-01

A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincaré map, power spectrum, Kaplan-Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x3 can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key. Supported by Hunan Provincial Natural Science Foundation of China under Grant No. 2016JJ4036, University Natural Science Foundation of Jiangsu Province under Grant No. 14KJB120007 and the National Natural Science Foundation of China under Grant Nos. 11504176 and 11602084

Identical synchronization of chaotic secure communication systems with channel induced coherence resonance

NASA Astrophysics Data System (ADS)

Sepantaie, Marc M.; Namazi, Nader M.; Sepantaie, Amir M.

2016-05-01

This paper is devoted to addressing the synchronization, and detection of random binary data exposed to inherent channel variations existing in Free Space Optical (FSO) communication systems. This task is achieved by utilizing the identical synchronization methodology of Lorenz chaotic communication system, and its synergetic interaction in adversities imposed by the FSO channel. Moreover, the Lorenz system has been analyzed, and revealed to induce Stochastic Resonance (SR) once exposed to Additive White Gaussian Noise (AWGN). In particular, the resiliency of the Lorenz chaotic system, in light of channel adversities, has been attributed to the success of the proposed communication system. Furthermore, this paper advocates the use of Haar wavelet transform for enhanced detection capability of the proposed chaotic communication system, which utilizes Chaotic Parameter Modulation (CPM) technique for means of transmission.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

PubMed

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

NASA Astrophysics Data System (ADS)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Using chaotic forcing to detect damage in a structure

USGS Publications Warehouse

Moniz, L.; Nichols, J.; Trickey, S.; Seaver, M.; Pecora, D.; Pecora, L.

2005-01-01

In this work we develop a numerical test for Holder continuity and apply it and another test for continuity to the difficult problem of detecting damage in structures. We subject a thin metal plate with incremental damage to the plate changes, its filtering properties, and therefore the phase space trajectories of the response chaotic excitation of various bandwidths. Damage to the plate changes its filtering properties and therefore the phase space of the response. Because the data are multivariate (the plate is instrumented with multiple sensors) we use a singular value decomposition of the set of the output time series to reduce the embedding dimension of the response time series. We use two geometric tests to compare an attractor reconstructed from data from an undamaged structure to that reconstructed from data from a damaged structure. These two tests translate to testing for both generalized and differentiable synchronization between responses. We show loss of synchronization of responses with damage to the structure. ?? 2005 American Institute of Physics.

Using chaotic forcing to detect damage in a structure.

USGS Publications Warehouse

Moniz, L.; Nichols, J.; Trickey, S.; Seaver, M.; Pecora, D.; Pecora, L.

2005-01-01

In this work we develop a numerical test for Holder continuity and apply it and another test for continuity to the difficult problem of detecting damage in structures. We subject a thin metal plate with incremental damage to the plate changes, its filtering properties, and therefore the phase space trajectories of the response chaotic excitation of various bandwidths. Damage to the plate changes its filtering properties and therefore the phase space of the response. Because the data are multivariate (the plate is instrumented with multiple sensors) we use a singular value decomposition of the set of the output time series to reduce the embedding dimension of the response time series. We use two geometric tests to compare an attractor reconstructed from data from an undamaged structure to that reconstructed from data from a damaged structure. These two tests translate to testing for both generalized and differentiable synchronization between responses. We show loss of synchronization of responses with damage to the structure.

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.

Active synchronization between two different chaotic dynamical system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maheri, M.; Arifin, N. Md; Ismail, F.

2015-05-15

In this paper we investigate on the synchronization problem between two different chaotic dynamical system based on the Lyapunov stability theorem by using nonlinear control functions. Active control schemes are used for synchronization Liu system as drive and Rossler system as response. Numerical simulation by using Maple software are used to show effectiveness of the proposed schemes.

Design and implementation of EP-based PID controller for chaos synchronization of Rikitake circuit systems.

PubMed

Hou, Yi-You

2017-09-01

This article addresses an evolutionary programming (EP) algorithm technique-based and proportional-integral-derivative (PID) control methods are established to guarantee synchronization of the master and slave Rikitake chaotic systems. For PID synchronous control, the evolutionary programming (EP) algorithm is used to find the optimal PID controller parameters k p , k i , k d by integrated absolute error (IAE) method for the convergence conditions. In order to verify the system performance, the basic electronic components containing operational amplifiers (OPAs), resistors, and capacitors are used to implement the proposed chaotic Rikitake systems. Finally, the experimental results validate the proposed Rikitake chaotic synchronization approach. Copyright © 2017. Published by Elsevier Ltd.

Time-delayed chameleon: Analysis, synchronization and FPGA implementation

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Jafari, Sajad; Laarem, Guessas

2017-12-01

In this paper we report a time-delayed chameleon-like chaotic system which can belong to different families of chaotic attractors depending on the choices of parameters. Such a characteristic of self-excited and hidden chaotic flows in a simple 3D system with time delay has not been reported earlier. Dynamic analysis of the proposed time-delayed systems are analysed in time-delay space and parameter space. A novel adaptive modified functional projective lag synchronization algorithm is derived for synchronizing identical time-delayed chameleon systems with uncertain parameters. The proposed time-delayed systems and the synchronization algorithm with controllers and parameter estimates are then implemented in FPGA using hardware-software co-simulation and the results are presented.

Slower speed and stronger coupling: adaptive mechanisms of chaos synchronization.

PubMed

Wang, Xiao Fan

2002-06-01

We show that two initially weakly coupled chaotic systems can achieve synchronization by adaptively reducing their speed and/or enhancing the coupling strength. Explicit adaptive algorithms for speed reduction and coupling enhancement are provided. We apply these algorithms to the synchronization of two coupled Lorenz systems. It is found that after a long-time adaptive process, the two coupled chaotic systems can achieve synchronization with almost the minimum required coupling-speed ratio.

Function projective synchronization in chaotic and hyperchaotic systems through open-plus-closed-loop coupling.

PubMed

Sudheer, K Sebastian; Sabir, M

2010-03-01

Recently introduced function projective synchronization in which chaotic systems synchronize up to a scaling function has important applications in secure communications. We design coupling function for unidirectional coupling in identical and mismatched oscillators to realize function projective synchronization through open-plus-closed-loop coupling method. Numerical simulations on Lorenz system, Rossler system, hyperchaotic Lorenz, and hyperchaotic Chen system are presented to verify the effectiveness of the proposed scheme.

Application of cross recurrence plot for identification of temperature fluctuations synchronization in parallel minichannels

NASA Astrophysics Data System (ADS)

Grzybowski, H.; Mosdorf, R.

2016-09-01

The temperature fluctuations occurring in flow boiling in parallel minichannels with diameter of 1 mm have been experimentally investigated and analysed. The wall temperature was recorded at each minichannel outlet by thermocouple with 0.08 mm diameter probe. The time series where recorded during dynamic two-phase flow instabilities which are accompanied by chaotic temperature fluctuations. Time series were denoised using wavelet decomposition and were analysed using cross recurrence plots (CRP) which enables the study of two time series synchronization.

Proceedings of the 2nd Experimental Chaos Conference

NASA Astrophysics Data System (ADS)

Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep

1995-02-01

The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud

Synchronization of coupled different chaotic FitzHugh-Nagumo neurons with unknown parameters under communication-direction-dependent coupling.

PubMed

Iqbal, Muhammad; Rehan, Muhammad; Khaliq, Abdul; Saeed-ur-Rehman; Hong, Keum-Shik

2014-01-01

This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.

A new scheme of general hybrid projective complete dislocated synchronization

NASA Astrophysics Data System (ADS)

Chu, Yan-dong; Chang, Ying-Xiang; An, Xin-lei; Yu, Jian-Ning; Zhang, Jian-Gang

2011-03-01

Based on the Lyapunov stability theorem, a new type of chaos synchronization, general hybrid projective complete dislocated synchronization (GHPCDS), is proposed under the framework of drive-response systems. The difference between the GHPCDS and complete synchronization is that every state variable of drive system does not equal the corresponding state variable, but equal other ones of response system while evolving in time. The GHPCDS includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. As examples, the Lorenz chaotic system, Rössler chaotic system, hyperchaotic Chen system and hyperchaotic Lü system are discussed. Numerical simulations are given to show the effectiveness of these methods.

A New Finite-Time Observer for Nonlinear Systems: Applications to Synchronization of Lorenz-Like Systems.

PubMed

Aguilar-López, Ricardo; Mata-Machuca, Juan L

2016-01-01

This paper proposes a synchronization methodology of two chaotic oscillators under the framework of identical synchronization and master-slave configuration. The proposed methodology is based on state observer design under the frame of control theory; the observer structure provides finite-time synchronization convergence by cancelling the upper bounds of the main nonlinearities of the chaotic oscillator. The above is showed via an analysis of the dynamic of the so called synchronization error. Numerical experiments corroborate the satisfactory results of the proposed scheme.

A New Finite-Time Observer for Nonlinear Systems: Applications to Synchronization of Lorenz-Like Systems

PubMed Central

Aguilar-López, Ricardo

2016-01-01

This paper proposes a synchronization methodology of two chaotic oscillators under the framework of identical synchronization and master-slave configuration. The proposed methodology is based on state observer design under the frame of control theory; the observer structure provides finite-time synchronization convergence by cancelling the upper bounds of the main nonlinearities of the chaotic oscillator. The above is showed via an analysis of the dynamic of the so called synchronization error. Numerical experiments corroborate the satisfactory results of the proposed scheme. PMID:27738651

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br; Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de

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 fullmore » 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.« less

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it

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 andmore » 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.« less

Phase Synchronization and Desynchronization of Structural Response Induced by Turbulent and External Sound

NASA Technical Reports Server (NTRS)

Maestrello, Lucio

2002-01-01

Acoustic and turbulent boundary layer flow loadings over a flexible structure are used to study the spatial-temporal dynamics of the response of the structure. The stability of the spatial synchronization and desynchronization by an active external force is investigated with an array of coupled transducers on the structure. In the synchronous state, the structural phase is locked, which leads to the formation of spatial patterns while the amplitude peaks exhibit chaotic behaviors. Large amplitude, spatially symmetric loading is superimposed on broadband, but in the desynchronized state, the spectrum broadens and the phase space is lost. The resulting pattern bears a striking resemblance to phase turbulence. The transition is achieved by using a low power external actuator to trigger broadband behaviors from the knowledge of the external acoustic load inducing synchronization. The changes are made favorably and efficiently to alter the frequency distribution of power, not the total power level. Before synchronization effects are seen, the panel response to the turbulent boundary layer loading is discontinuously spatio-temporally correlated. The stability develops from different competing wavelengths; the spatial scale is significantly shorter than when forced with the superimposed external sound. When the external sound level decreases and the synchronized phases are lost, changes in the character of the spectra can be linked to the occurrence of spatial phase transition. These changes can develop broadband response. Synchronized responses of fuselage structure panels have been observed in subsonic and supersonic aircraft; results from two flights tests are discussed.

One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1 < q < 2

PubMed Central

Zhou, Ping; Bai, Rongji

2014-01-01

Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme. PMID:25247207

Synchronization between uncertain nonidentical networks with quantum chaotic behavior

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2016-11-01

Synchronization between uncertain nonidentical networks with quantum chaotic behavior is researched. The identification laws of unknown parameters in state equations of network nodes, the adaptive laws of configuration matrix elements and outer coupling strengths are determined based on Lyapunov theorem. The conditions of realizing synchronization between uncertain nonidentical networks are discussed and obtained. Further, Jaynes-Cummings model in physics are taken as the nodes of two networks and simulation results show that the synchronization performance between networks is very stable.

Synchronization of unidirectionally coupled Mackey-Glass analog circuits with frequency bandwidth limitations.

PubMed

Kim, Min-Young; Sramek, Christopher; Uchida, Atsushi; Roy, Rajarshi

2006-07-01

Synchronization of chaotic systems has been studied extensively, and especially, the possible applications to the communication systems motivated many research areas. We demonstrate the effect of the frequency bandwidth limitations in the communication channel on the synchronization of two unidirectionally coupled Mackey-Glass (MG) analog circuits, both numerically and experimentally. MG system is known to generate high dimensional chaotic signals. The chaotic signal generated from the drive MG system is modified by a low pass filter and is then transmitted to the response MG system. Our results show that the inclusion of the dominant frequency component of the original drive signals is crucial to achieve synchronization between the drive and response circuits. The maximum cross correlation and the corresponding time shift reveal that the frequency-dependent coupling introduced by the low pass filtering effect in the communication channel change the quality of synchronization.

Local synchronization of chaotic neural networks with sampled-data and saturating actuators.

PubMed

Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian

2014-12-01

This paper investigates the problem of local synchronization of chaotic neural networks with sampled-data and actuator saturation. A new time-dependent Lyapunov functional is proposed for the synchronization error systems. The advantage of the constructed Lyapunov functional lies in the fact that it is positive definite at sampling times but not necessarily between sampling times, and makes full use of the available information about the actual sampling pattern. A local stability condition of the synchronization error systems is derived, based on which a sampled-data controller with respect to the actuator saturation is designed to ensure that the master neural networks and slave neural networks are locally asymptotically synchronous. Two optimization problems are provided to compute the desired sampled-data controller with the aim of enlarging the set of admissible initial conditions or the admissible sampling upper bound ensuring the local synchronization of the considered chaotic neural networks. A numerical example is used to demonstrate the effectiveness of the proposed design technique.

Synchronization of mobile chaotic oscillator networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp; Kurths, Jürgen; Díaz-Guilera, Albert

We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to themore » transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.« less

Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback.

PubMed

Nazhan, Salam; Ghassemlooy, Zabih; Busawon, Krishna

2016-01-01

In this paper, the influence of the rotating polarization-preserved optical feedback on the chaos synchronization of a vertical-cavity surface-emitting laser (VCSEL) is investigated experimentally. Two VCSELs' polarization modes (XP) and (YP) are gradually rotated and re-injected back into the VCSEL. The anti-phase dynamics synchronization of the two polarization modes is evaluated using the cross-correlation function. For a fixed optical feedback, a clear relationship is found between the cross-correlation coefficient and the polarization angle θp. It is shown that high-quality anti-phase polarization-resolved chaos synchronization is achieved at higher values of θp. The maximum value of the cross-correlation coefficient achieved is -0.99 with a zero time delay over a wide range of θp beyond 65° with a poor synchronization dynamic at θp less than 65°. Furthermore, it is observed that the antiphase irregular oscillation of the XP and YP modes changes with θp. VCSEL under the rotating polarization optical feedback can be a good candidate as a chaotic synchronization source for a secure communication system.

Bluetooth based chaos synchronization using particle swarm optimization and its applications to image encryption.

PubMed

Yau, Her-Terng; Hung, Tzu-Hsiang; Hsieh, Chia-Chun

2012-01-01

This study used the complex dynamic characteristics of chaotic systems and Bluetooth to explore the topic of wireless chaotic communication secrecy and develop a communication security system. The PID controller for chaos synchronization control was applied, and the optimum parameters of this PID controller were obtained using a Particle Swarm Optimization (PSO) algorithm. Bluetooth was used to realize wireless transmissions, and a chaotic wireless communication security system was developed in the design concept of a chaotic communication security system. The experimental results show that this scheme can be used successfully in image encryption.

A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganography

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Akgul, A.; Kaçar, S.; Çavuşoğlu, U.

2018-02-01

Hyperjerk systems have received significant interest in the literature because of their simple structure and complex dynamical properties. This work presents a new chaotic hyperjerk system having two exponential nonlinearities. Dynamical properties of the chaotic hyperjerk system are discovered through equilibrium point analysis, bifurcation diagram, dissipativity and Lyapunov exponents. Moreover, an adaptive backstepping controller is designed for the synchronization of the chaotic hyperjerk system. Also, a real circuit of the chaotic hyperjerk system has been carried out to show the feasibility of the theoretical hyperjerk model. The chaotic hyperjerk system can also be useful in scientific fields such as Random Number Generators (RNGs), data security, data hiding, etc. In this work, three implementations of the chaotic hyperjerk system, viz. RNG, image encryption and sound steganography have been performed by using complex dynamics characteristics of the system.

Quantized Synchronization of Chaotic Neural Networks With Scheduled Output Feedback Control.

PubMed

Wan, Ying; Cao, Jinde; Wen, Guanghui

In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.

Multisynchronization of chaotic oscillators via nonlinear observer approach.

PubMed

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L

2014-01-01

The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.

Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach

PubMed Central

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L.

2014-01-01

The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology. PMID:24578671

Hybrid Chaos Synchronization of Four-Scroll Systems via Active Control

NASA Astrophysics Data System (ADS)

Karthikeyan, Rajagopal; Sundarapandian, Vaidyanathan

2014-03-01

This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

Multiobjective synchronization of coupled systems

NASA Astrophysics Data System (ADS)

Tang, Yang; Wang, Zidong; Wong, W. K.; Kurths, Jürgen; Fang, Jian-an

2011-06-01

In this paper, multiobjective synchronization of chaotic systems is investigated by especially simultaneously minimizing optimization of control cost and convergence speed. The coupling form and coupling strength are optimized by an improved multiobjective evolutionary approach that includes a hybrid chromosome representation. The hybrid encoding scheme combines binary representation with real number representation. The constraints on the coupling form are also considered by converting the multiobjective synchronization into a multiobjective constraint problem. In addition, the performances of the adaptive learning method and non-dominated sorting genetic algorithm-II as well as the effectiveness and contributions of the proposed approach are analyzed and validated through the Rössler system in a chaotic or hyperchaotic regime and delayed chaotic neural networks.

Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Wu, Wei; Cui, Bao-Tong

2007-07-01

In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

Pseudo-Random Number Generator Based on Coupled Map Lattices

NASA Astrophysics Data System (ADS)

Lü, Huaping; Wang, Shihong; Hu, Gang

A one-way coupled chaotic map lattice is used for generating pseudo-random numbers. It is shown that with suitable cooperative applications of both chaotic and conventional approaches, the output of the spatiotemporally chaotic system can easily meet the practical requirements of random numbers, i.e., excellent random statistical properties, long periodicity of computer realizations, and fast speed of random number generations. This pseudo-random number generator system can be used as ideal synchronous and self-synchronizing stream cipher systems for secure communications.

A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter

NASA Astrophysics Data System (ADS)

Kiani-B, Arman; Fallahi, Kia; Pariz, Naser; Leung, Henry

2009-03-01

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. In this paper, for the first time, a fractional chaotic communication method using an extended fractional Kalman filter is presented. The chaotic synchronization is implemented by the EFKF design in the presence of channel additive noise and processing noise. Encoding chaotic communication achieves a satisfactory, typical secure communication scheme. In the proposed system, security is enhanced based on spreading the signal in frequency and encrypting it in time domain. In this paper, the main advantages of using fractional order systems, increasing nonlinearity and spreading the power spectrum are highlighted. To illustrate the effectiveness of the proposed scheme, a numerical example based on the fractional Lorenz dynamical system is presented and the results are compared to the integer Lorenz system.

Explosive synchronization transitions in complex neural networks.

PubMed

Chen, Hanshuang; He, Gang; Huang, Feng; Shen, Chuansheng; Hou, Zhonghuai

2013-09-01

It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [Gómez-Gardeñes et al. Phys. Rev. Lett. 106, 128701 (2011)] and chaotic oscillators [Leyva et al. Phys. Rev. Lett. 108, 168702 (2012)]. Here, we investigate the effect of a microscopic correlation between the dynamics and the interacting topology of coupled FitzHugh-Nagumo oscillators on phase synchronization transition in Barabási-Albert (BA) scale-free networks and Erdös-Rényi (ER) random networks. We show that, if natural frequencies of the oscillations are positively correlated with node degrees and the width of the frequency distribution is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system. In contrast to the results in BA networks, in more homogeneous ER networks, the synchronization transition is always of continuous type regardless of the width of the frequency distribution. Moreover, we consider the effect of degree-mixing patterns on the nature of the synchronization transition, and find that the degree assortativity is unfavorable for the occurrence of such an explosive transition.

Explosive synchronization transitions in complex neural networks

NASA Astrophysics Data System (ADS)

Chen, Hanshuang; He, Gang; Huang, Feng; Shen, Chuansheng; Hou, Zhonghuai

2013-09-01

It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [Gómez-Gardeñes et al. Phys. Rev. Lett. 106, 128701 (2011)] and chaotic oscillators [Leyva et al. Phys. Rev. Lett. 108, 168702 (2012)]. Here, we investigate the effect of a microscopic correlation between the dynamics and the interacting topology of coupled FitzHugh-Nagumo oscillators on phase synchronization transition in Barabási-Albert (BA) scale-free networks and Erdös-Rényi (ER) random networks. We show that, if natural frequencies of the oscillations are positively correlated with node degrees and the width of the frequency distribution is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system. In contrast to the results in BA networks, in more homogeneous ER networks, the synchronization transition is always of continuous type regardless of the width of the frequency distribution. Moreover, we consider the effect of degree-mixing patterns on the nature of the synchronization transition, and find that the degree assortativity is unfavorable for the occurrence of such an explosive transition.

Synchronization in counter-rotating oscillators.

PubMed

Bhowmick, Sourav K; Ghosh, Dibakar; Dana, Syamal K

2011-09-01

An oscillatory system can have opposite senses of rotation, clockwise or anticlockwise. We present a general mathematical description of how to obtain counter-rotating oscillators from the definition of a dynamical system. A type of mixed synchronization emerges in counter-rotating oscillators under diffusive scalar coupling when complete synchronization and antisynchronization coexist in different state variables. We present numerical examples of limit cycle van der Pol oscillator and chaotic Rössler and Lorenz systems. Stability conditions of mixed synchronization are analytically obtained for both Rössler and Lorenz systems. Experimental evidences of counter-rotating limit cycle and chaotic oscillators and mixed synchronization are given in electronic circuits.

Comment on "Synchronization of chaotic systems with delay using intermittent linear state feedback" [Chaos 18, 033122 (2008)].

PubMed

Zhang, Yinping; Wang, Qing-Guo

2008-12-01

In the referenced paper, there is technical carelessness in the third lemma and in the main result. Hence, it is a possible failure when the result is used to design the intermittent linear state feedback controller for exponential synchronization of two chaotic delayed systems.

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

NASA Astrophysics Data System (ADS)

Ouannas, Adel; Grassi, Giuseppe

2016-09-01

A new synchronization scheme for chaotic (hyperchaotic) maps with different dimensions is presented. Specifically, given a drive system map with dimension n and a response system with dimension m, the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states. The method, based on the Lyapunov stability theory and the pole placement technique, presents some useful features: (i) it enables synchronization to be achieved for both cases of n < m and n > m; (ii) it is rigorous, being based on theorems; (iii) it can be readily applied to any chaotic (hyperchaotic) maps defined to date. Finally, the capability of the approach is illustrated by synchronization examples between the two-dimensional Hénon map (as the drive system) and the three-dimensional hyperchaotic Wang map (as the response system), and the three-dimensional Hénon-like map (as the drive system) and the two-dimensional Lorenz discrete-time system (as the response system).

Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

PubMed

Liu, Meiqin

2009-09-01

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography.

PubMed

Kanter, Ido; Butkovski, Maria; Peleg, Yitzhak; Zigzag, Meital; Aviad, Yaara; Reidler, Igor; Rosenbluh, Michael; Kinzel, Wolfgang

2010-08-16

Random bit generators (RBGs) constitute an important tool in cryptography, stochastic simulations and secure communications. The later in particular has some difficult requirements: high generation rate of unpredictable bit strings and secure key-exchange protocols over public channels. Deterministic algorithms generate pseudo-random number sequences at high rates, however, their unpredictability is limited by the very nature of their deterministic origin. Recently, physical RBGs based on chaotic semiconductor lasers were shown to exceed Gbit/s rates. Whether secure synchronization of two high rate physical RBGs is possible remains an open question. Here we propose a method, whereby two fast RBGs based on mutually coupled chaotic lasers, are synchronized. Using information theoretic analysis we demonstrate security against a powerful computational eavesdropper, capable of noiseless amplification, where all parameters are publicly known. The method is also extended to secure synchronization of a small network of three RBGs.

Desynchronization in an ensemble of globally coupled chaotic bursting neuronal oscillators by dynamic delayed feedback control

NASA Astrophysics Data System (ADS)

Che, Yanqiu; Yang, Tingting; Li, Ruixue; Li, Huiyan; Han, Chunxiao; Wang, Jiang; Wei, Xile

2015-09-01

In this paper, we propose a dynamic delayed feedback control approach or desynchronization of chaotic-bursting synchronous activities in an ensemble of globally coupled neuronal oscillators. We demonstrate that the difference signal between an ensemble's mean field and its time delayed state, filtered and fed back to the ensemble, can suppress the self-synchronization in the ensemble. These individual units are decoupled and stabilized at the desired desynchronized states while the stimulation signal reduces to the noise level. The effectiveness of the method is illustrated by examples of two different populations of globally coupled chaotic-bursting neurons. The proposed method has potential for mild, effective and demand-controlled therapy of neurological diseases characterized by pathological synchronization.

Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nazhan, Salam; Ghassemlooy, Zabih; Busawon, Krishna

2016-01-15

In this paper, the influence of the rotating polarization-preserved optical feedback on the chaos synchronization of a vertical-cavity surface-emitting laser (VCSEL) is investigated experimentally. Two VCSELs' polarization modes (XP) and (YP) are gradually rotated and re-injected back into the VCSEL. The anti-phase dynamics synchronization of the two polarization modes is evaluated using the cross-correlation function. For a fixed optical feedback, a clear relationship is found between the cross-correlation coefficient and the polarization angle θ{sub p}. It is shown that high-quality anti-phase polarization-resolved chaos synchronization is achieved at higher values of θ{sub p}. The maximum value of the cross-correlation coefficient achievedmore » is −0.99 with a zero time delay over a wide range of θ{sub p} beyond 65° with a poor synchronization dynamic at θ{sub p} less than 65°. Furthermore, it is observed that the antiphase irregular oscillation of the XP and YP modes changes with θ{sub p}. VCSEL under the rotating polarization optical feedback can be a good candidate as a chaotic synchronization source for a secure communication system.« less

Mixed coherent states in coupled chaotic systems: Design of secure wireless communication

NASA Astrophysics Data System (ADS)

Vigneshwaran, M.; Dana, S. K.; Padmanaban, E.

2016-12-01

A general coupling design is proposed to realize a mixed coherent (MC) state: coexistence of complete synchronization, antisynchronization, and amplitude death in different pairs of similar state variables of the coupled chaotic system. The stability of coupled system is ensured by the Lyapunov function and a scaling of each variable is also separately taken care of. When heterogeneity as a parameter mismatch is introduced in the coupled system, the coupling function facilitates to retain its coherence and displays the global stability with renewed scaling factor. Robust synchronization features facilitated by a MC state enable to design a dual modulation scheme: binary phase shift key (BPSK) and parameter mismatch shift key (PMSK), for secure data transmission. Two classes of decoders (coherent and noncoherent) are discussed, the noncoherent decoder shows better performance over the coherent decoder, mostly a noncoherent demodulator is preferred in biological implant applications. Both the modulation schemes are demonstrated numerically by using the Lorenz oscillator and the BPSK scheme is demonstrated experimentally using radio signals.

Complete synchronization of uncertain chaotic systems via a single proportional adaptive controller: A comparative study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahmad, Israr, E-mail: iak-2000plus@yahoo.com; Saaban, Azizan Bin, E-mail: azizan.s@uum.edu.my; Ibrahim, Adyda Binti, E-mail: adyda@uum.edu.my

This paper addresses a comparative computational study on the synchronization quality, cost and converging speed for two pairs of identical chaotic and hyperchaotic systems with unknown time-varying parameters. It is assumed that the unknown time-varying parameters are bounded. Based on the Lyapunov stability theory and using the adaptive control method, a single proportional controller is proposed to achieve the goal of complete synchronizations. Accordingly, appropriate adaptive laws are designed to identify the unknown time-varying parameters. The designed control strategy is easy to implement in practice. Numerical simulations results are provided to verify the effectiveness of the proposed synchronization scheme.

On chaos synchronization and secure communication.

PubMed

Kinzel, W; Englert, A; Kanter, I

2010-01-28

Chaos synchronization, in particular isochronal synchronization of two chaotic trajectories to each other, may be used to build a means of secure communication over a public channel. In this paper, we give an overview of coupling schemes of Bernoulli units deduced from chaotic laser systems, different ways to transmit information by chaos synchronization and the advantage of bidirectional over unidirectional coupling with respect to secure communication. We present the protocol for using dynamical private commutative filters for tap-proof transmission of information that maps the task of a passive attacker to the class of non-deterministic polynomial time-complete problems. This journal is © 2010 The Royal Society

Long-distance multi-channel bidirectional chaos communication based on synchronized VCSELs subject to chaotic signal injection

NASA Astrophysics Data System (ADS)

Xie, Yi-Yuan; Li, Jia-Chao; He, Chao; Zhang, Zhen-Dong; Song, Ting-Ting; Xu, Chang-Jun; Wang, Gui-Jin

2016-10-01

A novel long-distance multi-channel bidirectional chaos communication system over multiple paths based on two synchronized 1550 nm vertical-cavity surface-emitting lasers (VCSELs) is proposed and studied theoretically. These two responding VCSELs (R-VCSELs) can output similar chaotic signals served as chaotic carrier in two linear polarization (LP) modes with identical signal injection from a driving VCSEL (D-VCSEL), which is subject to optical feedback and optical injection, simultaneously. Through the numerical simulations, high quality chaos synchronization between the two R-VCSELs can be obtained. Besides, the effects of varied qualities of chaos synchronization on communication performances in 20 km single mode fiber (SMF) channels are investigated by regulating different internal parameters mismatch after adopting chaos masking (CMS) technique. With the decrease of the maximum cross correlation coefficient (Max-C) between the two R-VCSELs, the bit error rate (BER) of decoded message increase. Meanwhile, the BER can still be less than 10-9 when the Max-C degrades to 0.982. Based on high quality synchronization, when the dispersion compensating fiber (DCF) links are introduced, 4n messages of 10 Gbit/s can transmit in 180 km SMF channels over n coupling paths, bidirectionally and simultaneously. Thorough tests are carried out with detailed analysis, demonstrating long-distance, multi-channel, bidirectional chaos communication based on VCSELs with chaotic signal injection.

Robust synchronization of master-slave chaotic systems using approximate model: An experimental study.

PubMed

Ahmed, Hafiz; Salgado, Ivan; Ríos, Héctor

2018-02-01

Robust synchronization of master slave chaotic systems are considered in this work. First an approximate model of the error system is obtained using the ultra-local model concept. Then a Continuous Singular Terminal Sliding-Mode (CSTSM) Controller is designed for the purpose of synchronization. The proposed approach is output feedback-based and uses fixed-time higher order sliding-mode (HOSM) differentiator for state estimation. Numerical simulation and experimental results are given to show the effectiveness of the proposed technique. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Chaotic carrier pulse position modulation communication system and method

DOEpatents

Abarbanel, Henry D. I.; Larson, Lawrence E.; Rulkov, Nikolai F.; Sushchik, Mikhail M.; Tsimring, Lev S.; Volkovskii, Alexander R.

2001-01-01

A chaotic carrier pulse position modulation communication system and method is disclosed. The system includes a transmitter and receiver having matched chaotic pulse regenerators. The chaotic pulse regenerator in the receiver produces a synchronized replica of a chaotic pulse train generated by the regenerator in the transmitter. The pulse train from the transmitter can therefore act as a carrier signal. Data is encoded by the transmitter through selectively altering the interpulse timing between pulses in the chaotic pulse train. The altered pulse train is transmitted as a pulse signal. The receiver can detect whether a particular interpulse interval in the pulse signal has been altered by reference to the synchronized replica it generates, and can therefore detect the data transmitted by the receiver. Preferably, the receiver predicts the earliest moment in time it can expect a next pulse after observation of at least two consecutive pulses. It then decodes the pulse signal beginning at a short time before expected arrival of a pulse.

Synchronization of an Inertial Neural Network With Time-Varying Delays and Its Application to Secure Communication.

PubMed

Lakshmanan, Shanmugam; Prakash, Mani; Lim, Chee Peng; Rakkiyappan, Rajan; Balasubramaniam, Pagavathigounder; Nahavandi, Saeid

2018-01-01

In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

Chaos synchronization in networks of semiconductor superlattices

NASA Astrophysics Data System (ADS)

Li, Wen; Aviad, Yaara; Reidler, Igor; Song, Helun; Huang, Yuyang; Biermann, Klaus; Rosenbluh, Michael; Zhang, Yaohui; Grahn, Holger T.; Kanter, Ido

2015-11-01

Chaos synchronization has been demonstrated as a useful building block for various tasks in secure communications, including a source of all-electronic ultrafast physical random number generators based on room temperature spontaneous chaotic oscillations in a DC-biased weakly coupled GaAs/Al0.45Ga0.55As semiconductor superlattice (SSL). Here, we experimentally demonstrate the emergence of several types of chaos synchronization, e.g. leader-laggard, face-to-face and zero-lag synchronization in network motifs of coupled SSLs consisting of unidirectional and mutual coupling as well as self-feedback coupling. Each type of synchronization clearly reflects the symmetry of the topology of its network motif. The emergence of a chaotic SSL without external feedback and synchronization among different structured SSLs open up the possibility for advanced secure multi-user communication methods based on large networks of coupled SSLs.

Neuronal synchrony: Peculiarity and generality

PubMed Central

Nowotny, Thomas; Huerta, Ramon; Rabinovich, Mikhail I.

2008-01-01

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale). PMID:19045493

Hopf bifurcation and chaos in a third-order phase-locked loop

NASA Astrophysics Data System (ADS)

Piqueira, José Roberto C.

2017-01-01

Phase-locked loops (PLLs) are devices able to recover time signals in several engineering applications. The literature regarding their dynamical behavior is vast, specifically considering that the process of synchronization between the input signal, coming from a remote source, and the PLL local oscillation is robust. For high-frequency applications it is usual to increase the PLL order by increasing the order of the internal filter, for guarantying good transient responses; however local parameter variations imply structural instability, thus provoking a Hopf bifurcation and a route to chaos for the phase error. Here, one usual architecture for a third-order PLL is studied and a range of permitted parameters is derived, providing a rule of thumb for designers. Out of this range, a Hopf bifurcation appears and, by increasing parameters, the periodic solution originated by the Hopf bifurcation degenerates into a chaotic attractor, therefore, preventing synchronization.

Model-free adaptive sliding mode controller design for generalized projective synchronization of the fractional-order chaotic system via radial basis function neural networks

NASA Astrophysics Data System (ADS)

Wang, L. M.

2017-09-01

A novel model-free adaptive sliding mode strategy is proposed for a generalized projective synchronization (GPS) between two entirely unknown fractional-order chaotic systems subject to the external disturbances. To solve the difficulties from the little knowledge about the master-slave system and to overcome the bad effects of the external disturbances on the generalized projective synchronization, the radial basis function neural networks are used to approach the packaged unknown master system and the packaged unknown slave system (including the external disturbances). Consequently, based on the slide mode technology and the neural network theory, a model-free adaptive sliding mode controller is designed to guarantee asymptotic stability of the generalized projective synchronization error. The main contribution of this paper is that a control strategy is provided for the generalized projective synchronization between two entirely unknown fractional-order chaotic systems subject to the unknown external disturbances, and the proposed control strategy only requires that the master system has the same fractional orders as the slave system. Moreover, the proposed method allows us to achieve all kinds of generalized projective chaos synchronizations by turning the user-defined parameters onto the desired values. Simulation results show the effectiveness of the proposed method and the robustness of the controlled system.

A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Castro-Ramírez, Joel, E-mail: ingcastro.7@gmail.com; Martínez-Guerra, Rafael, E-mail: rguerra@ctrl.cinvestav.mx; Cruz-Victoria, Juan Crescenciano, E-mail: juancrescenciano.cruz@uptlax.edu.mx

2015-10-15

This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system.

Multiswitching compound antisynchronization of four chaotic systems

NASA Astrophysics Data System (ADS)

Khan, Ayub; Khattar, Dinesh; Prajapati, Nitish

2017-12-01

Based on three drive-one response system, in this article, the authors investigate a novel synchronization scheme for a class of chaotic systems. The new scheme, multiswitching compound antisynchronization (MSCoAS), is a notable extension of the earlier multiswitching schemes concerning only one drive-one response system model. The concept of multiswitching synchronization is extended to compound synchronization scheme such that the state variables of three drive systems antisynchronize with different state variables of the response system, simultaneously. The study involving multiswitching of three drive systems and one response system is first of its kind. Various switched modified function projective antisynchronization schemes are obtained as special cases of MSCoAS, for a suitable choice of scaling factors. Using suitable controllers and Lyapunov stability theory, sufficient condition is obtained to achieve MSCoAS between four chaotic systems and the corresponding theoretical proof is given. Numerical simulations are performed using Lorenz system in MATLAB to demonstrate the validity of the presented method.

Phase synchronization of instrumental music signals

NASA Astrophysics Data System (ADS)

Mukherjee, Sayan; Palit, Sanjay Kumar; Banerjee, Santo; Ariffin, M. R. K.; Bhattacharya, D. K.

2014-06-01

Signal analysis is one of the finest scientific techniques in communication theory. Some quantitative and qualitative measures describe the pattern of a music signal, vary from one to another. Same musical recital, when played by different instrumentalists, generates different types of music patterns. The reason behind various patterns is the psycho-acoustic measures - Dynamics, Timber, Tonality and Rhythm, varies in each time. However, the psycho-acoustic study of the music signals does not reveal any idea about the similarity between the signals. For such cases, study of synchronization of long-term nonlinear dynamics may provide effective results. In this context, phase synchronization (PS) is one of the measures to show synchronization between two non-identical signals. In fact, it is very critical to investigate any other kind of synchronization for experimental condition, because those are completely non identical signals. Also, there exists equivalence between the phases and the distances of the diagonal line in Recurrence plot (RP) of the signals, which is quantifiable by the recurrence quantification measure τ-recurrence rate. This paper considers two nonlinear music signals based on same raga played by two eminent sitar instrumentalists as two non-identical sources. The psycho-acoustic study shows how the Dynamics, Timber, Tonality and Rhythm vary for the two music signals. Then, long term analysis in the form of phase space reconstruction is performed, which reveals the chaotic phase spaces for both the signals. From the RP of both the phase spaces, τ-recurrence rate is calculated. Finally by the correlation of normalized tau-recurrence rate of their 3D phase spaces and the PS of the two music signals has been established. The numerical results well support the analysis.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Shi-bing, E-mail: wang-shibing@dlut.edu.cn, E-mail: wangxy@dlut.edu.cn; Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024; Wang, Xing-yuan, E-mail: wang-shibing@dlut.edu.cn, E-mail: wangxy@dlut.edu.cn

With comprehensive consideration of generalized synchronization, combination synchronization and adaptive control, this paper investigates a novel adaptive generalized combination complex synchronization (AGCCS) scheme for different real and complex nonlinear systems with unknown parameters. On the basis of Lyapunov stability theory and adaptive control, an AGCCS controller and parameter update laws are derived to achieve synchronization and parameter identification of two real drive systems and a complex response system, as well as two complex drive systems and a real response system. Two simulation examples, namely, ACGCS for chaotic real Lorenz and Chen systems driving a hyperchaotic complex Lü system, and hyperchaoticmore » complex Lorenz and Chen systems driving a real chaotic Lü system, are presented to verify the feasibility and effectiveness of the proposed scheme.« less

Modelling of long-wave chaotic radar system for anti-stealth applications

NASA Astrophysics Data System (ADS)

Al-Suhail, Ghaida A.; Tahir, Fadhil Rahma; Abd, Mariam Hussien; Pham, Viet-Thanh; Fortuna, Luigi

2018-04-01

Although the Very Low-Frequency (VLF) waveforms have limited practical applications in acoustics (sonar) and secure military communications with radars and submarines; to this end; this paper presents a new and simple analytical model of VLF monostatic direct chaotic radar system. The model hypothetically depends on the two identical coupled time-delayed feedback chaotic systems which can generate and recover a long-wave chaotic signal. To resist the influence of positive Lyapunov exponents of the time-delay chaotic systems, the complete replacement of Pecaro and Carroll (PC) synchronization is employed. It can faithfully recover the chaotic signal from the back-scattered (echo) signal from the target over a noisy channel. The system performance is characterized in terms of the time series of synchronization in addition to the peak of the cross-correlation. Simulation results are conducted for substantial sensitivities of the chaotic signal to the system parameters and initial conditions. As a result, it is found that an effective and robust chaotic radar (CRADAR) model can be obtained when the signal-to-noise ratio (SNR) highly degrades to 0 dB, but with clear peak in correlation performance for detecting the target. Then, the model can be considered as a state of the art towards counter stealth technology and might be developed for other acoustic secure applications.

Ergodic properties of spiking neuronal networks with delayed interactions

NASA Astrophysics Data System (ADS)

Palmigiano, Agostina; Wolf, Fred

The dynamical stability of neuronal networks, and the possibility of chaotic dynamics in the brain pose profound questions to the mechanisms underlying perception. Here we advance on the tractability of large neuronal networks of exactly solvable neuronal models with delayed pulse-coupled interactions. Pulse coupled delayed systems with an infinite dimensional phase space can be studied in equivalent systems of fixed and finite degrees of freedom by introducing a delayer variable for each neuron. A Jacobian of the equivalent system can be analytically obtained, and numerically evaluated. We find that depending on the action potential onset rapidness and the level of heterogeneities, the asynchronous irregular regime characteristic of balanced state networks loses stability with increasing delays to either a slow synchronous irregular or a fast synchronous irregular state. In networks of neurons with slow action potential onset, the transition to collective oscillations leads to an increase of the exponential rate of divergence of nearby trajectories and of the entropy production rate of the chaotic dynamics. The attractor dimension, instead of increasing linearly with increasing delay as reported in many other studies, decreases until eventually the network reaches full synchrony

Local instability driving extreme events in a pair of coupled chaotic electronic circuits

NASA Astrophysics Data System (ADS)

de Oliveira, Gilson F.; Di Lorenzo, Orlando; de Silans, Thierry Passerat; Chevrollier, Martine; Oriá, Marcos; Cavalcante, Hugo L. D. de Souza

2016-06-01

For a long time, extreme events happening in complex systems, such as financial markets, earthquakes, and neurological networks, were thought to follow power-law size distributions. More recently, evidence suggests that in many systems the largest and rarest events differ from the other ones. They are dragon kings, outliers that make the distribution deviate from a power law in the tail. Understanding the processes of formation of extreme events and what circumstances lead to dragon kings or to a power-law distribution is an open question and it is a very important one to assess whether extreme events will occur too often in a specific system. In the particular system studied in this paper, we show that the rate of occurrence of dragon kings is controlled by the value of a parameter. The system under study here is composed of two nearly identical chaotic oscillators which fail to remain in a permanently synchronized state when coupled. We analyze the statistics of the desynchronization events in this specific example of two coupled chaotic electronic circuits and find that modifying a parameter associated to the local instability responsible for the loss of synchronization reduces the occurrence of dragon kings, while preserving the power-law distribution of small- to intermediate-size events with the same scaling exponent. Our results support the hypothesis that the dragon kings are caused by local instabilities in the phase space.

Quantum synchronization of chaotic oscillator behaviors among coupled BEC-optomechanical systems

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2017-03-01

We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.

Sound synchronization of bubble trains in a viscous fluid: experiment and modeling.

PubMed

Pereira, Felipe Augusto Cardoso; Baptista, Murilo da Silva; Sartorelli, José Carlos

2014-10-01

We investigate the dynamics of formation of air bubbles expelled from a nozzle immersed in a viscous fluid under the influence of sound waves. We have obtained bifurcation diagrams by measuring the time between successive bubbles, having the air flow (Q) as a parameter control for many values of the sound wave amplitude (A), the height (H) of the solution above the top of the nozzle, and three values of the sound frequency (fs). Our parameter spaces (Q,A) revealed a scenario for the onset of synchronization dominated by Arnold tongues (frequency locking) which gives place to chaotic phase synchronization for sufficiently large A. The experimental results were accurately reproduced by numerical simulations of a model combining a simple bubble growth model for the bubble train and a coupling term with the sound wave added to the equilibrium pressure.

Insensitivity of synchronization to network structure in chaotic pendulum systems with time-delay coupling.

PubMed

Yao, Chenggui; Zhan, Meng; Shuai, Jianwei; Ma, Jun; Kurths, Jürgen

2017-12-01

It has been generally believed that both time delay and network structure could play a crucial role in determining collective dynamical behaviors in complex systems. In this work, we study the influence of coupling strength, time delay, and network topology on synchronization behavior in delay-coupled networks of chaotic pendulums. Interestingly, we find that the threshold value of the coupling strength for complete synchronization in such networks strongly depends on the time delay in the coupling, but appears to be insensitive to the network structure. This lack of sensitivity was numerically tested in several typical regular networks, such as different locally and globally coupled ones as well as in several complex networks, such as small-world and scale-free networks. Furthermore, we find that the emergence of a synchronous periodic state induced by time delay is of key importance for the complete synchronization.

Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography.

PubMed

Kingni, Sifeu Takougang; Mbé, Jimmi Hervé Talla; Woafo, Paul

2012-09-01

In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.

Experimental study of firing death in a network of chaotic FitzHugh-Nagumo neurons

NASA Astrophysics Data System (ADS)

Ciszak, Marzena; Euzzor, Stefano; Arecchi, F. Tito; Meucci, Riccardo

2013-02-01

The FitzHugh-Nagumo neurons driven by a periodic forcing undergo a period-doubling route to chaos and a transition to mixed-mode oscillations. When coupled, their dynamics tend to be synchronized. We show that the chaotically spiking neurons change their internal dynamics to subthreshold oscillations, the phenomenon referred to as firing death. These dynamical changes are observed below the critical coupling strength at which the transition to full chaotic synchronization occurs. Moreover, we find various dynamical regimes in the subthreshold oscillations, namely, regular, quasiperiodic, and chaotic states. We show numerically that these dynamical states may coexist with large-amplitude spiking regimes and that this coexistence is characterized by riddled basins of attraction. The reported results are obtained for neurons implemented in the electronic circuits as well as for the model equations. Finally, we comment on the possible scenarios where the coupling-induced firing death could play an important role in biological systems.

Chimeras and clusters in networks of hyperbolic chaotic oscillators

NASA Astrophysics Data System (ADS)

Cano, A. V.; Cosenza, M. G.

2017-03-01

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.

Hardware implementation of Lorenz circuit systems for secure chaotic communication applications.

PubMed

Chen, Hsin-Chieh; Liau, Ben-Yi; Hou, Yi-You

2013-02-18

This paper presents the synchronization between the master and slave Lorenz chaotic systems by slide mode controller (SMC)-based technique. A proportional-integral (PI) switching surface is proposed to simplify the task of assigning the performance of the closed-loop error system in sliding mode. Then, extending the concept of equivalent control and using some basic electronic components, a secure communication system is constructed. Experimental results show the feasibility of synchronizing two Lorenz circuits via the proposed SMC. 

Coupled chaotic fluctuations in a model of international trade and innovation: Some preliminary results

NASA Astrophysics Data System (ADS)

Sushko, Iryna; Gardini, Laura; Matsuyama, Kiminori

2018-05-01

We consider a two-dimensional continuous noninvertible piecewise smooth map, which characterizes the dynamics of innovation activities in the two-country model of trade and product innovation proposed in [7]. This two-dimensional map can be viewed as a coupling of two one-dimensional skew tent maps, each of which characterizes the innovation dynamics in each country in the absence of trade, and the coupling parameter depends inversely on the trade cost between the two countries. Hence, this model offers a laboratory for studying how a decline in the trade cost, or globalization, might synchronize endogenous fluctuations of innovation activities in the two countries. In this paper, we focus on the bifurcation scenarios, how the phase portrait of the two-dimensional map changes with a gradual decline of the trade cost, leading to border collision, merging, expansion and final bifurcations of the coexisting chaotic attractors. An example of peculiar border collision bifurcation leading to an increase of dimension of the chaotic attractor is also presented.

On common noise-induced synchronization in complex networks with state-dependent noise diffusion processes

NASA Astrophysics Data System (ADS)

Russo, Giovanni; Shorten, Robert

2018-04-01

This paper is concerned with the study of common noise-induced synchronization phenomena in complex networks of diffusively coupled nonlinear systems. We consider the case where common noise propagation depends on the network state and, as a result, the noise diffusion process at the nodes depends on the state of the network. For such networks, we present an algebraic sufficient condition for the onset of synchronization, which depends on the network topology, the dynamics at the nodes, the coupling strength and the noise diffusion. Our result explicitly shows that certain noise diffusion processes can drive an unsynchronized network towards synchronization. In order to illustrate the effectiveness of our result, we consider two applications: collective decision processes and synchronization of chaotic systems. We explicitly show that, in the former application, a sufficiently large noise can drive a population towards a common decision, while, in the latter, we show how common noise can synchronize a network of Lorentz chaotic systems.

Huygens’ clocks revisited

PubMed Central

Kitanov, Petko M.; Langford, William F.

2017-01-01

In 1665, Huygens observed that two identical pendulum clocks, weakly coupled through a heavy beam, soon synchronized with the same period and amplitude but with the two pendula swinging in opposite directions. This behaviour is now called anti-phase synchronization. This paper presents an analysis of the behaviour of a large class of coupled identical oscillators, including Huygens' clocks, using methods of equivariant bifurcation theory. The equivariant normal form for such systems is developed and the possible solutions are characterized. The transformation of the physical system parameters to the normal form parameters is given explicitly and applied to the physical values appropriate for Huygens' clocks, and to those of more recent studies. It is shown that Huygens' physical system could only exhibit anti-phase motion, explaining why Huygens observed exclusively this. By contrast, some more recent researchers have observed in-phase or other more complicated motion in their own experimental systems. Here, it is explained which physical characteristics of these systems allow for the existence of these other types of stable solutions. The present analysis not only accounts for these previously observed solutions in a unified framework, but also introduces behaviour not classified by other authors, such as a synchronized toroidal breather and a chaotic toroidal breather. PMID:28989780

Simultaneous trilateral communication based on three mutually coupled chaotic semiconductor lasers with optical feedback.

PubMed

Li, Qiliang; Lu, Shanshan; Bao, Qi; Chen, Dewang; Hu, Miao; Zeng, Ran; Yang, Guowei; Li, Shuqin

2018-01-10

In this paper, we propose a chaos-based scheme allowing for trilateral communication among three mutually coupled chaotic semiconductor lasers. The coupling through a partially transparent optical mirror between two lasers induces the chaotic dynamics. We numerically solve the delay rate equations of three lasers and demonstrate that the dynamics is completely synchronous. Herein, each laser is not only a transmitter but a receiver; three different messages are encoded by simultaneously modulating bias current of the three lasers. By monitoring the synchronization error between transmitter and receiver, and comparing the error with the message of the local laser, we can decipher the message of the sender. The investigation indicates that these messages introduced on the two ends of each link among three lasers can be simultaneously transmitted and restored, so the system can realize simultaneous trilateral communication. In this scheme, an eavesdropper can monitor the synchronization error, but one has no way to obtain the bits that are being sent, so the trilateral communication is secure.

Asynchronous error-correcting secure communication scheme based on fractional-order shifting chaotic system

NASA Astrophysics Data System (ADS)

Chao, Luo

2015-11-01

In this paper, a novel digital secure communication scheme is firstly proposed. Different from the usual secure communication schemes based on chaotic synchronization, the proposed scheme employs asynchronous communication which avoids the weakness of synchronous systems and is susceptible to environmental interference. Moreover, as to the transmission errors and data loss in the process of communication, the proposed scheme has the ability to be error-checking and error-correcting in real time. In order to guarantee security, the fractional-order complex chaotic system with the shifting of order is utilized to modulate the transmitted signal, which has high nonlinearity and complexity in both frequency and time domains. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the scheme.

Emergence of chimeras through induced multistability

NASA Astrophysics Data System (ADS)

Ujjwal, Sangeeta Rani; Punetha, Nirmal; Prasad, Awadhesh; Ramaswamy, Ramakrishna

2017-03-01

Chimeras, namely coexisting desynchronous and synchronized dynamics, are formed in an ensemble of identically coupled identical chaotic oscillators when the coupling induces multiple stable attractors, and further when the basins of the different attractors are intertwined in a complex manner. When there is coupling-induced multistability, an ensemble of identical chaotic oscillators—with global coupling, or also under the influence of common noise or an external drive (chaotic, periodic, or quasiperiodic)—inevitably exhibits chimeric behavior. Induced multistability in the system leads to the formation of distinct subpopulations, one or more of which support synchronized dynamics, while in others the motion is asynchronous or incoherent. We study the mechanism for the emergence of such chimeric states, and we discuss the generality of our results.

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Adaptative synchronization in multi-output fractional-order complex dynamical networks and secure communications

NASA Astrophysics Data System (ADS)

Mata-Machuca, Juan L.; Aguilar-López, Ricardo

2018-01-01

This work deals with the adaptative synchronization of complex dynamical networks with fractional-order nodes and its application in secure communications employing chaotic parameter modulation. The complex network is composed of multiple fractional-order systems with mismatch parameters and the coupling functions are given to realize the network synchronization. We introduce a fractional algebraic synchronizability condition (FASC) and a fractional algebraic identifiability condition (FAIC) which are used to know if the synchronization and parameters estimation problems can be solved. To overcome these problems, an adaptative synchronization methodology is designed; the strategy consists in proposing multiple receiver systems which tend to follow asymptotically the uncertain transmitters systems. The coupling functions and parameters of the receiver systems are adjusted continually according to a convenient sigmoid-like adaptative controller (SLAC), until the measurable output errors converge to zero, hence, synchronization between transmitter and receivers is achieved and message signals are recovered. Indeed, the stability analysis of the synchronization error is based on the fractional Lyapunov direct method. Finally, numerical results corroborate the satisfactory performance of the proposed scheme by means of the synchronization of a complex network consisting of several fractional-order unified chaotic systems.

From globally coupled maps to complex-systems biology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaneko, Kunihiko, E-mail: kaneko@complex.c.u-tokyo.ac.jp

Studies of globally coupled maps, introduced as a network of chaotic dynamics, are briefly reviewed with an emphasis on novel concepts therein, which are universal in high-dimensional dynamical systems. They include clustering of synchronized oscillations, hierarchical clustering, chimera of synchronization and desynchronization, partition complexity, prevalence of Milnor attractors, chaotic itinerancy, and collective chaos. The degrees of freedom necessary for high dimensionality are proposed to equal the number in which the combinatorial exceeds the exponential. Future analysis of high-dimensional dynamical systems with regard to complex-systems biology is briefly discussed.

Intermittency of intermittencies

NASA Astrophysics Data System (ADS)

Hramov, Alexander E.; Koronovskii, Alexey A.; Moskalenko, Olga I.; Zhuravlev, Maxim O.; Ponomarenko, Vladimir I.; Prokhorov, Mikhail D.

2013-09-01

A phenomenon of intermittency of intermittencies is discovered in the temporal behavior of two coupled complex systems. We observe for the first time the coexistence of two types of intermittent behavior taking place simultaneously near the boundary of the synchronization regime of coupled chaotic oscillators. This phenomenon is found both in the numerical and physiological experiments. The laws for both the distribution and mean length of laminar phases versus the control parameter values are analytically deduced. A very good agreement between the theoretical results and simulation is shown.

A semi-symmetric image encryption scheme based on the function projective synchronization of two hyperchaotic systems

PubMed Central

Li, Jinqing; Qi, Hui; Cong, Ligang; Yang, Huamin

2017-01-01

Both symmetric and asymmetric color image encryption have advantages and disadvantages. In order to combine their advantages and try to overcome their disadvantages, chaos synchronization is used to avoid the key transmission for the proposed semi-symmetric image encryption scheme. Our scheme is a hybrid chaotic encryption algorithm, and it consists of a scrambling stage and a diffusion stage. The control law and the update rule of function projective synchronization between the 3-cell quantum cellular neural networks (QCNN) response system and the 6th-order cellular neural network (CNN) drive system are formulated. Since the function projective synchronization is used to synchronize the response system and drive system, Alice and Bob got the key by two different chaotic systems independently and avoid the key transmission by some extra security links, which prevents security key leakage during the transmission. Both numerical simulations and security analyses such as information entropy analysis, differential attack are conducted to verify the feasibility, security, and efficiency of the proposed scheme. PMID:28910349

Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations.

PubMed

Kügler, Philipp; Bulelzai, M A K; Erhardt, André H

2017-04-04

Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations. In this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed. EADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations.

Strong generalized synchronization with a particular relationship R between the coupled systems

NASA Astrophysics Data System (ADS)

Grácio, Clara; Fernandes, Sara; Mário Lopes, Luís

2018-03-01

The question of the chaotic synchronization of two coupled dynamical systems is an issue that interests researchers in many fields, from biology to psychology, through economics, chemistry, physics, and many others. The different forms of couplings and the different types of synchronization, give rise to many problems, most of them little studied. In this paper we deal with general couplings of two dynamical systems and we study strong generalized synchronization with a particular relationship R between them. Our results include the definition of a window in the domain of the coupling strength, where there is an exponentially stable solution, and the explicit determination of this window. In the case of unidirectional or symmetric couplings, this window is presented in terms of the maximum Lyapunov exponent of the systems. Examples of applications to chaotic systems of dimension one and two are presented.

Exponential Synchronization of Networked Chaotic Delayed Neural Network by a Hybrid Event Trigger Scheme.

PubMed

Fei, Zhongyang; Guan, Chaoxu; Gao, Huijun; Zhongyang Fei; Chaoxu Guan; Huijun Gao; Fei, Zhongyang; Guan, Chaoxu; Gao, Huijun

2018-06-01

This paper is concerned with the exponential synchronization for master-slave chaotic delayed neural network with event trigger control scheme. The model is established on a network control framework, where both external disturbance and network-induced delay are taken into consideration. The desired aim is to synchronize the master and slave systems with limited communication capacity and network bandwidth. In order to save the network resource, we adopt a hybrid event trigger approach, which not only reduces the data package sending out, but also gets rid of the Zeno phenomenon. By using an appropriate Lyapunov functional, a sufficient criterion for the stability is proposed for the error system with extended ( , , )-dissipativity performance index. Moreover, hybrid event trigger scheme and controller are codesigned for network-based delayed neural network to guarantee the exponential synchronization between the master and slave systems. The effectiveness and potential of the proposed results are demonstrated through a numerical example.

Forecasting fluctuating outbreaks in seasonally driven epidemics

NASA Astrophysics Data System (ADS)

Stone, Lewi

2009-03-01

Seasonality is a driving force that has major impact on the spatio-temporal dynamics of natural systems and their populations. This is especially true for the transmission of common infectious diseases such as influenza, measles, chickenpox, and pertussis. Here we gain new insights into the nonlinear dynamics of recurrent diseases through the analysis of the classical seasonally forced SIR epidemic model. Despite many efforts over the last decades, it has been difficult to gain general analytical insights because of the complex synchronization effects that can evolve between the external forcing and the model's natural oscillations. The analysis advanced here attempts to make progress in this direction by focusing on the dynamics of ``skips'' where we identify and predict years in which the epidemic is absent rather than outbreak years. Skipping events are intrinsic to the forced SIR model when parameterised in the chaotic regime. In fact, it is difficult if not impossible to locate realistic chaotic parameter regimes in which outbreaks occur regularly each year. This contrasts with the well known Rossler oscillator whose outbreaks recur regularly but whose amplitude vary chaotically in time (Uniform Phase Chaotic Amplitude oscillations). The goal of the present study is to develop a ``language of skips'' that makes it possible to predict under what conditions the next outbreak is likely to occur, and how many ``skips'' might be expected after any given outbreak. We identify a new threshold effect and give clear analytical conditions that allow accurate predictions. Moreover, the time of occurrence (i.e., phase) of an outbreak proves to be a useful new parameter that carries important epidemiological information. In forced systems, seasonal changes can prevent late-initiating outbreaks (i.e., having high phase) from running to completion. These principles yield forecasting tools that should have relevance for the study of newly emerging and reemerging diseases.

Binary asteroid population. 3. Secondary rotations and elongations

NASA Astrophysics Data System (ADS)

Pravec, P.; Scheirich, P.; Kušnirák, P.; Hornoch, K.; Galád, A.; Naidu, S. P.; Pray, D. P.; Világi, J.; Gajdoš, Š.; Kornoš, L.; Krugly, Yu. N.; Cooney, W. R.; Gross, J.; Terrell, D.; Gaftonyuk, N.; Pollock, J.; Husárik, M.; Chiorny, V.; Stephens, R. D.; Durkee, R.; Reddy, V.; Dyvig, R.; Vraštil, J.; Žižka, J.; Mottola, S.; Hellmich, S.; Oey, J.; Benishek, V.; Kryszczyńska, A.; Higgins, D.; Ries, J.; Marchis, F.; Baek, M.; Macomber, B.; Inasaridze, R.; Kvaratskhelia, O.; Ayvazian, V.; Rumyantsev, V.; Masi, G.; Colas, F.; Lecacheux, J.; Montaigut, R.; Leroy, A.; Brown, P.; Krzeminski, Z.; Molotov, I.; Reichart, D.; Haislip, J.; LaCluyze, A.

2016-03-01

We collected data on rotations and elongations of 46 secondaries of binary and triple systems among near-Earth, Mars-crossing and small main belt asteroids. 24 were found or are strongly suspected to be synchronous (in 1:1 spin-orbit resonance), and the other 22, generally on more distant and/or eccentric orbits, were found or are suggested to have asynchronous rotations. For 18 of the synchronous secondaries, we constrained their librational angles, finding that their long axes pointed to within 20° of the primary on most epochs. The observed anti-correlation of secondary synchroneity with orbital eccentricity and the limited librational angles agree with the theories by Ćuk and Nesvorný (Ćuk, M., Nesvorný, D. [2010]. Icarus 207, 732-743) and Naidu and Margot (Naidu, S.P., Margot, J.-L. [2015]. Astron. J. 149, 80). A reason for the asynchronous secondaries being on wider orbits than synchronous ones may be longer tidal circularization time scales at larger semi-major axes. The asynchronous secondaries show relatively fast spins; their rotation periods are typically < 10 h. An intriguing observation is a paucity of chaotic secondary rotations; with an exception of (35107) 1991 VH, the secondary rotations are single-periodic with no signs of chaotic rotation and their periods are constant on timescales from weeks to years. The secondary equatorial elongations show an upper limit of a2 /b2 ∼ 1.5 . The lack of synchronous secondaries with greater elongations appears consistent, considering uncertainties of the axis ratio estimates, with the theory by Ćuk and Nesvorný that predicts large regions of chaotic rotation in the phase space for a2 /b2 ≳√{ 2 } . Alternatively, secondaries may not form or stay very elongated in gravitational (tidal) field of the primary. It could be due to the secondary fission mechanism suggested by Jacobson and Scheeres (Jacobson, S.A., Scheeres, D.J. [2011]. Icarus 214, 161-178), as its efficiency is correlated with the secondary elongation. Sharma (Sharma, I. [2014]. Icarus 229, 278-294) found that rubble-pile satellites with a2 /b2 ≲ 1.5 are more stable to finite structural perturbations than more elongated ones. It appears that more elongated secondaries, if they originally formed in spin fission of parent asteroid, are less likely to survive intact and they more frequently fail or fission.

Synchronization Tomography: Modeling and Exploring Complex Brain Dynamics

NASA Astrophysics Data System (ADS)

Fieseler, Thomas

2002-03-01

Phase synchronization (PS) plays an important role both under physiological and pathological conditions. With standard averaging techniques of MEG data, it is difficult to reliably detect cortico-cortical and cortico-muscular PS processes that are not time-locked to an external stimulus. For this reason, novel synchronization analysis techniques were developed and directly applied to MEG signals. Of course, due to the lack of an inverse modeling (i.e. source localization), the spatial resolution of this approach was limited. To detect and localize cerebral PS, we here present the synchronization tomography (ST): For this, we first estimate the cerebral current source density by means of the magnetic field tomography (MFT). We then apply the single-run PS analysis to the current source density in each voxel of the reconstruction space. In this way we study simulated PS, voxel by voxel in order to determine the spatio-temporal resolution of the ST. To this end different generators of ongoing rhythmic cerebral activity are simulated by current dipoles at different locations and directions, which are modeled by slightly detuned chaotic oscillators. MEG signals for these generators are simulated for a spherical head model and a whole-head MEG system. MFT current density solutions are calculated from these simulated signals within a hemispherical source space. We compare the spatial resolution of the ST with that of the MFT. Our results show that adjacent sources which are indistinguishable for the MFT, can nevertheless be separated with the ST, provided they are not strongly phase synchronized. This clearly demonstrates the potential of combining spatial information (i.e. source localization) with temporal information for the anatomical localization of phase synchronization in the human brain.

Phase synchronization of baroclinic waves in a differentially heated rotating annulus experiment subject to periodic forcing with a variable duty cycle

NASA Astrophysics Data System (ADS)

Read, P. L.; Morice-Atkinson, X.; Allen, E. J.; Castrejón-Pita, A. A.

2017-12-01

A series of laboratory experiments in a thermally driven, rotating fluid annulus are presented that investigate the onset and characteristics of phase synchronization and frequency entrainment between the intrinsic, chaotic, oscillatory amplitude modulation of travelling baroclinic waves and a periodic modulation of the (axisymmetric) thermal boundary conditions, subject to time-dependent coupling. The time-dependence is in the form of a prescribed duty cycle in which the periodic forcing of the boundary conditions is applied for only a fraction δ of each oscillation. For the rest of the oscillation, the boundary conditions are held fixed. Two profiles of forcing were investigated that capture different parts of the sinusoidal variation and δ was varied over the range 0.1 ≤δ≤1 . Reducing δ was found to act in a similar way to a reduction in a constant coupling coefficient in reducing the width of the interval in forcing frequency or period over which complete synchronization was observed (the "Arnol'd tongue") with respect to the detuning, although for the strongest pulse-like forcing profile some degree of synchronization was discernible even at δ=0.1 . Complete phase synchronization was obtained within the Arnol'd tongue itself, although the strength of the amplitude modulation of the baroclinic wave was not significantly affected. These experiments demonstrate a possible mechanism for intraseasonal and/or interannual "teleconnections" within the climate system of the Earth and other planets that does not rely on Rossby wave propagation across the planet along great circles.

Understanding transient uncoupling induced synchronization through modified dynamic coupling

NASA Astrophysics Data System (ADS)

Ghosh, Anupam; Godara, Prakhar; Chakraborty, Sagar

2018-05-01

An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continuously coupled. However, why this is so is an open problem? To answer this question, we recall the conventional wisdom that the eigenvalues of the Jacobian of the transverse dynamics measure whether a trajectory at a phase point is locally contracting or diverging with respect to another nearby trajectory. Subsequently, we go on to highlight a lesser appreciated fact that even when, under the corresponding linearised flow, the nearby trajectory asymptotically diverges away, its distance from the reference trajectory may still be contracting for some intermediate period. We term this phenomenon transient decay in line with the phenomenon of the transient growth. Using these facts, we show that an optimal coupling region, i.e., a region of the phase space where coupling is on, should ideally be such that at any of the constituent phase point either the maximum of the real parts of the eigenvalues is negative or the magnitude of the positive maximum is lesser than that of the negative minimum. We also invent and employ a modified dynamics coupling scheme—a significant improvement over the well-known dynamic coupling scheme—as a decisive tool to justify our results.

Chaotic dynamics and synchronization in microchip solid-state lasers with optoelectronic feedback.

PubMed

Uchida, Atsushi; Mizumura, Keisuke; Yoshimori, Shigeru

2006-12-01

We experimentally observe the dynamics of a two-mode Nd:YVO4 microchip solid-state laser with optoelectronic feedback. The total laser output is detected and fed back to the injection current of the laser diode for pumping. Chaotic oscillations are observed in the microchip laser with optoelectronic self-feedback. We also observe the dynamics of two microchip lasers coupled mutually with optoelectronic link. The output of one laser is detected by a photodiode and the electronic signal converted from the laser output is sent to the pumping of the other laser. Chaotic fluctuation of the laser output is observed when the relaxation oscillation frequency is close to each other between the two microchip lasers. Synchronization of periodic wave form is also obtained when the microchip lasers have a single-longitudinal mode.

On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Mahmoud, Gamal M.

Dynamical systems described by real and complex variables are currently one of the most popular areas of scientific research. These systems play an important role in several fields of physics, engineering, and computer sciences, for example, laser systems, control (or chaos suppression), secure communications, and information science. Dynamical basic properties, chaos (hyperchaos) synchronization, chaos control, and generating hyperchaotic behavior of these systems are briefly summarized. The main advantage of introducing complex variables is the reduction of phase space dimensions by a half. They are also used to describe and simulate the physics of detuned laser and thermal convection of liquid flows, where the electric field and the atomic polarization amplitudes are both complex. Clearly, if the variables of the system are complex the equations involve twice as many variables and control parameters, thus making it that much harder for a hostile agent to intercept and decipher the coded message. Chaotic and hyperchaotic complex systems are stated as examples. Finally there are many open problems in the study of chaotic and hyperchaotic complex nonlinear dynamical systems, which need further investigations. Some of these open problems are given.

Phase synchronization based minimum spanning trees for analysis of financial time series with nonlinear correlations

NASA Astrophysics Data System (ADS)

Radhakrishnan, Srinivasan; Duvvuru, Arjun; Sultornsanee, Sivarit; Kamarthi, Sagar

2016-02-01

The cross correlation coefficient has been widely applied in financial time series analysis, in specific, for understanding chaotic behaviour in terms of stock price and index movements during crisis periods. To better understand time series correlation dynamics, the cross correlation matrices are represented as networks, in which a node stands for an individual time series and a link indicates cross correlation between a pair of nodes. These networks are converted into simpler trees using different schemes. In this context, Minimum Spanning Trees (MST) are the most favoured tree structures because of their ability to preserve all the nodes and thereby retain essential information imbued in the network. Although cross correlations underlying MSTs capture essential information, they do not faithfully capture dynamic behaviour embedded in the time series data of financial systems because cross correlation is a reliable measure only if the relationship between the time series is linear. To address the issue, this work investigates a new measure called phase synchronization (PS) for establishing correlations among different time series which relate to one another, linearly or nonlinearly. In this approach the strength of a link between a pair of time series (nodes) is determined by the level of phase synchronization between them. We compare the performance of phase synchronization based MST with cross correlation based MST along selected network measures across temporal frame that includes economically good and crisis periods. We observe agreement in the directionality of the results across these two methods. They show similar trends, upward or downward, when comparing selected network measures. Though both the methods give similar trends, the phase synchronization based MST is a more reliable representation of the dynamic behaviour of financial systems than the cross correlation based MST because of the former's ability to quantify nonlinear relationships among time series or relations among phase shifted time series.

Encryption key distribution via chaos synchronization

NASA Astrophysics Data System (ADS)

Keuninckx, Lars; Soriano, Miguel C.; Fischer, Ingo; Mirasso, Claudio R.; Nguimdo, Romain M.; van der Sande, Guy

2017-02-01

We present a novel encryption scheme, wherein an encryption key is generated by two distant complex nonlinear units, forced into synchronization by a chaotic driver. The concept is sufficiently generic to be implemented on either photonic, optoelectronic or electronic platforms. The method for generating the key bitstream from the chaotic signals is reconfigurable. Although derived from a deterministic process, the obtained bit series fulfill the randomness conditions as defined by the National Institute of Standards test suite. We demonstrate the feasibility of our concept on an electronic delay oscillator circuit and test the robustness against attacks using a state-of-the-art system identification method.

Exponential synchronization of chaotic systems with time-varying delays and parameter mismatches via intermittent control.

PubMed

Cai, Shuiming; Hao, Junjun; Liu, Zengrong

2011-06-01

This paper studies the synchronization of coupled chaotic systems with time-varying delays in the presence of parameter mismatches by means of periodically intermittent control. Some novel and useful quasisynchronization criteria are obtained by using the methods which are different from the techniques employed in the existing works, and the derived results are less conservative. Especially, a strong constraint on the control width that the control width should be larger than the time delay imposed by the current references is released in this paper. Moreover, our results show that the synchronization criteria depend on the ratio of control width to control period, but not the control width or the control period. Finally, some numerical simulations are given to show the effectiveness of the theoretical results.

Disturbance observer based active and adaptive synchronization of energy resource chaotic system.

PubMed

Wei, Wei; Wang, Meng; Li, Donghai; Zuo, Min; Wang, Xiaoyi

2016-11-01

In this paper, synchronization of a three-dimensional energy resource chaotic system is considered. For the sake of achieving the synchronization between the drive and response systems, two different nonlinear control approaches, i.e. active control with known parameters and adaptive control with unknown parameters, have been designed. In order to guarantee the transient performance, finite-time boundedness (FTB) and finite-time stability (FTS) are introduced in the design of active control and adaptive control, respectively. Simultaneously, in view of the existence of disturbances, a new disturbance observer is proposed to estimate the disturbance. The conditions of the asymptotic stability for the closed-loop system are obtained. Numerical simulations are provided to illustrate the proposed approaches. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Near-Earth asteroid satellite spins under spin-orbit coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naidu, Shantanu P.; Margot, Jean-Luc

We develop a fourth-order numerical integrator to simulate the coupled spin and orbital motions of two rigid bodies having arbitrary mass distributions under the influence of their mutual gravitational potential. We simulate the dynamics of components in well-characterized binary and triple near-Earth asteroid systems and use surface of section plots to map the possible spin configurations of the satellites. For asynchronous satellites, the analysis reveals large regions of phase space where the spin state of the satellite is chaotic. For synchronous satellites, we show that libration amplitudes can reach detectable values even for moderately elongated shapes. The presence of chaoticmore » regions in the phase space has important consequences for the evolution of binary asteroids. It may substantially increase spin synchronization timescales, explain the observed fraction of asychronous binaries, delay BYORP-type evolution, and extend the lifetime of binaries. The variations in spin rate due to large librations also affect the analysis and interpretation of light curve and radar observations.« less

Relation between delayed feedback and delay-coupled systems and its application to chaotic lasers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soriano, Miguel C., E-mail: miguel@ifisc.uib-csic.es; Flunkert, Valentin; Fischer, Ingo

2013-12-15

We present a systematic approach to identify the similarities and differences between a chaotic system with delayed feedback and two mutually delay-coupled systems. We consider the general case in which the coupled systems are either unsynchronized or in a generally synchronized state, in contrast to the mostly studied case of identical synchronization. We construct a new time-series for each of the two coupling schemes, respectively, and present analytic evidence and numerical confirmation that these two constructed time-series are statistically equivalent. From the construction, it then follows that the distribution of time-series segments that are small compared to the overall delaymore » in the system is independent of the value of the delay and of the coupling scheme. By focusing on numerical simulations of delay-coupled chaotic lasers, we present a practical example of our findings.« less

Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

2016-06-08

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.

Predictive control of a chaotic permanent magnet synchronous generator in a wind turbine system

NASA Astrophysics Data System (ADS)

Manal, Messadi; Adel, Mellit; Karim, Kemih; Malek, Ghanes

2015-01-01

This paper investigates how to address the chaos problem in a permanent magnet synchronous generator (PMSG) in a wind turbine system. Predictive control approach is proposed to suppress chaotic behavior and make operating stable; the advantage of this method is that it can only be applied to one state of the wind turbine system. The use of the genetic algorithms to estimate the optimal parameter values of the wind turbine leads to maximization of the power generation. Moreover, some simulation results are included to visualize the effectiveness and robustness of the proposed method. Project supported by the CMEP-TASSILI Project (Grant No. 14MDU920).

Encryption key distribution via chaos synchronization

PubMed Central

Keuninckx, Lars; Soriano, Miguel C.; Fischer, Ingo; Mirasso, Claudio R.; Nguimdo, Romain M.; Van der Sande, Guy

2017-01-01

We present a novel encryption scheme, wherein an encryption key is generated by two distant complex nonlinear units, forced into synchronization by a chaotic driver. The concept is sufficiently generic to be implemented on either photonic, optoelectronic or electronic platforms. The method for generating the key bitstream from the chaotic signals is reconfigurable. Although derived from a deterministic process, the obtained bit series fulfill the randomness conditions as defined by the National Institute of Standards test suite. We demonstrate the feasibility of our concept on an electronic delay oscillator circuit and test the robustness against attacks using a state-of-the-art system identification method. PMID:28233876

A nonlinear controller design for permanent magnet motors using a synchronization-based technique inspired from the Lorenz system.

PubMed

Zaher, Ashraf A

2008-03-01

The dynamic behavior of a permanent magnet synchronous machine (PMSM) is analyzed. Nominal and special operating conditions are explored to show that the PMSM can experience chaos. A nonlinear controller is introduced to control these unwanted chaotic oscillations and to bring the PMSM to a stable steady state. The designed controller uses a pole-placement approach to force the closed-loop system to follow the performance of a simple first-order linear system with zero steady-state error to a desired set point. The similarity between the mathematical model of the PMSM and the famous chaotic Lorenz system is utilized to design a synchronization-based state observer using only the angular speed for feedback. Simulation results verify the effectiveness of the proposed controller in eliminating the chaotic oscillations while using a single feedback signal. The superiority of the proposed controller is further demonstrated by comparing it with a conventional PID controller. Finally, a laboratory-based experiment was conducted using the MCK2812 C Pro-MS(BL) motion control kit to confirm the theoretical results and to verify both the causality and versatility of the proposed controller.

Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling.

PubMed

Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad

2014-11-01

This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Intrinsic line shape of electromagnetic radiation from a stack of intrinsic Josephson junctions synchronized by an internal cavity resonance

NASA Astrophysics Data System (ADS)

Koshelev, Alexei

2013-03-01

Stacks of intrinsic Josephson-junctions are realized in mesas fabricated out of layered superconducting single crystals, such as Bi2Sr2CaCu2O8 (BSCCO). Synchronization of phase oscillations in different junctions can be facilitated by the coupling to the internal cavity mode leading to powerful and coherent electromagnetic radiation in the terahertz frequency range. An important characteristic of this radiation is the shape of the emission line. A finite line width appears due to different noise sources leading to phase diffusion. We investigated the intrinsic line shape caused by the thermal noise for a mesa fabricated on the top of a BSCCO single crystal. In the ideal case of fully synchronized stack the finite line width is coming from two main contributions, the quasiparticle-current noise inside the mesa and the fluctuating radiation in the base crystal. We compute both contributions and conclude that for realistic mesa's parameters the second mechanism typically dominates. The role of the cavity quality factor in the emission line spectrum is clarified. Analytical results were verified by numerical simulations. In real mesa structures part of the stack may not be synchronized and chaotic dynamics of unsynchronized junctions may determine the real line width. Work supported by UChicago Argonne, LLC, under contract No. DE-AC02-06CH11357.

Robust synchronization of spin-torque oscillators with an LCR load.

PubMed

Pikovsky, Arkady

2013-09-01

We study dynamics of a serial array of spin-torque oscillators with a parallel inductor-capacitor-resistor (LCR) load. In a large range of parameters the fully synchronous regime, where all the oscillators have the same state and the output field is maximal, is shown to be stable. However, not always such a robust complete synchronization develops from a random initial state; in many cases nontrivial clustering is observed, with a partial synchronization resulting in a quasiperiodic or chaotic mean-field dynamics.

Isotropy of Angular Frequencies and Weak Chimeras with Broken Symmetry

NASA Astrophysics Data System (ADS)

Bick, Christian

2017-04-01

The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here, we generalize the definition of a weak chimera to a more general class of equivariant dynamical systems by characterizing solutions in terms of the isotropy of their angular frequency vector—for coupled phase oscillators the angular frequency vector is given by the average of the vector field along a trajectory. Symmetries of solutions automatically imply angular frequency synchronization. We show that the presence of such symmetries is not necessary by giving a result for the existence of weak chimeras without instantaneous or setwise symmetries for coupled phase oscillators. Moreover, we construct a coupling function that gives rise to chaotic weak chimeras without symmetry in weakly coupled populations of phase oscillators with generalized coupling.

Cryptanalysis of a chaotic communication scheme using adaptive observer.

PubMed

Liu, Ying; Tang, Wallace K S

2008-12-01

This paper addresses the cryptanalysis of a secure communication scheme recently proposed by Wu [Chaos 16, 043118 (2006)], where the information signal is modulated into a system parameter of a unified chaotic system. With the Kerckhoff principle, assuming that the structure of the cryptosystem is known, an adaptive observer can be designed to synchronize the targeted system, so that the transmitted information and the user-specific parameters are obtained. The success of adaptive synchronization is mathematically proved with the use of Lyapunov stability theory, based on the original assumption, i.e., the dynamical evolution of the information signal is available. A more practical case, but yet much more difficult, is also considered. As demonstrated with simulations, generalized synchronization is still possible, even if the derivative of the information signal is kept secret. Hence, the message can be coarsely estimated, making the security of the considered system questionable.

Spin dynamics of close-in planets exhibiting large transit timing variations

NASA Astrophysics Data System (ADS)

Delisle, J.-B.; Correia, A. C. M.; Leleu, A.; Robutel, P.

2017-09-01

We study the spin evolution of close-in planets in compact multi-planetary systems. The rotation period of these planets is often assumed to be synchronous with the orbital period due to tidal dissipation. Here we show that planet-planet perturbations can drive the spin of these planets into non-synchronous or even chaotic states. In particular, we show that the transit timing variation (TTV) is a very good probe to study the spin dynamics, since both are dominated by the perturbations of the mean longitude of the planet. We apply our model to KOI-227 b and Kepler-88 b, which are both observed undergoing strong TTVs. We also perform numerical simulations of the spin evolution of these two planets. We show that for KOI-227 b non-synchronous rotation is possible, while for Kepler-88 b the rotation can be chaotic.

Physiologically motivated multiplex Kuramoto model describes phase diagram of cortical activity

NASA Astrophysics Data System (ADS)

Sadilek, Maximilian; Thurner, Stefan

2015-05-01

We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of interconnected cortical regions. This is mathematically possible due to the existence of a unique, stable limit cycle, weak coupling, and inhibitory synaptic time delays. We study the phase diagram of this model numerically as a function of the inter-regional connection strength that is related to cerebral blood flow, and a phase shift parameter that is associated with synaptic GABA concentrations. We find three macroscopic phases of cortical activity: background activity (unsynchronized oscillations), epileptiform activity (highly synchronized oscillations) and resting-state activity (synchronized clusters/chaotic behaviour). Previous network models could hitherto not explain the existence of all three phases. We further observe a shift of the average oscillation frequency towards lower values together with the appearance of coherent slow oscillations at the transition from resting-state to epileptiform activity. This observation is fully in line with experimental data and could explain the influence of GABAergic drugs both on gamma oscillations and epileptic states. Compared to previous models for gamma oscillations and resting-state activity, the multiplex Kuramoto model not only provides a unifying framework, but also has a direct connection to measurable physiological parameters.

Physiologically motivated multiplex Kuramoto model describes phase diagram of cortical activity.

PubMed

Sadilek, Maximilian; Thurner, Stefan

2015-05-21

We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of interconnected cortical regions. This is mathematically possible due to the existence of a unique, stable limit cycle, weak coupling, and inhibitory synaptic time delays. We study the phase diagram of this model numerically as a function of the inter-regional connection strength that is related to cerebral blood flow, and a phase shift parameter that is associated with synaptic GABA concentrations. We find three macroscopic phases of cortical activity: background activity (unsynchronized oscillations), epileptiform activity (highly synchronized oscillations) and resting-state activity (synchronized clusters/chaotic behaviour). Previous network models could hitherto not explain the existence of all three phases. We further observe a shift of the average oscillation frequency towards lower values together with the appearance of coherent slow oscillations at the transition from resting-state to epileptiform activity. This observation is fully in line with experimental data and could explain the influence of GABAergic drugs both on gamma oscillations and epileptic states. Compared to previous models for gamma oscillations and resting-state activity, the multiplex Kuramoto model not only provides a unifying framework, but also has a direct connection to measurable physiological parameters.

Synchronized Chaos in Geophysical Fluid Dynamics and in the Predictive Modeling of Natural Systems

NASA Astrophysics Data System (ADS)

Duane, Gregory S.

2008-03-01

The ubiquitous phenomenon of synchronization among regular oscillators in Nature has been shown, in the past two decades, to extend to chaotic systems. Despite sensitive dependence on initial conditions, two chaotic systems will commonly fall into synchronized motion along their strange attractors when only some of the many degrees of freedom of one system are coupled to corresponding variables in the other. In geophysical fluid models, synchronization can mediate scale interactions, so that coupling of degrees of freedom that describe medium-scale components of the flow can result in synchronization, or partial synchronization, at all scales. Chaos synchronization has been used to interpret non-local "teleconnection" patterns in the Earth's climate system and to predict new ones. In the realm of practical meteorology, the fact that two PDE systems, conceived as "truth" and "model", respectively, can be made to synchronize when coupled at only a discrete set of points, explains how observations at a discrete set of weather stations can be sufficient for weather prediction by a synchronously coupled model. Minimizing synchronization error leads to general recipes for assimilation of observed data into a running model that systematize the treatment of nonlinearities in the dynamical equations. Equations can generally be added to adapt parameters as well as states as the model is running, so that the model "learns". The synchronization view of predictive modelling extends to any translationally- any PDE with constant coefficients, the general form of physical theories. The reliance on synchronicity as an organizing principle in Nature, alternative to causality, has philosophical roots in the collaboration of Carl Jung and Wolfgang Pauli, on the one hand, and in traditions outside of European science, on the other.

Synchronization and coordination of sequences in two neural ensembles

NASA Astrophysics Data System (ADS)

Venaille, Antoine; Varona, Pablo; Rabinovich, Mikhail I.

2005-06-01

There are many types of neural networks involved in the sequential motor behavior of animals. For high species, the control and coordination of the network dynamics is a function of the higher levels of the central nervous system, in particular the cerebellum. However, in many cases, especially for invertebrates, such coordination is the result of direct synaptic connections between small circuits. We show here that even the chaotic sequential activity of small model networks can be coordinated by electrotonic synapses connecting one or several pairs of neurons that belong to two different networks. As an example, we analyzed the coordination and synchronization of the sequential activity of two statocyst model networks of the marine mollusk Clione. The statocysts are gravity sensory organs that play a key role in postural control of the animal and the generation of a complex hunting motor program. Each statocyst network was modeled by a small ensemble of neurons with Lotka-Volterra type dynamics and nonsymmetric inhibitory interactions. We studied how two such networks were synchronized by electrical coupling in the presence of an external signal which lead to winnerless competition among the neurons. We found that as a function of the number and the strength of connections between the two networks, it is possible to coordinate and synchronize the sequences that each network generates with its own chaotic dynamics. In spite of the chaoticity, the coordination of the signals is established through an activation sequence lock for those neurons that are active at a particular instant of time.

Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems

NASA Astrophysics Data System (ADS)

Jacobson, Seth A.; Scheeres, Daniel J.

2011-07-01

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high- e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, "rubble pile" asteroid geophysics, and gravitational interactions. The YORP effect torques a "rubble pile" asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.

Bifurcation study of phase oscillator systems with attractive and repulsive interaction.

PubMed

Burylko, Oleksandr; Kazanovich, Yakov; Borisyuk, Roman

2014-08-01

We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations.

Bifurcation study of phase oscillator systems with attractive and repulsive interaction

NASA Astrophysics Data System (ADS)

Burylko, Oleksandr; Kazanovich, Yakov; Borisyuk, Roman

2014-08-01

We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations.

Zero-lag synchronization and bubbling in delay-coupled lasers.

PubMed

Tiana-Alsina, J; Hicke, K; Porte, X; Soriano, M C; Torrent, M C; Garcia-Ojalvo, J; Fischer, I

2012-02-01

We show experimentally that two semiconductor lasers mutually coupled via a passive relay fiber loop exhibit chaos synchronization at zero lag, and study how this synchronized regime is lost as the lasers' pump currents are increased. We characterize the synchronization properties of the system with high temporal resolution in two different chaotic regimes, namely, low-frequency fluctuations and coherence collapse, identifying significant differences between them. In particular, a marked decrease in synchronization quality develops as the lasers enter the coherence collapse regime. Our high-resolution measurements allow us to establish that synchronization loss is associated with bubbling events, the frequency of which increases with increasing pump current.

Synchronized chaotic targeting and acceleration of surface chemistry in prebiotic hydrothermal microenvironments

PubMed Central

Priye, Aashish; Yu, Yuncheng; Hassan, Yassin A.; Ugaz, Victor M.

2017-01-01

Porous mineral formations near subsea alkaline hydrothermal vents embed microenvironments that make them potential hot spots for prebiotic biochemistry. But, synthesis of long-chain macromolecules needed to support higher-order functions in living systems (e.g., polypeptides, proteins, and nucleic acids) cannot occur without enrichment of chemical precursors before initiating polymerization, and identifying a suitable mechanism has become a key unanswered question in the origin of life. Here, we apply simulations and in situ experiments to show how 3D chaotic thermal convection—flows that naturally permeate hydrothermal pore networks—supplies a robust mechanism for focused accumulation at discrete targeted surface sites. This interfacial enrichment is synchronized with bulk homogenization of chemical species, yielding two distinct processes that are seemingly opposed yet synergistically combine to accelerate surface reaction kinetics by several orders of magnitude. Our results suggest that chaotic thermal convection may play a previously unappreciated role in mediating surface-catalyzed synthesis in the prebiotic milieu. PMID:28119504

Synchronizability of nonidentical weakly dissipative systems

NASA Astrophysics Data System (ADS)

Sendiña-Nadal, Irene; Letellier, Christophe

2017-10-01

Synchronization is a very generic process commonly observed in a large variety of dynamical systems which, however, has been rarely addressed in systems with low dissipation. Using the Rössler, the Lorenz 84, and the Sprott A systems as paradigmatic examples of strongly, weakly, and non-dissipative chaotic systems, respectively, we show that a parameter or frequency mismatch between two coupled such systems does not affect the synchronizability and the underlying structure of the joint attractor in the same way. By computing the Shannon entropy associated with the corresponding recurrence plots, we were able to characterize how two coupled nonidentical chaotic oscillators organize their dynamics in different dissipation regimes. While for strongly dissipative systems, the resulting dynamics exhibits a Shannon entropy value compatible with the one having an average parameter mismatch, for weak dissipation synchronization dynamics corresponds to a more complex behavior with higher values of the Shannon entropy. In comparison, conservative dynamics leads to a less rich picture, providing either similar chaotic dynamics or oversimplified periodic ones.

On the Synchronization of EEG Spindle Waves

NASA Astrophysics Data System (ADS)

Long, Wen; Zhang, ChengFu; Zhao, SiLan; Shi, RuiHong

2000-06-01

Based on recently sleeping cellular substrates, a network model synaptically coupled by N three-cell circuits is provided. Simulation results show that: (i) the dynamic behavior of every circuit is chaotic; (ii) the synchronization of the network is incomplete; (iii) the incomplete synchronization can integrate burst firings of cortical cells into waxing-and-wanning EEG spindle waves. These results enlighten us that this kind of incomplete synchronization may integrate microscopic, electrical activities of neurons in billions into macroscopic, functional states in human brain. In addition, the effects of coupling strength, connectional mode and noise to the synchronization are discussed.

Synchronization behaviors of coupled systems composed of hidden attractors

NASA Astrophysics Data System (ADS)

Zhang, Ge; Wu, Fuqiang; Wang, Chunni; Ma, Jun

2017-10-01

Based on a class of chaotic system composed of hidden attractors, in which the equilibrium points are described by a circular function, complete synchronization between two identical systems, pattern formation and synchronization of network is investigated, respectively. A statistical factor of synchronization is defined and calculated by using the mean field theory, the dependence of synchronization on bifurcation parameters discussed in numerical way. By setting a chain network, which local kinetic is described by hidden attractors, synchronization approach is investigated. It is found that the synchronization and pattern formation are dependent on the coupling intensity and also the selection of coupling variables. In the end, open problems are proposed for readers’ extensive guidance and investigation.

Special Section on Synchronization in Nonlinear Science and Engineering

NASA Astrophysics Data System (ADS)

Ikeguchi, Tohru; Tokuda, Isao

Synchronization is a ubiquitous phenomenon of coupled nonlinear oscillators, commonly found in physics, engineering, biology, and other diverse disciplines. It has a long research history back to Christiaan Huygens, who discovered synchronized motion of two pendulum clocks in 1673. It is very easy to observe synchronization in our daily life: e.g., metronomes, candle fires, pet-bottle oscillators, saltwater oscillators, and so on(See, for example, experimental movies at http://www.youtube.com/user/IkeguchiLab?feature=watch). For the last few decades, significant development has been made from both theories and experiments on synchronization of coupled limit cycle oscillators as well as coupled chaotic oscillators. Applications have been also developed to communication technologies, controlling techniques, and data analysis. Combined with the idea from complex network theory, neuroscience, and systems biology, the research speed of synchronization has been even accelerated. This Special Section of NOLTA is primarily dedicated to the recent advanced development of basics and applications of synchronization in science and engineering. A number of qualified works is included, ranging from experimental study on synchronization of Huygens' system, analog circuits, and singing voice to applied study of synchronization in communication networks. One invited paper is devoted to comprehensive reviews on generalized synchronization of chaotic oscillators. On behalf of the editorial committee of the special section, the guest editors would like to express their sincere thanks to all the authors for their excellent contributions. In particular, they are grateful to Prof. Dr. Ulrich Parlitz for contributing his distinguished review article. They would also like to thank the reviewers and the members of the guest editorial committee, especially Prof. Hiroo Sekiya of Chiba University and the editorial staffs of the NOLTA journal, for their supports on publishing this Special Section.

Security-enhanced chaos communication with time-delay signature suppression and phase encryption.

PubMed

Xue, Chenpeng; Jiang, Ning; Lv, Yunxin; Wang, Chao; Li, Guilan; Lin, Shuqing; Qiu, Kun

2016-08-15

A security-enhanced chaos communication scheme with time delay signature (TDS) suppression and phase-encrypted feedback light is proposed, in virtue of dual-loop feedback with independent high-speed phase modulation. We numerically investigate the property of TDS suppression in the intensity and phase space and quantitatively discuss security of the proposed system by calculating the bit error rate of eavesdroppers who try to crack the system by directly filtering the detected signal or by using a similar semiconductor laser to synchronize the link signal and extract the data. The results show that TDS embedded in the chaotic carrier can be well suppressed by properly setting the modulation frequency, which can keep the time delay a secret from the eavesdropper. Moreover, because the feedback light is encrypted, without the accurate time delay and key, the eavesdropper cannot reconstruct the symmetric operation conditions and decode the correct data.

Adaptive fuzzy dynamic surface control for the chaotic permanent magnet synchronous motor using Nussbaum gain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Shaohua

This paper is concerned with the problem of adaptive fuzzy dynamic surface control (DSC) for the permanent magnet synchronous motor (PMSM) system with chaotic behavior, disturbance and unknown control gain and parameters. Nussbaum gain is adopted to cope with the situation that the control gain is unknown. And the unknown items can be estimated by fuzzy logic system. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal. Finally, the numerical simulations indicate that the proposed scheme can suppress the chaosmore » of PMSM and show the effectiveness and robustness of the proposed method.« less

Adaptive fuzzy dynamic surface control for the chaotic permanent magnet synchronous motor using Nussbaum gain.

PubMed

Luo, Shaohua

2014-09-01

This paper is concerned with the problem of adaptive fuzzy dynamic surface control (DSC) for the permanent magnet synchronous motor (PMSM) system with chaotic behavior, disturbance and unknown control gain and parameters. Nussbaum gain is adopted to cope with the situation that the control gain is unknown. And the unknown items can be estimated by fuzzy logic system. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal. Finally, the numerical simulations indicate that the proposed scheme can suppress the chaos of PMSM and show the effectiveness and robustness of the proposed method.

Active control and synchronization chaotic satellite via the geomagnetic Lorentz force

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Yehia

2016-07-01

The use of geomagnetic Lorentz force is considered in this paper for the purpose of satellite attitude control. A satellite with an electrostatic charge will interact with the Earth's magnetic field and experience the Lorentz force. An analytical attitude control and synchronization two identical chaotic satellite systems with different initial condition Master/ Slave are proposed to allows a charged satellite remains near the desired attitude. Asymptotic stability for the closed-loop system are investigated by means of Lyapunov stability theorem. The control feasibility depend on the charge requirement. Given a significantly and sufficiently accurate insertion, a charged satellite could maintains the desired attitude orientation without propellant. Simulations is performed to prove the efficacy of the proposed method.

Exponential H ∞ Synchronization of Chaotic Cryptosystems Using an Improved Genetic Algorithm

PubMed Central

Hsiao, Feng-Hsiag

2015-01-01

This paper presents a systematic design methodology for neural-network- (NN-) based secure communications in multiple time-delay chaotic (MTDC) systems with optimal H ∞ performance and cryptography. On the basis of the Improved Genetic Algorithm (IGA), which is demonstrated to have better performance than that of a traditional GA, a model-based fuzzy controller is then synthesized to stabilize the MTDC systems. A fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H ∞ performance by minimizing the disturbance attenuation level. Furthermore, the error of the recovered message is stated by using the n-shift cipher and key. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach. PMID:26366432

Synchronization and chaotic dynamics of coupled mechanical metronomes

NASA Astrophysics Data System (ADS)

Ulrichs, Henning; Mann, Andreas; Parlitz, Ulrich

2009-12-01

Synchronization scenarios of coupled mechanical metronomes are studied by means of numerical simulations showing the onset of synchronization for two, three, and 100 globally coupled metronomes in terms of Arnol'd tongues in parameter space and a Kuramoto transition as a function of coupling strength. Furthermore, we study the dynamics of metronomes where overturning is possible. In this case hyperchaotic dynamics associated with some diffusion process in configuration space is observed, indicating the potential complexity of metronome dynamics.

Stochastic bifurcations in the nonlinear parallel Ising model.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2016-11-01

We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

New type of chaos synchronization in discrete-time systems: the F-M synchronization

NASA Astrophysics Data System (ADS)

Ouannas, Adel; Grassi, Giuseppe; Karouma, Abdulrahman; Ziar, Toufik; Wang, Xiong; Pham, Viet-Thanh

2018-04-01

In this paper, a new type of synchronization for chaotic (hyperchaotic) maps with different dimensions is proposed. The novel scheme is called F - M synchronization, since it combines the inverse generalized synchronization (based on a functional relationship F) with the matrix projective synchronization (based on a matrix M). In particular, the proposed approach enables F - M synchronization with index d to be achieved between n-dimensional drive system map and m-dimensional response system map, where the synchronization index d corresponds to the dimension of the synchronization error. The technique, which exploits nonlinear controllers and Lyapunov stability theory, proves to be effective in achieving the F - M synchronization not only when the synchronization index d equals n or m, but even if the synchronization index d is larger than the map dimensions n and m. Finally, simulation results are reported, with the aim to illustrate the capabilities of the novel scheme proposed herein.

Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns

NASA Astrophysics Data System (ADS)

Gu, Hua-Guang; Chen, Sheng-Gen; Li, Yu-Ye

2015-05-01

We investigated the synchronization dynamics of a coupled neuronal system composed of two identical Chay model neurons. The Chay model showed coexisting period-1 and period-2 bursting patterns as a parameter and initial values are varied. We simulated multiple periodic and chaotic bursting patterns with non-(NS), burst phase (BS), spike phase (SS), complete (CS), and lag synchronization states. When the coexisting behavior is near period-2 bursting, the transitions of synchronization states of the coupled system follows very complex transitions that begins with transitions between BS and SS, moves to transitions between CS and SS, and to CS. Most initial values lead to the CS state of period-2 bursting while only a few lead to the CS state of period-1 bursting. When the coexisting behavior is near period-1 bursting, the transitions begin with NS, move to transitions between SS and BS, to transitions between SS and CS, and then to CS. Most initial values lead to the CS state of period-1 bursting but a few lead to the CS state of period-2 bursting. The BS was identified as chaos synchronization. The patterns for NS and transitions between BS and SS are insensitive to initial values. The patterns for transitions between CS and SS and the CS state are sensitive to them. The number of spikes per burst of non-CS bursting increases with increasing coupling strength. These results not only reveal the initial value- and parameter-dependent synchronization transitions of coupled systems with coexisting behaviors, but also facilitate interpretation of various bursting patterns and synchronization transitions generated in the nervous system with weak coupling strength. Project supported by the National Natural Science Foundation of China (Grant Nos. 11372224 and 11402039) and the Fundamental Research Funds for Central Universities designated to Tongji University (Grant No. 1330219127).

Chaotic dynamics of controlled electric power systems

NASA Astrophysics Data System (ADS)

Kozlov, V. N.; Trosko, I. U.

2016-12-01

The conditions for appearance of chaotic dynamics of electromagnetic and electromechanical processes in energy systems described by the Park-Gorev bilinear differential equations with account for lags of coordinates and restrictions on control have been formulated. On the basis of classical equations, the parameters of synchronous generators and power lines, at which the chaotic dynamics of energy systems appears, have been found. The qualitative and quantitative characteristics of chaotic processes in energy associations of two types, based on the Hopf theorem, and methods of nonstationary linearization and decompositions are given. The properties of spectral characteristics of chaotic processes have been investigated, and the qualitative similarity of bilinear equations of power systems and Lorentz equations have been found. These results can be used for modernization of the systems of control of energy objects. The qualitative and quantitative characteristics for power energy systems as objects of control and for some laws of control with the feedback have been established.

Public-channel cryptography based on mutual chaos pass filters.

PubMed

Klein, Einat; Gross, Noam; Kopelowitz, Evi; Rosenbluh, Michael; Khaykovich, Lev; Kinzel, Wolfgang; Kanter, Ido

2006-10-01

We study the mutual coupling of chaotic lasers and observe both experimentally and in numeric simulations that there exists a regime of parameters for which two mutually coupled chaotic lasers establish isochronal synchronization, while a third laser coupled unidirectionally to one of the pair does not synchronize. We then propose a cryptographic scheme, based on the advantage of mutual coupling over unidirectional coupling, where all the parameters of the system are public knowledge. We numerically demonstrate that in such a scheme the two communicating lasers can add a message signal (compressed binary message) to the transmitted coupling signal and recover the message in both directions with high fidelity by using a mutual chaos pass filter procedure. An attacker, however, fails to recover an errorless message even if he amplifies the coupling signal.

Improved synchronization criteria for time-delayed chaotic Lur'e systems using sampled-data control

NASA Astrophysics Data System (ADS)

Duan, Wenyong; Li, Yan; Fu, Xiaorong; Du, Baozhu

2017-02-01

This paper is concerned with the synchronization for a class of time-delayed chaotic Lur’e systems using sampled-data control. Both of time-varying and time-invariant delays are considered. New criteria are proposed in terms of linear matrix inequalities (LMIs) by employing a modified LKF combined with the delay-fraction theory and some novel terms. The criteria are less conservative than some previous ones and a longer sampling period is achieved under the new results. Furthermore, the derived conditions are employed to design a sampled-data controller. The desired controller gain matrix can be obtained by means of the LMI approach. Finally, a numerical examples and simulations on Chua’s circuit is presented to show the effectiveness of the proposed approach.

Evidence for breathing modes in direct current, pulsed, and high power impulse magnetron sputtering plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Yuchen; Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720; Zhou, Xue

2016-01-18

We present evidence for breathing modes in magnetron sputtering plasmas: periodic axial variations of plasma parameters with characteristic frequencies between 10 and 100 kHz. A set of azimuthally distributed probes shows synchronous oscillations of the floating potential. They appear most clearly when considering the intermediate current regime in which the direction of azimuthal spoke motion changes. Breathing oscillations were found to be superimposed on azimuthal spoke motion. Depending on pressure and current, one can also find a regime of chaotic fluctuations and one of stable discharges, the latter at high current. A pressure-current phase diagram for the different situations is proposed.

Detection of generalized synchronization using echo state networks

NASA Astrophysics Data System (ADS)

Ibáñez-Soria, D.; Garcia-Ojalvo, J.; Soria-Frisch, A.; Ruffini, G.

2018-03-01

Generalized synchronization between coupled dynamical systems is a phenomenon of relevance in applications that range from secure communications to physiological modelling. Here, we test the capabilities of reservoir computing and, in particular, echo state networks for the detection of generalized synchronization. A nonlinear dynamical system consisting of two coupled Rössler chaotic attractors is used to generate temporal series consisting of time-locked generalized synchronized sequences interleaved with unsynchronized ones. Correctly tuned, echo state networks are able to efficiently discriminate between unsynchronized and synchronized sequences even in the presence of relatively high levels of noise. Compared to other state-of-the-art techniques of synchronization detection, the online capabilities of the proposed Echo State Network based methodology make it a promising choice for real-time applications aiming to monitor dynamical synchronization changes in continuous signals.

Parameter Estimation of Fractional-Order Chaotic Systems by Using Quantum Parallel Particle Swarm Optimization Algorithm

PubMed Central

Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng

2015-01-01

Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm. PMID:25603158

Chaotic dynamics of large-scale double-diffusive convection in a porous medium

NASA Astrophysics Data System (ADS)

Kondo, Shutaro; Gotoda, Hiroshi; Miyano, Takaya; Tokuda, Isao T.

2018-02-01

We have studied chaotic dynamics of large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan-Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.

Clustering stock market companies via chaotic map synchronization

NASA Astrophysics Data System (ADS)

Basalto, N.; Bellotti, R.; De Carlo, F.; Facchi, P.; Pascazio, S.

2005-01-01

A pairwise clustering approach is applied to the analysis of the Dow Jones index companies, in order to identify similar temporal behavior of the traded stock prices. To this end, the chaotic map clustering algorithm is used, where a map is associated to each company and the correlation coefficients of the financial time series to the coupling strengths between maps. The simulation of a chaotic map dynamics gives rise to a natural partition of the data, as companies belonging to the same industrial branch are often grouped together. The identification of clusters of companies of a given stock market index can be exploited in the portfolio optimization strategies.

Preliminary chaotic model of snapover on high voltage solar cells

NASA Technical Reports Server (NTRS)

Mackey, Willie R.

1995-01-01

High voltage power systems in space will interact with the space plasma in a variety of ways. One of these, snapover, is characterized by sudden enlargement of the current collection area across normally insulating surfaces generating enhanced electron current collection. Power drain on solar array power systems results from this enhanced current collection. Optical observations of the snapover phenomena in the laboratory indicates a functional relation between glow area and bia potential as a consequence of the fold/cusp bifurcation in chaos theory. Successful characterizations of snapover as a chaotic phenomena may provide a means of snapover prevention and control through chaotic synchronization.

Multiple period-doubling bifurcation route to chaos in periodically pulsed Murali-Lakshmanan-Chua circuit-controlling and synchronization of chaos.

PubMed

Parthasarathy, S; Manikandakumar, K

2007-12-01

We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system.

Video encryption using chaotic masks in joint transform correlator

NASA Astrophysics Data System (ADS)

Saini, Nirmala; Sinha, Aloka

2015-03-01

A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest-Shamir-Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique.

Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder

NASA Astrophysics Data System (ADS)

Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.; Kofane, T. C.

2010-08-01

In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.

Bifurcation behaviors of synchronized regions in logistic map networks with coupling delay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang, Longkun, E-mail: tomlk@hqu.edu.cn, E-mail: xqwu@whu.edu.cn; Wu, Xiaoqun, E-mail: tomlk@hqu.edu.cn, E-mail: xqwu@whu.edu.cn; Lu, Jun-an, E-mail: jalu@whu.edu.cn

2015-03-15

Network synchronized regions play an extremely important role in network synchronization according to the master stability function framework. This paper focuses on network synchronous state stability via studying the effects of nodal dynamics, coupling delay, and coupling way on synchronized regions in Logistic map networks. Theoretical and numerical investigations show that (1) network synchronization is closely associated with its nodal dynamics. Particularly, the synchronized region bifurcation points through which the synchronized region switches from one type to another are in good agreement with those of the uncoupled node system, and chaotic nodal dynamics can greatly impede network synchronization. (2) Themore » coupling delay generally impairs the synchronizability of Logistic map networks, which is also dominated by the parity of delay for some nodal parameters. (3) A simple nonlinear coupling facilitates network synchronization more than the linear one does. The results found in this paper will help to intensify our understanding for the synchronous state stability in discrete-time networks with coupling delay.« less

The Lyapunov-Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators

NASA Astrophysics Data System (ADS)

Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.

2017-05-01

This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.

Preliminary Chaotic Model of Snapover on High Voltage Solar Cells

NASA Technical Reports Server (NTRS)

Mackey, Willie R.

1995-01-01

High voltage power systems in space will interact with the space plasma in a variety of ways. One of these, Snapover, is characterized by a sudden enlargement of the electron current collection area across normally insulating surfaces. A power drain on solar array power systems will results from this enhanced current collection. Optical observations of the snapover phenomena in the laboratory indicates a functional relation between bia potential and surface glow area. This paper shall explore the potential benefits of modeling the relation between current and bia potential as an aspect of bifurcation analysis in chaos theory. Successful characterizations of snapover as a chaotic phenomena may provide a means of snapover prevention and control through chaotic synchronization.

Physical layer one-time-pad data encryption through synchronized semiconductor laser networks

NASA Astrophysics Data System (ADS)

Argyris, Apostolos; Pikasis, Evangelos; Syvridis, Dimitris

2016-02-01

Semiconductor lasers (SL) have been proven to be a key device in the generation of ultrafast true random bit streams. Their potential to emit chaotic signals under conditions with desirable statistics, establish them as a low cost solution to cover various needs, from large volume key generation to real-time encrypted communications. Usually, only undemanding post-processing is needed to convert the acquired analog timeseries to digital sequences that pass all established tests of randomness. A novel architecture that can generate and exploit these true random sequences is through a fiber network in which the nodes are semiconductor lasers that are coupled and synchronized to central hub laser. In this work we show experimentally that laser nodes in such a star network topology can synchronize with each other through complex broadband signals that are the seed to true random bit sequences (TRBS) generated at several Gb/s. The potential for each node to access real-time generated and synchronized with the rest of the nodes random bit streams, through the fiber optic network, allows to implement an one-time-pad encryption protocol that mixes the synchronized true random bit sequence with real data at Gb/s rates. Forward-error correction methods are used to reduce the errors in the TRBS and the final error rate at the data decoding level. An appropriate selection in the sampling methodology and properties, as well as in the physical properties of the chaotic seed signal through which network locks in synchronization, allows an error free performance.

Consistency properties of chaotic systems driven by time-delayed feedback

NASA Astrophysics Data System (ADS)

Jüngling, T.; Soriano, M. C.; Oliver, N.; Porte, X.; Fischer, I.

2018-04-01

Consistency refers to the property of an externally driven dynamical system to respond in similar ways to similar inputs. In a delay system, the delayed feedback can be considered as an external drive to the undelayed subsystem. We analyze the degree of consistency in a generic chaotic system with delayed feedback by means of the auxiliary system approach. In this scheme an identical copy of the nonlinear node is driven by exactly the same signal as the original, allowing us to verify complete consistency via complete synchronization. In the past, the phenomenon of synchronization in delay-coupled chaotic systems has been widely studied using correlation functions. Here, we analytically derive relationships between characteristic signatures of the correlation functions in such systems and unequivocally relate them to the degree of consistency. The analytical framework is illustrated and supported by numerical calculations of the logistic map with delayed feedback for different replica configurations. We further apply the formalism to time series from an experiment based on a semiconductor laser with a double fiber-optical feedback loop. The experiment constitutes a high-quality replica scheme for studying consistency of the delay-driven laser and confirms the general theoretical results.

Introduction to focus issue: Synchronization in large networks and continuous media—data, models, and supermodels

NASA Astrophysics Data System (ADS)

Duane, Gregory S.; Grabow, Carsten; Selten, Frank; Ghil, Michael

2017-12-01

The synchronization of loosely coupled chaotic systems has increasingly found applications to large networks of differential equations and to models of continuous media. These applications are at the core of the present Focus Issue. Synchronization between a system and its model, based on limited observations, gives a new perspective on data assimilation. Synchronization among different models of the same system defines a supermodel that can achieve partial consensus among models that otherwise disagree in several respects. Finally, novel methods of time series analysis permit a better description of synchronization in a system that is only observed partially and for a relatively short time. This Focus Issue discusses synchronization in extended systems or in components thereof, with particular attention to data assimilation, supermodeling, and their applications to various areas, from climate modeling to macroeconomics.

Introduction to focus issue: Synchronization in large networks and continuous media-data, models, and supermodels.

PubMed

Duane, Gregory S; Grabow, Carsten; Selten, Frank; Ghil, Michael

2017-12-01

The synchronization of loosely coupled chaotic systems has increasingly found applications to large networks of differential equations and to models of continuous media. These applications are at the core of the present Focus Issue. Synchronization between a system and its model, based on limited observations, gives a new perspective on data assimilation. Synchronization among different models of the same system defines a supermodel that can achieve partial consensus among models that otherwise disagree in several respects. Finally, novel methods of time series analysis permit a better description of synchronization in a system that is only observed partially and for a relatively short time. This Focus Issue discusses synchronization in extended systems or in components thereof, with particular attention to data assimilation, supermodeling, and their applications to various areas, from climate modeling to macroeconomics.

Dynamical noise filter and conditional entropy analysis in chaos synchronization.

PubMed

Wang, Jiao; Lai, C-H

2006-06-01

It is shown that, in a chaotic synchronization system whose driving signal is exposed to channel noise, the estimation of the drive system states can be greatly improved by applying the dynamical noise filtering to the response system states. If the noise is bounded in a certain range, the estimation errors, i.e., the difference between the filtered responding states and the driving states, can be made arbitrarily small. This property can be used in designing an alternative digital communication scheme. An analysis based on the conditional entropy justifies the application of dynamical noise filtering in generating quality synchronization.

A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization.

PubMed

Zhao, Shouwei

2011-06-01

A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.

Terminal Transient Phase of Chaotic Transients

NASA Astrophysics Data System (ADS)

Lilienkamp, Thomas; Parlitz, Ulrich

2018-03-01

Transient chaos in spatially extended systems can be characterized by the length of the transient phase, which typically grows quickly with the system size (supertransients). For a large class of these systems, the chaotic phase terminates abruptly, without any obvious precursors in commonly used observables. Here we investigate transient spatiotemporal chaos in two different models of this class. By probing the state space using perturbed trajectories we show the existence of a "terminal transient phase," which occurs prior to the abrupt collapse of chaotic dynamics. During this phase the impact of perturbations is significantly different from the earlier transient and particular patterns of (non)susceptible regions in state space occur close to the chaotic trajectories. We therefore hypothesize that even without perturbations proper precursors for the collapse of chaotic transients exist, which might be highly relevant for coping with spatiotemporal chaos in cardiac arrhythmias or brain functionality, for example.

Underwater Chaotic Lidar using Blue Laser Diodes

NASA Astrophysics Data System (ADS)

Rumbaugh, Luke K.

The thesis proposes and explores an underwater lidar system architecture based on chaotic modulation of recently introduced, commercially available, low cost blue laser diodes. This approach is experimentally shown to allow accurate underwater impulse response measurements while eliminating the need for several major components typically found in high-performance underwater lidar systems. The proposed approach is to: 1. Generate wideband, noise-like intensity modulation signals using optical chaotic modulation of blue-green laser diodes, and then 2. Use this signal source to develop an underwater chaotic lidar system that uses no electrical signal generator, no electro-optic modulator, no optical frequency doubler, and no large-aperture photodetector. The outcome of this thesis is the demonstration of a new underwater lidar system architecture that could allow high resolution ranging, imaging, and water profiling measurements in turbid water, at a reduced size, weight, power and cost relative to state-of-the-art high-performance underwater lidar sensors. This work also makes contributions to the state of the art in optics, nonlinear dynamics, and underwater sensing by demonstrating for the first time: 1. Wideband noise-like intensity modulation of a blue laser diode using no electrical signal generator or electro-optic modulator. Optical chaotic modulation of a 462 nm blue InGaN laser diode by self-feedback is explored for the first time. The usefulness of the signal to chaotic lidar is evaluated in terms of bandwidth, modulation depth, and autocorrelation peak-to-sidelobe-ratio (PSLR) using both computer and laboratory experiments. In laboratory experiments, the optical feedback technique is shown to be effective in generating wideband, noise-like chaotic signals with strong modulation depth when the diode is operated in an external-cavity dominated state. The modulation signal strength is shown to be limited by the onset of lasing within the diode's internal cavity. The possibility of overcoming this limit by increasing optical feedback strength is discussed. 2. Power scaling in the blue-green spectrum using no optical frequency doubler. Synchronization of two 462 nm blue InGaN laser diodes by bi-directional optical injection is demonstrated for the first time in laboratory experiments. The improvement in chaotic intensity modulation signal strength is demonstrated to be 2.5x over the single-diode case. The signal strength is again shown to be limited by the onset of internal cavity lasing. The synchronized-laser arrangement is shown to be theoretically equivalent to a single-diode scenario in which the optical feedback is amplified by 2x, supporting the idea that increased optical feedback strength can be used to scale optical chaotic modulation of InGaN diodes to high powers. 3. Underwater impulse response measurements using a calibrated chaotic lidar system. An underwater chaotic lidar system using two synchronized diodes as transmitters is demonstrated in laboratory experiments for the first time. Reflective impulse response measurements using the lidar system are made in free space, and in a variety of clear and turbid water conditions, using a quasi-monostatic (i.e. co-located transmitter and receiver) arrangement. A calibration routine is implemented that increases accuracy and instantaneous dynamic range of the impulse response measurement, resulting in a baseline temporal resolution of 750 ps and a PSLR of over 10 dB. The calibrated system is shown to be able to simultaneously measure localized and distributed reflections, and to allow separation of the localized ( i.e. surface and target) reflections from the distributed ( i.e. backscatter) returns in several domains. Accurate range measurement with sub-inch typical error is demonstrated in laboratory water tank tests, which show accurate measurement through >6 feet of turbid water, as limited by the experimental water tank setup. Strong performance to the limit of the setup is shown at dwell times down to 1 mus. 4. Range measurement through turbid water using no large-aperture photodetector. The possibility of using a synchronized optical receiver to make range measurements through an attenuating channel (i.e. turbid water) is tested using two InGaN diodes for the first time. Using a variable optical attenuator to simulate channel attenuation, synchronization is maintained through 30 dB channel attenuation in the current experimental setup. Distance measurements are demonstrated by using the output of only one of the two diodes, suggesting that this method could be used to measure distance between two bi-static (i.e. physically separated), cooperative chaotic lidar systems in some water conditions. This thesis concludes that the proposed approach is a feasible path to a novel high resolution underwater lidar sensor capable of operating in turbid water, which would have significant size, weight, power, and cost reductions because it would not use an electrical signal generator, an electro-optic modulator, or an optical frequency doubler. The work also suggests the possibility of range measurement in a limited range of water conditions using no large-aperture photodetector, most feasibly in a bi-static cooperative arrangement.

A Spatiotemporal-Chaos-Based Cryptosystem Taking Advantage of Both Synchronous and Self-Synchronizing Schemes

NASA Astrophysics Data System (ADS)

Lü, Hua-Ping; Wang, Shi-Hong; Li, Xiao-Wen; Tang, Guo-Ning; Kuang, Jin-Yu; Ye, Wei-Ping; Hu, Gang

2004-06-01

Two-dimensional one-way coupled map lattices are used for cryptography where multiple space units produce chaotic outputs in parallel. One of the outputs plays the role of driving for synchronization of the decryption system while the others perform the function of information encoding. With this separation of functions the receiver can establish a self-checking and self-correction mechanism, and enjoys the advantages of both synchronous and self-synchronizing schemes. A comparison between the present system with the system of advanced encryption standard (AES) is presented in the aspect of channel noise influence. Numerical investigations show that our system is much stronger than AES against channel noise perturbations, and thus can be better used for secure communications with large channel noise.

Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network.

PubMed

Keplinger, Keegan; Wackerbauer, Renate

2014-03-01

Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.

Reconstructions of parameters of radiophysical chaotic generator with delayed feedback from short time series

NASA Astrophysics Data System (ADS)

Ishbulatov, Yu. M.; Karavaev, A. S.; Kiselev, A. R.; Semyachkina-Glushkovskaya, O. V.; Postnov, D. E.; Bezruchko, B. P.

2018-04-01

A method for the reconstruction of time-delayed feedback system is investigated, which is based on the detection of synchronous response of a slave time-delay system with respect to the driving from the master system under study. The structure of the driven system is similar to the structure of the studied time-delay system, but the feedback circuit is broken in the driven system. The method efficiency is tested using short and noisy data gained from an electronic chaotic oscillator with time-delayed feedback.

Synchronization and bidirectional communication without delay line using strong mutually coupled semiconductor lasers

NASA Astrophysics Data System (ADS)

Li, Guang-Hui; Wang, An-Bang; Feng, Ye; Wang, Yang

2010-07-01

This paper numerically demonstrates synchronization and bidirectional communication without delay line by using two semiconductor lasers with strong mutual injection in a face-to-face configuration. These results show that both of the two lasers' outputs synchronize with their input chaotic carriers. In addition, simulations demonstrate that this kind of synchronization can be used to realize bidirectional communications without delay line. Further studies indicate that within a small deviation in message amplitudes of two sides (±6%), the message can be extracted with signal-noise-ratio more than 10 dB; and the signal-noise-ratio is extremely sensitive to the message rates mismatch of two sides, which may be used as a key of bidirectional communication.

Atypical transistor-based chaotic oscillators: Design, realization, and diversity

NASA Astrophysics Data System (ADS)

Minati, Ludovico; Frasca, Mattia; OświÈ©cimka, Paweł; Faes, Luca; DroŻdŻ, Stanisław

2017-07-01

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.

Atypical transistor-based chaotic oscillators: Design, realization, and diversity.

PubMed

Minati, Ludovico; Frasca, Mattia; Oświȩcimka, Paweł; Faes, Luca; Drożdż, Stanisław

2017-07-01

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.

Non-stationary dynamics in the bouncing ball: A wavelet perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Behera, Abhinna K., E-mail: abhinna@iiserkol.ac.in; Panigrahi, Prasanta K., E-mail: pprasanta@iiserkol.ac.in; Sekar Iyengar, A. N., E-mail: ansekar.iyengar@saha.ac.in

2014-12-01

The non-stationary dynamics of a bouncing ball, comprising both periodic as well as chaotic behavior, is studied through wavelet transform. The multi-scale characterization of the time series displays clear signatures of self-similarity, complex scaling behavior, and periodicity. Self-similar behavior is quantified by the generalized Hurst exponent, obtained through both wavelet based multi-fractal detrended fluctuation analysis and Fourier methods. The scale dependent variable window size of the wavelets aptly captures both the transients and non-stationary periodic behavior, including the phase synchronization of different modes. The optimal time-frequency localization of the continuous Morlet wavelet is found to delineate the scales corresponding tomore » neutral turbulence, viscous dissipation regions, and different time varying periodic modulations.« less

Noise and coupling induced synchronization in a network of chaotic neurons

NASA Astrophysics Data System (ADS)

Ciszak, Marzena; Euzzor, Stefano; Geltrude, Andrea; Tito Arecchi, F.; Meucci, Riccardo

2013-04-01

The synchronization in four forced FitzHugh-Nagumo (FHN) systems is studied, both experimentally and by numerical simulations of a model. We show that synchronization may be achieved either by coupling of systems through bidirectional diffusive interactions, by introducing a common noise to all systems or by combining both ingredients, noise and coupling together. Here we consider white and colored noises, showing that the colored noise is more efficient in synchronizing the systems respect to white noise. Moreover, a small addition of common noise allows the synchronization to occur at smaller values of the coupling strength. When the diffusive coupling in the absence of noise is considered, the system undergoes the transition to subthreshold oscillations, giving a spike suppression regime. We show that noise destroys the appearance of this dynamical regime induced by coupling.

Time-shifted synchronization of chaotic oscillator chains without explicit coupling delays.

PubMed

Blakely, Jonathan N; Stahl, Mark T; Corron, Ned J

2009-12-01

We examine chains of unidirectionally coupled oscillators in which time-shifted synchronization occurs without explicit delays in the coupling. In numerical simulations and in an experimental system of electronic oscillators, we examine the time shift and the degree of distortion (primarily in the form of attenuation) of the waveforms of the oscillators located far from the drive oscillator. Surprisingly, under weak coupling we observe minimal attenuation in spite of a significant total time shift. In contrast, at higher coupling strengths the observed attenuation increases dramatically and approaches the value predicted by an analytically derived estimate. In this regime, we verify directly that generalized synchronization is maintained over the entire chain length despite severe attenuation. These results suggest that weak coupling generally may produce higher quality synchronization in systems for which truly identical synchronization is not possible.

Synchronization control in multiplex networks of nonlinear multi-agent systems

NASA Astrophysics Data System (ADS)

He, Wangli; Xu, Zhiwei; Du, Wenli; Chen, Guanrong; Kubota, Naoyuki; Qian, Feng

2017-12-01

This paper is concerned with synchronization control of a multiplex network, in which two different kinds of relationships among agents coexist. Hybrid coupling, including continuous linear coupling and impulsive coupling, is proposed to model the coexisting distinguishable interactions. First, by adding impulsive controllers on a small portion of agents, local synchronization is analyzed by linearizing the error system at the desired trajectory. Then, global synchronization is studied based on the Lyapunov stability theory, where a time-varying coupling strength is involved. To further deal with the time-varying coupling strength, an adaptive updating law is introduced and a corresponding sufficient condition is obtained to ensure synchronization of the multiplex network towards the desired trajectory. Networks of Chua's circuits and other chaotic systems with double layers of interactions are simulated to verify the proposed method.

Synchronizability of random rectangular graphs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Estrada, Ernesto, E-mail: ernesto.estrada@strath.ac.uk; Chen, Guanrong

2015-08-15

Random rectangular graphs (RRGs) represent a generalization of the random geometric graphs in which the nodes are embedded into hyperrectangles instead of on hypercubes. The synchronizability of RRG model is studied. Both upper and lower bounds of the eigenratio of the network Laplacian matrix are determined analytically. It is proven that as the rectangular network is more elongated, the network becomes harder to synchronize. The synchronization processing behavior of a RRG network of chaotic Lorenz system nodes is numerically investigated, showing complete consistence with the theoretical results.

Chaotic attractors with separated scrolls

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bouallegue, Kais, E-mail: kais-bouallegue@yahoo.fr

2015-07-15

This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This newmore » approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results.« less

Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks.

PubMed

Chen, Wu-Hua; Lu, Xiaomei; Zheng, Wei Xing

2015-04-01

This paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs). Two types of DDNNs with stabilizing impulses are studied. By introducing the time-varying Lyapunov functional to capture the dynamical characteristics of discrete-time impulsive delayed neural networks (DIDNNs) and by using a convex combination technique, new exponential stability criteria are derived in terms of linear matrix inequalities. The stability criteria for DIDNNs are independent of the size of time delay but rely on the lengths of impulsive intervals. With the newly obtained stability results, sufficient conditions on the existence of linear-state feedback impulsive controllers are derived. Moreover, a novel impulsive synchronization scheme for two identical DDNNs is proposed. The novel impulsive synchronization scheme allows synchronizing two identical DDNNs with unknown delays. Simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of DDNNs. Finally, an application of the obtained impulsive synchronization result for two identical chaotic DDNNs to a secure communication scheme is presented.

Interaction Control to Synchronize Non-synchronizable Networks.

PubMed

Schröder, Malte; Chakraborty, Sagar; Witthaut, Dirk; Nagler, Jan; Timme, Marc

2016-11-17

Synchronization constitutes one of the most fundamental collective dynamics across networked systems and often underlies their function. Whether a system may synchronize depends on the internal unit dynamics as well as the topology and strength of their interactions. For chaotic units with certain interaction topologies synchronization might be impossible across all interaction strengths, meaning that these networks are non-synchronizable. Here we propose the concept of interaction control, generalizing transient uncoupling, to induce desired collective dynamics in complex networks and apply it to synchronize even such non-synchronizable systems. After highlighting that non-synchronizability prevails for a wide range of networks of arbitrary size, we explain how a simple binary control may localize interactions in state space and thereby synchronize networks. Intriguingly, localizing interactions by a fixed control scheme enables stable synchronization across all connected networks regardless of topological constraints. Interaction control may thus ease the design of desired collective dynamics even without knowledge of the networks' exact interaction topology and consequently have implications for biological and self-organizing technical systems.

Interaction Control to Synchronize Non-synchronizable Networks

PubMed Central

Schröder, Malte; Chakraborty, Sagar; Witthaut, Dirk; Nagler, Jan; Timme, Marc

2016-01-01

Synchronization constitutes one of the most fundamental collective dynamics across networked systems and often underlies their function. Whether a system may synchronize depends on the internal unit dynamics as well as the topology and strength of their interactions. For chaotic units with certain interaction topologies synchronization might be impossible across all interaction strengths, meaning that these networks are non-synchronizable. Here we propose the concept of interaction control, generalizing transient uncoupling, to induce desired collective dynamics in complex networks and apply it to synchronize even such non-synchronizable systems. After highlighting that non-synchronizability prevails for a wide range of networks of arbitrary size, we explain how a simple binary control may localize interactions in state space and thereby synchronize networks. Intriguingly, localizing interactions by a fixed control scheme enables stable synchronization across all connected networks regardless of topological constraints. Interaction control may thus ease the design of desired collective dynamics even without knowledge of the networks’ exact interaction topology and consequently have implications for biological and self-organizing technical systems. PMID:27853266

Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam

NASA Astrophysics Data System (ADS)

Awrejcewicz, J.; Krysko, V. A.; Yakovleva, T. V.; Pavlov, S. P.; Krysko, V. A.

2018-05-01

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

Secure Communication Based on a Hybrid of Chaos and Ica Encryptions

NASA Astrophysics Data System (ADS)

Chen, Wei Ching; Yuan, John

Chaos and independent component analysis (ICA) encryptions are two novel schemes for secure communications. In this paper, a new scheme combining chaos and ICA techniques is proposed to enhance the security level during communication. In this scheme, a master chaotic system is embedded at the transmitter. The message signal is mixed with a chaotic signal and a Gaussian white noise into two mixed signals and then transmitted to the receiver through the public channels. A signal for synchronization is transmitted through another public channel to the receiver where a slave chaotic system is embedded to reproduce the chaotic signal. A modified ICA is used to recover the message signal at the receiver. Since only two of the three transmitted signals contain the information of message signal, a hacker would not be able to retrieve the message signal by using ICA even though all the transmitted signals are intercepted. Spectrum analyses are used to prove that the message signal can be securely hidden under this scheme.

Elimination of spiral waves in a locally connected chaotic neural network by a dynamic phase space constraint.

PubMed

Li, Yang; Oku, Makito; He, Guoguang; Aihara, Kazuyuki

2017-04-01

In this study, a method is proposed that eliminates spiral waves in a locally connected chaotic neural network (CNN) under some simplified conditions, using a dynamic phase space constraint (DPSC) as a control method. In this method, a control signal is constructed from the feedback internal states of the neurons to detect phase singularities based on their amplitude reduction, before modulating a threshold value to truncate the refractory internal states of the neurons and terminate the spirals. Simulations showed that with appropriate parameter settings, the network was directed from a spiral wave state into either a plane wave (PW) state or a synchronized oscillation (SO) state, where the control vanished automatically and left the original CNN model unaltered. Each type of state had a characteristic oscillation frequency, where spiral wave states had the highest, and the intra-control dynamics was dominated by low-frequency components, thereby indicating slow adjustments to the state variables. In addition, the PW-inducing and SO-inducing control processes were distinct, where the former generally had longer durations but smaller average proportions of affected neurons in the network. Furthermore, variations in the control parameter allowed partial selectivity of the control results, which were accompanied by modulation of the control processes. The results of this study broaden the applicability of DPSC to chaos control and they may also facilitate the utilization of locally connected CNNs in memory retrieval and the exploration of traveling wave dynamics in biological neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Synchronicity from synchronized chaos

DOE PAGES

Duane, Gregory

2015-04-01

The synchronization of loosely-coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical concept of “synchronicity”—the commonplace notion that related events mysteriously occur at the same time. When extended to continuous media and/or large discrete arrays, and when general (non-identical) correspondences are considered between states, intermittent synchronous relationships indeed become ubiquitous. Meaningful synchronicity follows naturally if meaningful events are identified with coherent structures, defined by internal synchronization between remote degrees of freedom; a condition that has been posited as necessary for synchronizability with an external system. The important case of synchronization between mind andmore » matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system, as in meteorological data assimilation. Evidence for the ubiquity of synchronization is reviewed along with recent proposals that: (1) synchronization of different models of the same objective process may be an expeditious route to improved computational modeling and may also describe the functioning of conscious brains; and (2) the nonlocality in quantum phenomena implied by Bell’s theorem may be explained in a variety of deterministic (hidden variable) interpretations if the quantum world resides on a generalized synchronization “manifold”.« less

Synchronicity from synchronized chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duane, Gregory

The synchronization of loosely-coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical concept of “synchronicity”—the commonplace notion that related events mysteriously occur at the same time. When extended to continuous media and/or large discrete arrays, and when general (non-identical) correspondences are considered between states, intermittent synchronous relationships indeed become ubiquitous. Meaningful synchronicity follows naturally if meaningful events are identified with coherent structures, defined by internal synchronization between remote degrees of freedom; a condition that has been posited as necessary for synchronizability with an external system. The important case of synchronization between mind andmore » matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system, as in meteorological data assimilation. Evidence for the ubiquity of synchronization is reviewed along with recent proposals that: (1) synchronization of different models of the same objective process may be an expeditious route to improved computational modeling and may also describe the functioning of conscious brains; and (2) the nonlocality in quantum phenomena implied by Bell’s theorem may be explained in a variety of deterministic (hidden variable) interpretations if the quantum world resides on a generalized synchronization “manifold”.« less

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Karthikeyan, Anitha; Duraisamy, Prakash

2017-06-01

In this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

Controlling chaos with localized heterogeneous forces in oscillator chains.

PubMed

Chacón, Ricardo

2006-10-01

The effects of decreasing the impulse transmitted by localized periodic pulses on the chaotic behavior of homogeneous chains of coupled nonlinear oscillators are studied. It is assumed that when the oscillators are driven synchronously, i.e., all driving pulses transmit the same impulse, the chains display chaotic dynamics. It is shown that decreasing the impulse transmitted by the pulses of the two free end oscillators results in regularization with the whole array exhibiting frequency synchronization, irrespective of the chain size. A maximum level of amplitude desynchrony as the pulses of the two end oscillators narrow is typically found, which is explained as the result of two competing universal mechanisms: desynchronization induced by localized heterogeneous pulses and oscillation death of the complete chain induced by drastic decreasing of the impulse transmitted by such localized pulses. These findings demonstrate that decreasing the impulse transmitted by localized external forces can suppress chaos and lead to frequency-locked states in networks of dissipative systems.

Finite-time synchronization for memristor-based neural networks with time-varying delays.

PubMed

Abdurahman, Abdujelil; Jiang, Haijun; Teng, Zhidong

2015-09-01

Memristive network exhibits state-dependent switching behaviors due to the physical properties of memristor, which is an ideal tool to mimic the functionalities of the human brain. In this paper, finite-time synchronization is considered for a class of memristor-based neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, several new sufficient conditions ensuring the finite-time synchronization of memristor-based chaotic neural networks are obtained by using analysis technique, finite time stability theorem and adding a suitable feedback controller. Besides, the upper bounds of the settling time of synchronization are estimated. Finally, a numerical example is given to show the effectiveness and feasibility of the obtained results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Enhancing synchrony in chaotic oscillators by dynamic relaying

NASA Astrophysics Data System (ADS)

Banerjee, Ranjib; Ghosh, Dibakar; Padmanaban, E.; Ramaswamy, R.; Pecora, L. M.; Dana, Syamal K.

2012-02-01

In a chain of mutually coupled oscillators, the coupling threshold for synchronization between the outermost identical oscillators decreases when a type of impurity (in terms of parameter mismatch) is introduced in the inner oscillator(s). The outer oscillators interact indirectly via dynamic relaying, mediated by the inner oscillator(s). We confirm this enhancing of critical coupling in the chaotic regimes of the Lorenz system, in the Rössler system in the absence of coupling delay, and in the Mackey-Glass system with delay coupling. The enhancing effect is experimentally verified in the electronic circuit of Rössler oscillators.

Chaotic behavior in Casimir oscillators: A case study for phase-change materials.

PubMed

Tajik, Fatemeh; Sedighi, Mehdi; Khorrami, Mohammad; Masoudi, Amir Ali; Palasantzas, George

2017-10-01

Casimir forces between material surfaces at close proximity of less than 200 nm can lead to increased chaotic behavior of actuating devices depending on the strength of the Casimir interaction. We investigate these phenomena for phase-change materials in torsional oscillators, where the amorphous to crystalline phase transitions lead to transitions between high and low Casimir force and torque states, respectively, without material compositions. For a conservative system bifurcation curve and Poincare maps analysis show the absence of chaotic behavior but with the crystalline phase (high force-torque state) favoring more unstable behavior and stiction. However, for a nonconservative system chaotic behavior can take place introducing significant risk for stiction, which is again more pronounced for the crystalline phase. The latter illustrates the more general scenario that stronger Casimir forces and torques increase the possibility for chaotic behavior. The latter is making it impossible to predict whether stiction or stable actuation will occur on a long-term basis, and it is setting limitations in the design of micronano devices operating at short-range nanoscale separations.

Urey Prize Lecture - Chaotic dynamics in the solar system

NASA Technical Reports Server (NTRS)

Wisdom, Jack

1987-01-01

Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.

Synchronicity in predictive modelling: a new view of data assimilation

NASA Astrophysics Data System (ADS)

Duane, G. S.; Tribbia, J. J.; Weiss, J. B.

2006-11-01

The problem of data assimilation can be viewed as one of synchronizing two dynamical systems, one representing "truth" and the other representing "model", with a unidirectional flow of information between the two. Synchronization of truth and model defines a general view of data assimilation, as machine perception, that is reminiscent of the Jung-Pauli notion of synchronicity between matter and mind. The dynamical systems paradigm of the synchronization of a pair of loosely coupled chaotic systems is expected to be useful because quasi-2D geophysical fluid models have been shown to synchronize when only medium-scale modes are coupled. The synchronization approach is equivalent to standard approaches based on least-squares optimization, including Kalman filtering, except in highly non-linear regions of state space where observational noise links regimes with qualitatively different dynamics. The synchronization approach is used to calculate covariance inflation factors from parameters describing the bimodality of a one-dimensional system. The factors agree in overall magnitude with those used in operational practice on an ad hoc basis. The calculation is robust against the introduction of stochastic model error arising from unresolved scales.

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1990-01-01

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

Distributed MIMO chaotic radar based on wavelength-division multiplexing technology.

PubMed

Yao, Tingfeng; Zhu, Dan; Ben, De; Pan, Shilong

2015-04-15

A distributed multiple-input multiple-output chaotic radar based on wavelength-division multiplexing technology (WDM) is proposed and demonstrated. The wideband quasi-orthogonal chaotic signals generated by different optoelectronic oscillators (OEOs) are emitted by separated antennas to gain spatial diversity against the fluctuation of a target's radar cross section and enhance the detection capability. The received signals collected by the receive antennas and the reference signals from the OEOs are delivered to the central station for joint processing by exploiting WDM technology. The centralized signal processing avoids precise time synchronization of the distributed system and greatly simplifies the remote units, which improves the localization accuracy of the entire system. A proof-of-concept experiment for two-dimensional localization of a metal target is demonstrated. The maximum position error is less than 6.5 cm.

Forced synchronization of large-scale circulation to increase predictability of surface states

NASA Astrophysics Data System (ADS)

Shen, Mao-Lin; Keenlyside, Noel; Selten, Frank; Wiegerinck, Wim; Duane, Gregory

2016-04-01

Numerical models are key tools in the projection of the future climate change. The lack of perfect initial condition and perfect knowledge of the laws of physics, as well as inherent chaotic behavior limit predictions. Conceptually, the atmospheric variables can be decomposed into a predictable component (signal) and an unpredictable component (noise). In ensemble prediction the anomaly of ensemble mean is regarded as the signal and the ensemble spread the noise. Naturally the prediction skill will be higher if the signal-to-noise ratio (SNR) is larger in the initial conditions. We run two ensemble experiments in order to explore a way to reduce the SNR of surface winds and temperature. One ensemble experiment is AGCM with prescribing sea surface temperature (SST); the other is AGCM with both prescribing SST and nudging the high-level temperature and winds to ERA-Interim. Each ensemble has 30 members. Larger SNR is expected and found over the tropical ocean in the first experiment because the tropical circulation is associated with the convection and the associated surface wind convergence as these are to a large extent driven by the SST. However, small SNR is found over high latitude ocean and land surface due to the chaotic and non-synchronized atmosphere states. In the second experiment the higher level temperature and winds are forced to be synchronized (nudged to reanalysis) and hence a larger SNR of surface winds and temperature is expected. Furthermore, different nudging coefficients are also tested in order to understand the limitation of both synchronization of large-scale circulation and the surface states. These experiments will be useful for the developing strategies to synchronize the 3-D states of atmospheric models that can be later used to build a super model.

Partially chaotic orbits in a perturbed cubic force model

NASA Astrophysics Data System (ADS)

Muzzio, J. C.

2017-11-01

Three types of orbits are theoretically possible in autonomous Hamiltonian systems with 3 degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity or that a long enough follow-up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three-dimensional cubic force toy model, and a generalization of the Poincaré maps to show that partially chaotic orbits are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbit.

Transition to complete synchronization and global intermittent synchronization in an array of time-delay systems.

PubMed

Suresh, R; Senthilkumar, D V; Lakshmanan, M; Kurths, J

2012-07-01

We report the nature of transitions from the nonsynchronous to a complete synchronization (CS) state in arrays of time-delay systems, where the systems are coupled with instantaneous diffusive coupling. We demonstrate that the transition to CS occurs distinctly for different coupling configurations. In particular, for unidirectional coupling, locally (microscopically) synchronization transition occurs in a very narrow range of coupling strength but for a global one (macroscopically) it occurs sequentially in a broad range of coupling strength preceded by an intermittent synchronization. On the other hand, in the case of mutual coupling, a very large value of coupling strength is required for local synchronization and, consequently, all the local subsystems synchronize immediately for the same value of the coupling strength and, hence, globally, synchronization also occurs in a narrow range of the coupling strength. In the transition regime, we observe a type of synchronization transition where long intervals of high-quality synchronization which are interrupted at irregular times by intermittent chaotic bursts simultaneously in all the systems and which we designate as global intermittent synchronization. We also relate our synchronization transition results to the above specific types using unstable periodic orbit theory. The above studies are carried out in a well-known piecewise linear time-delay system.

Improving performance of DS-CDMA systems using chaotic complex Bernoulli spreading codes

NASA Astrophysics Data System (ADS)

Farzan Sabahi, Mohammad; Dehghanfard, Ali

2014-12-01

The most important goal of spreading spectrum communication system is to protect communication signals against interference and exploitation of information by unintended listeners. In fact, low probability of detection and low probability of intercept are two important parameters to increase the performance of the system. In Direct Sequence Code Division Multiple Access (DS-CDMA) systems, these properties are achieved by multiplying the data information in spreading sequences. Chaotic sequences, with their particular properties, have numerous applications in constructing spreading codes. Using one-dimensional Bernoulli chaotic sequence as spreading code is proposed in literature previously. The main feature of this sequence is its negative auto-correlation at lag of 1, which with proper design, leads to increase in efficiency of the communication system based on these codes. On the other hand, employing the complex chaotic sequences as spreading sequence also has been discussed in several papers. In this paper, use of two-dimensional Bernoulli chaotic sequences is proposed as spreading codes. The performance of a multi-user synchronous and asynchronous DS-CDMA system will be evaluated by applying these sequences under Additive White Gaussian Noise (AWGN) and fading channel. Simulation results indicate improvement of the performance in comparison with conventional spreading codes like Gold codes as well as similar complex chaotic spreading sequences. Similar to one-dimensional Bernoulli chaotic sequences, the proposed sequences also have negative auto-correlation. Besides, construction of complex sequences with lower average cross-correlation is possible with the proposed method.

Transient Resetting: A Novel Mechanism for Synchrony and Its Biological Examples

PubMed Central

Li, Chunguang; Chen, Luonan; Aihara, Kazuyuki

2006-01-01

The study of synchronization in biological systems is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. In this paper, by using simple dynamical systems theory, we present a novel mechanism, named transient resetting, for the synchronization of uncoupled biological oscillators with stimuli. This mechanism not only can unify and extend many existing results on (deterministic and stochastic) stimulus-induced synchrony, but also may actually play an important role in biological rhythms. We argue that transient resetting is a possible mechanism for the synchronization in many biological organisms, which might also be further used in the medical therapy of rhythmic disorders. Examples of the synchronization of neural and circadian oscillators as well as a chaotic neuron model are presented to verify our hypothesis. PMID:16933980

Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays

NASA Astrophysics Data System (ADS)

Zhang, Chuan; Wang, Xingyuan; Luo, Chao; Li, Junqiu; Wang, Chunpeng

2018-03-01

In this paper, we focus on the robust outer synchronization problem between two nonlinear complex networks with parametric disturbances and mixed time-varying delays. Firstly, a general complex network model is proposed. Besides the nonlinear couplings, the network model in this paper can possess parametric disturbances, internal time-varying delay, discrete time-varying delay and distributed time-varying delay. Then, according to the robust control strategy, linear matrix inequality and Lyapunov stability theory, several outer synchronization protocols are strictly derived. Simple linear matrix controllers are designed to driver the response network synchronize to the drive network. Additionally, our results can be applied on the complex networks without parametric disturbances. Finally, by utilizing the delayed Lorenz chaotic system as the dynamics of all nodes, simulation examples are given to demonstrate the effectiveness of our theoretical results.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oliveira, Gilson F. de, E-mail: gilson@otica.ufpb.br; Lorenzo, Orlando di; Chevrollier, Martine

We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complexmore » systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.« less

Discrete-time systems with random switches: From systems stability to networks synchronization.

PubMed

Guo, Yao; Lin, Wei; Ho, Daniel W C

2016-03-01

In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developed approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.

Discrete-time systems with random switches: From systems stability to networks synchronization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Yao; Lin, Wei, E-mail: wlin@fudan.edu.cn; Shanghai Key Laboratory of Contemporary Applied Mathematics, LMNS, and Shanghai Center for Mathematical Sciences, Shanghai 200433

2016-03-15

In this article, we develop some approaches, which enable us to more accurately and analytically identify the essential patterns that guarantee the almost sure stability of discrete-time systems with random switches. We allow for the case that the elements in the switching connection matrix even obey some unbounded and continuous-valued distributions. In addition to the almost sure stability, we further investigate the almost sure synchronization in complex dynamical networks consisting of randomly connected nodes. Numerical examples illustrate that a chaotic dynamics in the synchronization manifold is preserved when statistical parameters enter some almost sure synchronization region established by the developedmore » approach. Moreover, some delicate configurations are considered on probability space for ensuring synchronization in networks whose nodes are described by nonlinear maps. Both theoretical and numerical results on synchronization are presented by setting only a few random connections in each switch duration. More interestingly, we analytically find it possible to achieve almost sure synchronization in the randomly switching complex networks even with very large population sizes, which cannot be easily realized in non-switching but deterministically connected networks.« less

Secure multiple access for indoor optical wireless communications with time-slot coding and chaotic phase.

PubMed

Liang, Tian; Wang, Ke; Lim, Christina; Wong, Elaine; Song, Tingting; Nirmalathas, Ampalavanapillai

2017-09-04

In this paper, we report a novel mechanism to simultaneously provide secure connections for multiple users in indoor optical wireless communication systems by employing the time-slot coding scheme together with chaotic phase sequence. The chaotic phase sequence is generated according to the logistic map and applied to each symbol to secure the transmission. Proof-of-concept experiments are carried out for multiple system capacities based on both 4-QAM and 16-QAM modulation formats, i.e. 1.25 Gb/s, 2 Gb/s and 2.5 Gb/s for 4-QAM, and 2.5 Gb/s, 3.33 Gb/s and 4 Gb/s for 16-QAM. Experimental results show that in all cases the added chaotic phase does not degrade the legitimate user's signal quality while the illegal user cannot detect the signal without the key.

Parametric electroconvection in a weakly conducting fluid in a horizontal parallel-plate capacitor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kartavykh, N. N.; Smorodin, B. L., E-mail: bsmorodin@yandex.ru; Il’in, V. A.

2015-07-15

We study the flows of a nonuniformly heated weakly conducting fluid in an ac electric field of a horizontal parallel-plate capacitor. Analysis is carried out for fluids in which the charge formation is governed by electroconductive mechanism associated with the temperature dependence of the electrical conductivity of the medium. Periodic and chaotic regimes of fluid flow are investigated in the limiting case of instantaneous charge relaxation and for a finite relaxation time. Bifurcation diagrams and electroconvective regimes charts are constructed. The regions where fluid oscillations synchronize with the frequency of the external field are determined. Hysteretic transitions between electroconvection regimesmore » are studied. The scenarios of transition to chaotic oscillations are analyzed. Depending on the natural frequency of electroconvective system and the external field frequency, the transition from periodic to chaotic oscillations can occur via quasiperiodicity, a subharmonic cascade, or intermittence.« less

Breaking chaotic secure communication using a spectrogram

NASA Astrophysics Data System (ADS)

Yang, Tao; Yang, Lin-Bao; Yang, Chun-Mei

1998-10-01

We present the results of breaking a kind of chaotic secure communication system called chaotic switching scheme, also known as chaotic shift keying, in which a binary message signal is scrambled by two chaotic attractors. The spectrogram which can reveal the energy evolving process in the spectral-temporal space is used to distinguish the two different chaotic attractors, which are qualitatively and statistically similar in phase space. Then mathematical morphological filters are used to decode the binary message signal without the knowledge of the binary message signal and the transmitter. The computer experimental results are provided to show how our method works when both the chaotic and hyper-chaotic transmitter are used.

Multi-scale dynamical behavior of spatially distributed systems: a deterministic point of view

NASA Astrophysics Data System (ADS)

Mangiarotti, S.; Le Jean, F.; Drapeau, L.; Huc, M.

2015-12-01

Physical and biophysical systems are spatially distributed systems. Their behavior can be observed or modelled spatially at various resolutions. In this work, a deterministic point of view is adopted to analyze multi-scale behavior taking a set of ordinary differential equation (ODE) as elementary part of the system.To perform analyses, scenes of study are thus generated based on ensembles of identical elementary ODE systems. Without any loss of generality, their dynamics is chosen chaotic in order to ensure sensitivity to initial conditions, that is, one fundamental property of atmosphere under instable conditions [1]. The Rössler system [2] is used for this purpose for both its topological and algebraic simplicity [3,4].Two cases are thus considered: the chaotic oscillators composing the scene of study are taken either independent, or in phase synchronization. Scale behaviors are analyzed considering the scene of study as aggregations (basically obtained by spatially averaging the signal) or as associations (obtained by concatenating the time series). The global modeling technique is used to perform the numerical analyses [5].One important result of this work is that, under phase synchronization, a scene of aggregated dynamics can be approximated by the elementary system composing the scene, but modifying its parameterization [6]. This is shown based on numerical analyses. It is then demonstrated analytically and generalized to a larger class of ODE systems. Preliminary applications to cereal crops observed from satellite are also presented.[1] Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130-141 (1963).[2] Rössler, An equation for continuous chaos, Phys. Lett. A, 57, 397-398 (1976).[3] Gouesbet & Letellier, Global vector-field reconstruction by using a multivariate polynomial L2 approximation on nets, Phys. Rev. E 49, 4955-4972 (1994).[4] Letellier, Roulin & Rössler, Inequivalent topologies of chaos in simple equations, Chaos, Solitons & Fractals, 28, 337-360 (2006).[5] Mangiarotti, Coudret, Drapeau, & Jarlan, Polynomial search and global modeling, Phys. Rev. E 86(4), 046205 (2012).[6] Mangiarotti, Modélisation globale et Caractérisation Topologique de dynamiques environnementales. Habilitation à Diriger des Recherches, Univ. Toulouse 3 (2014).

Public channel cryptography: chaos synchronization and Hilbert's tenth problem.

PubMed

Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang

2008-08-22

The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.

Orbital structure in oscillating galactic potentials

NASA Astrophysics Data System (ADS)

Terzić, Balša; Kandrup, Henry E.

2004-01-01

Subjecting a galactic potential to (possibly damped) nearly periodic, time-dependent variations can lead to large numbers of chaotic orbits experiencing systematic changes in energy, and the resulting chaotic phase mixing could play an important role in explaining such phenomena as violent relaxation. This paper focuses on the simplest case of spherically symmetric potentials subjected to strictly periodic driving with the aim of understanding precisely why orbits become chaotic and under what circumstances they will exhibit systematic changes in energy. Four unperturbed potentials V0(r) were considered, each subjected to a time dependence of the form V(r, t) =V0(r)(1 +m0 sinωt). In each case, the orbits divide clearly into regular and chaotic, distinctions which appear absolute. In particular, transitions from regularity to chaos are seemingly impossible. Over finite time intervals, chaotic orbits subdivide into what can be termed `sticky' chaotic orbits, which exhibit no large-scale secular changes in energy and remain trapped in the phase-space region where they started; and `wildly' chaotic orbits, which do exhibit systematic drifts in energy as the orbits diffuse to different phase-space regions. This latter distinction is not absolute, transitions corresponding apparently to orbits penetrating a `leaky' phase-space barrier. The three different orbit types can be identified simply in terms of the frequencies for which their Fourier spectra have the most power. An examination of the statistical properties of orbit ensembles as a function of driving frequency ω allows us to identify the specific resonances that determine orbital structure. Attention focuses also on how, for fixed amplitude m0, such quantities as the mean energy shift, the relative measure of chaotic orbits and the mean value of the largest Lyapunov exponent vary with driving frequency ω and how, for fixed ω, the same quantities depend on m0.

Phase Synchronization of Hemodynamic Variables at Rest and after Deep Breathing Measured during the Course of Pregnancy

PubMed Central

Papousek, Ilona; Roessler, Andreas; Hinghofer-Szalkay, Helmut; Lang, Uwe; Kolovetsiou-Kreiner, Vassiliki

2013-01-01

Background The autonomic nervous system plays a central role in the functioning of systems critical for the homeostasis maintenance. However, its role in the cardiovascular adaptation to pregnancy-related demands is poorly understood. We explored the maternal cardiovascular systems throughout pregnancy to quantify pregnancy-related autonomic nervous system adaptations. Methodology Continuous monitoring of heart rate (R-R interval; derived from the 3-lead electrocardiography), blood pressure, and thoracic impedance was carried out in thirty-six women at six time-points throughout pregnancy. In order to quantify in addition to the longitudinal effects on baseline levels throughout gestation the immediate adaptive heart rate and blood pressure changes at each time point, a simple reflex test, deep breathing, was applied. Consequently, heart rate variability and blood pressure variability in the low (LF) and high (HF) frequency range, respiration and baroreceptor sensitivity were analyzed in resting conditions and after deep breathing. The adjustment of the rhythms of the R-R interval, blood pressure and respiration partitioned for the sympathetic and the parasympathetic branch of the autonomic nervous system were quantified by the phase synchronization index γ, which has been adopted from the analysis of weakly coupled chaotic oscillators. Results Heart rate and LF/HF ratio increased throughout pregnancy and these effects were accompanied by a continuous loss of baroreceptor sensitivity. The increases in heart rate and LF/HF ratio levels were associated with an increasing decline in the ability to flexibly respond to additional demands (i.e., diminished adaptive responses to deep breathing). The phase synchronization index γ showed that the observed effects could be explained by a decreased coupling of respiration and the cardiovascular system (HF components of heart rate and blood pressure). Conclusions/Significance The findings suggest that during the course of pregnancy the individual systems become increasingly independent to meet the increasing demands placed on the maternal cardiovascular and respiratory system. PMID:23577144

Small-world networks exhibit pronounced intermittent synchronization

NASA Astrophysics Data System (ADS)

Choudhary, Anshul; Mitra, Chiranjit; Kohar, Vivek; Sinha, Sudeshna; Kurths, Jürgen

2017-11-01

We report the phenomenon of temporally intermittently synchronized and desynchronized dynamics in Watts-Strogatz networks of chaotic Rössler oscillators. We consider topologies for which the master stability function (MSF) predicts stable synchronized behaviour, as the rewiring probability (p) is tuned from 0 to 1. MSF essentially utilizes the largest non-zero Lyapunov exponent transversal to the synchronization manifold in making stability considerations, thereby ignoring the other Lyapunov exponents. However, for an N-node networked dynamical system, we observe that the difference in its Lyapunov spectra (corresponding to the N - 1 directions transversal to the synchronization manifold) is crucial and serves as an indicator of the presence of intermittently synchronized behaviour. In addition to the linear stability-based (MSF) analysis, we further provide global stability estimate in terms of the fraction of state-space volume shared by the intermittently synchronized state, as p is varied from 0 to 1. This fraction becomes appreciably large in the small-world regime, which is surprising, since this limit has been otherwise considered optimal for synchronized dynamics. Finally, we characterize the nature of the observed intermittency and its dominance in state-space as network rewiring probability (p) is varied.

Control and Synchronization of Heteroclinic Chaos: Implications for Neurodynamics

NASA Astrophysics Data System (ADS)

Arecchi, F. Tito

2004-12-01

Heteroclinic chaos (HC) implies the recurrent return of the dynamical trajectory to a saddle focus (SF) in whose neighborhood the system response to an external perturbation is very high and hence it is very easy to lock to an external stimulus. Thus HC appears as the easiest way to encode information in time by a train of equal spikes occurring at erratic times. Implementing such a dynamics with a single mode CO2 laser with feedback, we have a heteroclinic connection between the SF and a saddle node (SN) whose role it to regularize the phase space orbit away from SF. Due to these two different fixed points, the laser intensity displays identical spikes separated by erratic ISIs (interspike intervals). Such a dynamics is highly prone to spike-synchronization, either by an external signal or by mutual interaction in a network of identical systems. Applications to communication and noise induced synchronization will be reported. In experimental neuroscience a recent finding is that feature binding ,that is, combination of external stimuli with internal memories into new coherent patterns of meaning, implies the mutual synchronization of axonal spike trains in neurons which can be far away and yet share the same sequence. Several dynamical systems have been proposed to model such a behavior. We introduce a measurable parameter, namely, the synchronization "propensity". Propensity is the amount of synchronization achieved in a chaotic system by a small sinusoidal perturbation of a control parameter. It is very low for coupled Lorenz or FitzHugh-Nagumo chains. It displays isolated peaks for the Hindmarsh-Rose model, showing that this is a convenient description of the bursting behavior typical of neurons in the CPG (central pattern generator) system. Instead, HC shows a high propensity over a wide input frequency range, demonstrating that it is the most convenient model for semantic neurons.

Force Analysis and Energy Operation of Chaotic System of Permanent-Magnet Synchronous Motor

NASA Astrophysics Data System (ADS)

Qi, Guoyuan; Hu, Jianbing

2017-12-01

The disadvantage of a nondimensionalized model of a permanent-magnet synchronous Motor (PMSM) is identified. The original PMSM model is transformed into a Kolmogorov system to aid dynamic force analysis. The vector field of the PMSM is analogous to the force field including four types of torque — inertial, internal, dissipative, and generalized external. Using the feedback thought, the error torque between external torque and dissipative torque is identified. The pitchfork bifurcation of the PMSM is performed. Four forms of energy are identified for the system — kinetic, potential, dissipative, and supplied. The physical interpretations of the decomposition of force and energy exchange are given. Casimir energy is stored energy, and its rate of change is the error power between the dissipative energy and the energy supplied to the motor. Error torque and error power influence the different types of dynamic modes. The Hamiltonian energy and Casimir energy are compared to find the function of each in producing the dynamic modes. A supremum bound for the chaotic attractor is proposed using the error power and Lagrange multiplier.

The design and research of anti-color-noise chaos M-ary communication system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Yongqing, E-mail: fuyongqing@hrbeu.edu.cn; Li, Xingyuan; Li, Yanan

Previously a novel chaos M-ary digital communication method based on spatiotemporal chaos Hamilton oscillator has been proposed. Without chaos synchronization circumstance, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-white-noise performance compared with traditional communication method. In this paper, the channel noise influence on chaotic modulation signals and the construction problem of anti-color-noise chaotic M-ary communication system are studied. The formula of zone partition demodulator’s boundary in additive white Gaussian noise is derived, besides, the problem about how to determine the boundary of zone partition demodulator in additive color noise is deeply studied; Then an approach on constructingmore » anti-color-noise chaos M-ary communication system is proposed, in which a pre-distortion filter is added after the chaos baseband modulator in the transmitter and whitening filter is added before zone partition demodulator in the receiver. Finally, the chaos M-ary communication system based on Hamilton oscillator is constructed and simulated in different channel noise. The result shows that the proposed method in this paper can improve the anti-color-noise performance of the whole communication system compared with the former system, and it has better anti-fading and resisting disturbance performance than Quadrature Phase Shift Keying system.« less

Title: Chimeras in small, globally coupled networks: Experiments and stability analysis

NASA Astrophysics Data System (ADS)

Hart, Joseph D.; Bansal, Kanika; Murphy, Thomas E.; Roy, Rajarshi

Since the initial observation of chimera states, there has been much discussion of the conditions under which these states emerge. The emphasis thus far has mainly been to analyze large networks of coupled oscillators; however, recent studies have begun to focus on the opposite limit: what is the smallest system of coupled oscillators in which chimeras can exist? We experimentally observe chimeras and other partially synchronous patterns in a network of four globally-coupled chaotic opto-electronic oscillators. By examining the equations of motion, we demonstrate that symmetries in the network topology allow a variety of synchronous states to exist, including cluster synchronous states and a chimera state. Using the group theoretical approach recently developed for analyzing cluster synchronization, we show how to derive the variational equations for these synchronous patterns and calculate their linear stability. The stability analysis gives good agreement with our experimental results. Both experiments and simulations suggest that these chimera states often appear in regions of multistability between global, cluster, and desynchronized states.

Synchronization in a chaotic neural network with time delay depending on the spatial distance between neurons

NASA Astrophysics Data System (ADS)

Tang, Guoning; Xu, Kesheng; Jiang, Luoluo

2011-10-01

The synchronization is investigated in a two-dimensional Hindmarsh-Rose neuronal network by introducing a global coupling scheme with time delay, where the length of time delay is proportional to the spatial distance between neurons. We find that the time delay always disturbs synchronization of the neuronal network. When both the coupling strength and length of time delay per unit distance (i.e., enlargement factor) are large enough, the time delay induces the abnormal membrane potential oscillations in neurons. Specifically, the abnormal membrane potential oscillations for the symmetrically placed neurons form an antiphase, so that the large coupling strength and enlargement factor lead to the desynchronization of the neuronal network. The complete and intermittently complete synchronization of the neuronal network are observed for the right choice of parameters. The physical mechanism underlying these phenomena is analyzed.

Stabilization and synchronization for a mechanical system via adaptive sliding mode control.

PubMed

Song, Zhankui; Sun, Kaibiao; Ling, Shuai

2017-05-01

In this paper, we investigate the synchronization problem of chaotic centrifugal flywheel governor with parameters uncertainty and lumped disturbances. A slave centrifugal flywheel governor system is considered as an underactuated following-system which a control input is designed to follow a master centrifugal flywheel governor system. To tackle lumped disturbances and uncertainty parameters, a novel synchronization control law is developed by employing sliding mode control strategy and Nussbaum gain technique. Adaptation updating algorithms are derived in the sense of Lyapunov stability analysis such that the lumped disturbances can be suppressed and the adverse effect caused by uncertainty parameters can be compensated. In addition, the synchronization tracking-errors are proven to converge to a small neighborhood of the origin. Finally, simulation results demonstrate the effectiveness of the proposed control scheme. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Emergence and transitions of dynamic patterns of thickness oscillation of the plasmodium of the true slime mold Physarum polycephalum

NASA Astrophysics Data System (ADS)

Takagi, Seiji; Ueda, Tetsuo

2008-03-01

The emergence and transitions of various spatiotemporal patterns of thickness oscillation were studied in the freshly isolated protoplasm of the Physarum plasmodium. New patterns, such as standing waves, and chaotic and rotating spirals, developed successively before the well-documented synchronous pattern appeared. There was also a spontaneous opposite transition from synchrony to chaotic and rotating spirals. Rotating spiral waves were observed in the large migrating plasmodium, where the vein structures were being destroyed. Thus, the Physarum plasmodium exhibits versatile patterns, which are generally expected in coupled oscillator systems. This paper discusses the physiological roles of spatiotemporal patterns, comparing them with other biological systems.

Adaptive Fractional-order Control for Synchronization of Two Coupled Neurons in the External Electrical Stimulation

PubMed Central

Mehdiabadi, M. R. Rahmani; Rouhani, E.; Mashhadi, S. K. Mousavi; Jalali, A. A.

2014-01-01

This paper addresses synchronizing two coupled chaotic FitzHugh–Nagumo (FHN) neurons with weakly gap junction under external electrical stimulation (EES). To transmit information among coupled neurons, by generalization of the integer-order FHN equations of the coupled system into the fractional-order in frequency domain using Crone approach, the behavior of each coupled neuron relies on its past behavior and the memorized system can be a better fit for the neuron response. An adaptive fractional-order controller based on the Lyaponuv stability theory was designed to synchronize two neurons electrically coupled with gap junction in EES. The proposed controller is also robust to the inevitable random noise such as disturbances of ionic channels. The simulation results demonstrate the effectiveness of the control scheme. PMID:25337373

Competition between Chaotic and Nonchaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model.

PubMed

Chen, Xin; Fan, Ruihua; Chen, Yiming; Zhai, Hui; Zhang, Pengfei

2017-11-17

The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality, and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK models with a different number of Majorana modes coupled by quadratic terms. This model is also solvable, and the solution shows a zero-temperature quantum phase transition between two non-Fermi liquid chaotic phases. This phase transition is driven by tuning the ratio of two mode numbers, and a nonchaotic Fermi liquid sits at the critical point with an equal number of modes. At a finite temperature, the Fermi liquid phase expands to a finite regime. More intriguingly, a different non-Fermi liquid phase emerges at a finite temperature. We characterize the phase diagram in terms of the spectral function, the Lyapunov exponent, and the entropy. Our results illustrate a concrete example of the quantum phase transition and critical behavior between two non-Fermi liquid phases.

Working Towards Führer: A Chaotic View

NASA Astrophysics Data System (ADS)

Cakar, Ulas

Leadership is a concept that has been discussed since the beginning of history. Even though there have been many theories in the field accepting leadership's role in bringing order, chaotic aspects of leadership are generally neglected. This chapter aims to examine the leadership beyond an orderly interpretation of universe. For this purpose, Third Reich period and leadership during this period will be examined. Ian Kershaw's "Working Towards Führer" concept provides a unique understanding of leadership concept. It goes beyond the dualist depiction of Third Reich, it does not state Adolf Hitler as an all powerful dictator, or a weak one. Rather, he expresses that due to the conditions in the Third Reich, Adolf Hitler was both of this. This complex situation can be understood deeper when it is examined through the lens of chaos theory. This study contributes to the field by being the first in using chaos theory for examining "Working Towards Führer" concept and its development. Seemingly orderly nature of synchronization process and its vortex will be shown. Adolf Hitler's storm spot position in the chaotic system and its dynamics are explained. War's entropic power and its effect on the downfall of the system is crucial in understanding this unique chaotic system. The chaotic pattern of "Working Towards Führer" offers an opportunity to analyze the complexities of the leadership concept.

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

NASA Technical Reports Server (NTRS)

Jensen, R. V.; Sanders, M. M.; Saraceno, M.; Sundaram, B.

1989-01-01

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

Error function attack of chaos synchronization based encryption schemes.

PubMed

Wang, Xingang; Zhan, Meng; Lai, C-H; Gang, Hu

2004-03-01

Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor. Copyright 2004 American Institute of Physics.

A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

NASA Astrophysics Data System (ADS)

Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

Experimental observation of chimera and cluster states in a minimal globally coupled network

NASA Astrophysics Data System (ADS)

Hart, Joseph D.; Bansal, Kanika; Murphy, Thomas E.; Roy, Rajarshi

2016-09-01

A "chimera state" is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic opto-electronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.

Quantitative Measures of Chaotic Charged Particle Dynamics in the Magnetotail

NASA Astrophysics Data System (ADS)

Holland, D. L.; Martin, R. F., Jr.; Burris, C.

2017-12-01

It has long been noted that the motion of charged particles in magnetotail-like magnetic fields is chaotic, however, efforts to quantify the degree of chaos have had conflicting conclusions. In this paper we re-examine the question by focusing on quantitative measures of chaos. We first examine the percentage of orbits that enter the chaotic region of phase space and the average trapping time of those particles. We then examine the average exponential divergence rate (AEDR) of the chaotic particles between their first and last crossing of the mid-plane. We show that at resonant energies where the underlying phase space has a high degree of symmetry, only a small number of particle enter the chaotic region, but they are trapped for long periods of time and the time asymptotic value of the AEDR is very close to the average value of the AEDR. At the off-resonant energies where the phase space is highly asymmetric, the majority of the particle enter the chaotic region for fairly short periods of time and the time asymptotic value of the AEDR is much smaller than the average value. The root cause is that in the resonant case, the longest-lived orbits tend interact with the current many times and sample the entire chaotic region, whereas in the non-resonant case the longest-lived orbits only interact with the current sheet a small number of times but have very long mirrorings where the motion is nearly regular. Additionally we use an ad-hoc model where we model the current sheet as a Lorentz scattering system with each interaction with the current sheet being considered as a "collision". We find that the average kick per collision is greatest at off-resonant energies. Finally, we propose a chaos parameter as the product of the AEDR times the average chaotic particle trapping time times the percentage of orbits that are chaotic. We find that this takes on peak values at the resonant energies.

Inferring Functional Neural Connectivity with Phase Synchronization Analysis: A Review of Methodology

PubMed Central

Sun, Junfeng; Li, Zhijun; Tong, Shanbao

2012-01-01

Functional neural connectivity is drawing increasing attention in neuroscience research. To infer functional connectivity from observed neural signals, various methods have been proposed. Among them, phase synchronization analysis is an important and effective one which examines the relationship of instantaneous phase between neural signals but neglecting the influence of their amplitudes. In this paper, we review the advances in methodologies of phase synchronization analysis. In particular, we discuss the definitions of instantaneous phase, the indexes of phase synchronization and their significance test, the issues that may affect the detection of phase synchronization and the extensions of phase synchronization analysis. In practice, phase synchronization analysis may be affected by observational noise, insufficient samples of the signals, volume conduction, and reference in recording neural signals. We make comments and suggestions on these issues so as to better apply phase synchronization analysis to inferring functional connectivity from neural signals. PMID:22577470

Via generalized function projective synchronization in nonlinear Schrödinger equation for secure communication

NASA Astrophysics Data System (ADS)

Zhao, L. W.; Du, J. G.; Yin, J. L.

2018-05-01

This paper proposes a novel secured communication scheme in a chaotic system by applying generalized function projective synchronization of the nonlinear Schrödinger equation. This phenomenal approach guarantees a secured and convenient communication. Our study applied the Melnikov theorem with an active control strategy to suppress chaos in the system. The transmitted information signal is modulated into the parameter of the nonlinear Schrödinger equation in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical nonlinear Schrödinger equation with the unknown parameter asymptotically synchronized. The numerical simulation results of our study confirmed the validity, effectiveness and the feasibility of the proposed novel synchronization method and error estimate for a secure communication. The Chaos masking signals of the information communication scheme, further guaranteed a safer and secured information communicated via this approach.

Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy.

PubMed

Pillai, Nikhil; Craig, Morgan; Dokoumetzidis, Aristeidis; Schwartz, Sorell L; Bies, Robert; Freedman, Immanuel

2018-06-19

In mathematical pharmacology, models are constructed to confer a robust method for optimizing treatment. The predictive capability of pharmacological models depends heavily on the ability to track the system and to accurately determine parameters with reference to the sensitivity in projected outcomes. To closely track chaotic systems, one may choose to apply chaos synchronization. An advantageous byproduct of this methodology is the ability to quantify model parameters. In this paper, we illustrate the use of chaos synchronization combined with Nelder-Mead search to estimate parameters of the well-known Kirschner-Panetta model of IL-2 immunotherapy from noisy data. Chaos synchronization with Nelder-Mead search is shown to provide more accurate and reliable estimates than Nelder-Mead search based on an extended least squares (ELS) objective function. Our results underline the strength of this approach to parameter estimation and provide a broader framework of parameter identification for nonlinear models in pharmacology. Copyright © 2018 Elsevier Ltd. All rights reserved.

Dynamics and circuit of a chaotic system with a curve of equilibrium points

NASA Astrophysics Data System (ADS)

Pham, Viet-Thanh; Volos, Christos; Kapitaniak, Tomasz; Jafari, Sajad; Wang, Xiong

2018-03-01

Although chaotic systems have been intensively studied since the 1960s, new systems with mysterious features are still of interest. A novel chaotic system including hyperbolic functions is proposed in this work. Especially, the system has an infinite number of equilibrium points. Dynamics of the system are investigated by using non-linear tools such as phase portrait, bifurcation diagram, and Lyapunov exponent. It is interesting that the system can display coexisting chaotic attractors. An electronic circuit for realising the chaotic system has been implemented. Experimental results show a good agreement with theoretical ones.

Stochastic dynamics and combinatorial optimization

NASA Astrophysics Data System (ADS)

Ovchinnikov, Igor V.; Wang, Kang L.

2017-11-01

Natural dynamics is often dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares, etc., that exhibit scale-free statistics much in the spirit of the logarithmic Ritcher scale for earthquake magnitudes. On phase diagrams, stochastic dynamical systems (DSs) exhibiting this type of dynamics belong to the finite-width phase (N-phase for brevity) that precedes ordinary chaotic behavior and that is known under such names as noise-induced chaos, self-organized criticality, dynamical complexity, etc. Within the recently proposed supersymmetric theory of stochastic dynamics, the N-phase can be roughly interpreted as the noise-induced “overlap” between integrable and chaotic deterministic dynamics. As a result, the N-phase dynamics inherits the properties of the both. Here, we analyze this unique set of properties and conclude that the N-phase DSs must naturally be the most efficient optimizers: on one hand, N-phase DSs have integrable flows with well-defined attractors that can be associated with candidate solutions and, on the other hand, the noise-induced attractor-to-attractor dynamics in the N-phase is effectively chaotic or aperiodic so that a DS must avoid revisiting solutions/attractors thus accelerating the search for the best solution. Based on this understanding, we propose a method for stochastic dynamical optimization using the N-phase DSs. This method can be viewed as a hybrid of the simulated and chaotic annealing methods. Our proposition can result in a new generation of hardware devices for efficient solution of various search and/or combinatorial optimization problems.

Phase synchronization of oscillations in cardiovascular and respiratory systems in humans

NASA Astrophysics Data System (ADS)

Tankanag, Arina V.; Grinevich, Andrey A.; Tikhonova, Irina V.; Chaplygina, Alina V.; Chemeris, Nikolay K.

2017-04-01

Phase synchronization between blood flow oscillations of left and right forearm skin sites, heart rate variability (HRV) and breath rate were studied from healthy volunteers at rest. The degree of synchronization between the phases of the analyzed signals was estimated from the value of the wavelet phase coherence. High medians of values of phase wavelet coherence function were obtained for the endothelial, neurogenic, myogenic and cardiac intervals. Significant phase synchronization were demonstrated between HRV and skin blood flow oscillations in both left and right forearms in a wide frequency range from 0.04 to 0.4 Hz. Six participants exhibited low phase synchronization (< 0.5) between the breath rate and HRV, while nine participants had high phase synchronization (> 0.5). This distribution was not affected by the sex or sympathovagal status of volunteers. Participants with low phase synchronization between breath rate and HRV featured low phase synchronization (< 0.5) between breath rate and blood flow oscillations in both forearms. Contrariwise, in subjects with high phase synchronization between respiratory rhythm and HRV both low and high phase synchronization between breath rate and blood flow oscillations in both forearms was observed. The results obtained allow us to suggest that the organism possesses a mechanism mediating the synchronization of blood flow oscillations in the skin microvasculature with all other periodical processes across the cardiovascular system, in particular, with HRV and breath rate over a wide frequency range.

Mechanisms of appearance of amplitude and phase chimera states in ensembles of nonlocally coupled chaotic systems

NASA Astrophysics Data System (ADS)

Bogomolov, Sergey A.; Slepnev, Andrei V.; Strelkova, Galina I.; Schöll, Eckehard; Anishchenko, Vadim S.

2017-02-01

We explore the bifurcation transition from coherence to incoherence in ensembles of nonlocally coupled chaotic systems. It is firstly shown that two types of chimera states, namely, amplitude and phase, can be found in a network of coupled logistic maps, while only amplitude chimera states can be observed in a ring of continuous-time chaotic systems. We reveal a bifurcation mechanism by analyzing the evolution of space-time profiles and the coupling function with varying coupling coefficient and formulate the necessary and sufficient conditions for realizing the chimera states in the ensembles.

An image encryption algorithm based on 3D cellular automata and chaotic maps

NASA Astrophysics Data System (ADS)

Del Rey, A. Martín; Sánchez, G. Rodríguez

2015-05-01

A novel encryption algorithm to cipher digital images is presented in this work. The digital image is rendering into a three-dimensional (3D) lattice and the protocol consists of two phases: the confusion phase where 24 chaotic Cat maps are applied and the diffusion phase where a 3D cellular automata is evolved. The encryption method is shown to be secure against the most important cryptanalytic attacks.

On the relevance of chaos for halo stars in the solar neighbourhood II

NASA Astrophysics Data System (ADS)

Maffione, Nicolas P.; Gómez, Facundo A.; Cincotta, Pablo M.; Giordano, Claudia M.; Grand, Robert J. J.; Marinacci, Federico; Pakmor, Rüdiger; Simpson, Christine M.; Springel, Volker; Frenk, Carlos S.

2018-05-01

In a previous paper based on dark matter only simulations we show that, in the approximation of an analytic and static potential describing the strongly triaxial and cuspy shape of Milky Way-sized haloes, diffusion due to chaotic mixing in the neighbourhood of the Sun does not efficiently erase phase space signatures of past accretion events. In this second paper we further explore the effect of chaotic mixing using multicomponent Galactic potential models and solar neighbourhood-like volumes extracted from fully cosmological hydrodynamic simulations, thus naturally accounting for the gravitational potential associated with baryonic components, such as the bulge and disc. Despite the strong change in the global Galactic potentials with respect to those obtained in dark matter only simulations, our results confirm that a large fraction of halo particles evolving on chaotic orbits exhibit their chaotic behaviour after periods of time significantly larger than a Hubble time. In addition, significant diffusion in phase space is not observed on those particles that do exhibit chaotic behaviour within a Hubble time.

Chaotic behavior of renal sympathetic nerve activity: effect of baroreceptor denervation and cardiac failure.

PubMed

DiBona, G F; Jones, S Y; Sawin, L L

2000-09-01

Nonlinear dynamic analysis was used to examine the chaotic behavior of renal sympathetic nerve activity in conscious rats subjected to either complete baroreceptor denervation (sinoaortic and cardiac baroreceptor denervation) or induction of congestive heart failure (CHF). The peak interval sequence of synchronized renal sympathetic nerve discharge was extracted and used for analysis. In control rats, this yielded a system whose correlation dimension converged to a low value over the embedding dimension range of 10-15 and whose greatest Lyapunov exponent was positive. Complete baroreceptor denervation was associated with a decrease in the correlation dimension of the system (before 2.65 +/- 0.27, after 1.64 +/- 0.17; P < 0.01) and a reduction in chaotic behavior (greatest Lyapunov exponent: 0.201 +/- 0.008 bits/data point before, 0.177 +/- 0.004 bits/data point after, P < 0.02). CHF, a state characterized by impaired sinoaortic and cardiac baroreceptor regulation of renal sympathetic nerve activity, was associated with a similar decrease in the correlation dimension (control 3.41 +/- 0.23, CHF 2.62 +/- 0.26; P < 0.01) and a reduction in chaotic behavior (greatest Lyapunov exponent: 0.205 +/- 0.048 bits/data point control, 0.136 +/- 0.033 bits/data point CHF, P < 0.02). These results indicate that removal of sinoaortic and cardiac baroreceptor regulation of renal sympathetic nerve activity, occurring either physiologically or pathophysiologically, is associated with a decrease in the correlation dimensions of the system and a reduction in chaotic behavior.

Chaotic neoclassical separatrix dissipation in parametric drift-wave decay.

PubMed

Kabantsev, A A; Tsidulko, Yu A; Driscoll, C F

2014-02-07

Experiments and theory characterize a parametric decay instability between plasma drift waves when the nonlinear coupling is modified by an electrostatic barrier. Novel mode coupling terms representing enhanced dissipation and mode phase shifts are caused by chaotic separatrix crossings on the wave-ruffled separatrix. Experimental determination of these coupling terms is in broad agreement with new chaotic neoclassical transport analyses.

Basic dynamics from a pulse-coupled network of autonomous integrate-and-fire chaotic circuits.

PubMed

Nakano, H; Saito, T

2002-01-01

This paper studies basic dynamics from a novel pulse-coupled network (PCN). The unit element of the PCN is an integrate-and-fire circuit (IFC) that exhibits chaos. We an give an iff condition for the chaos generation. Using two IFC, we construct a master-slave PCN. It exhibits interesting chaos synchronous phenomena and their breakdown phenomena. We give basic classification of the phenomena and their existence regions can be elucidated in the parameter space. We then construct a ring-type PCN and elucidate that the PCN exhibits interesting grouping phenomena based on the chaos synchronization patterns. Using a simple test circuit, some of typical phenomena can be verified in the laboratory.

Image encryption using a synchronous permutation-diffusion technique

NASA Astrophysics Data System (ADS)

Enayatifar, Rasul; Abdullah, Abdul Hanan; Isnin, Ismail Fauzi; Altameem, Ayman; Lee, Malrey

2017-03-01

In the past decade, the interest on digital images security has been increased among scientists. A synchronous permutation and diffusion technique is designed in order to protect gray-level image content while sending it through internet. To implement the proposed method, two-dimensional plain-image is converted to one dimension. Afterward, in order to reduce the sending process time, permutation and diffusion steps for any pixel are performed in the same time. The permutation step uses chaotic map and deoxyribonucleic acid (DNA) to permute a pixel, while diffusion employs DNA sequence and DNA operator to encrypt the pixel. Experimental results and extensive security analyses have been conducted to demonstrate the feasibility and validity of this proposed image encryption method.

Lag and anticipating synchronization without time-delay coupling.

PubMed

Corron, Ned J; Blakely, Jonathan N; Pethel, Shawn D

2005-06-01

We describe a new method for achieving approximate lag and anticipating synchronization in unidirectionally coupled chaotic oscillators. The method uses a specific parameter mismatch between the drive and response that is a first-order approximation to true time-delay coupling. As a result, an adjustable lag or anticipation effect can be achieved without the need for a variable delay line, making the method simpler and more economical to implement in many physical systems. We present a stability analysis, demonstrate the method numerically, and report experimental observation of the effect in radio-frequency electronic oscillators. In the circuit experiments, both lag and anticipation are controlled by tuning a single capacitor in the response oscillator.

How to induce multiple delays in coupled chaotic oscillators?

NASA Astrophysics Data System (ADS)

Bhowmick, Sourav K.; Ghosh, Dibakar; Roy, Prodyot K.; Kurths, Jürgen; Dana, Syamal K.

2013-12-01

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.

Experimental observation of chimera and cluster states in a minimal globally coupled network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hart, Joseph D.; Department of Physics, University of Maryland, College Park, Maryland 20742; Bansal, Kanika

A “chimera state” is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic opto-electronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belongingmore » to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.« less

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos.

PubMed

Zou, Yong; Donner, Reik V; Kurths, Jürgen

2012-03-01

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.

Wavelength division multiplexing of chaotic secure and fiber-optic communications.

PubMed

Zhang, Jian-Zhong; Wang, An-Bang; Wang, Juan-Fen; Wang, Yun-Cai

2009-04-13

Wavelength division multiplexing (WDM) transmission of chaotic optical communication (COC) and conventional fiber-optic communication (CFOC) is numerically confirmed and analyzed. For an 80-km-long two-channel communication system, a 1-Gb/s secure message in COC channel and 10-Gb/s digital signal in CFOC channel are simultaneously achieved with 100 GHz channel spacing. Our numerical simulations demonstrate that the COC and CFOC can realize no-crosstalk transmission of 80 km when the peak power of CFOC channel is less than 8dBm. We also find that the crosstalk between COC and CFOC does not depend on channel spacing when the channel spacing exceeds 100GHz. Moreover, the crosstalk does not limit channel number by comparing the synchronization performance of COC in four- and six-channel WDM systems.

Robust Adaptive Synchronization of Ring Configured Uncertain Chaotic FitzHugh–Nagumo Neurons under Direction-Dependent Coupling

PubMed Central

Iqbal, Muhammad; Rehan, Muhammad; Hong, Keum-Shik

2018-01-01

This paper exploits the dynamical modeling, behavior analysis, and synchronization of a network of four different FitzHugh–Nagumo (FHN) neurons with unknown parameters linked in a ring configuration under direction-dependent coupling. The main purpose is to investigate a robust adaptive control law for the synchronization of uncertain and perturbed neurons, communicating in a medium of bidirectional coupling. The neurons are assumed to be different and interconnected in a ring structure. The strength of the gap junctions is taken to be different for each link in the network, owing to the inter-neuronal coupling medium properties. Robust adaptive control mechanism based on Lyapunov stability analysis is employed and theoretical criteria are derived to realize the synchronization of the network of four FHN neurons in a ring form with unknown parameters under direction-dependent coupling and disturbances. The proposed scheme for synchronization of dissimilar neurons, under external electrical stimuli, coupled in a ring communication topology, having all parameters unknown, and subject to directional coupling medium and perturbations, is addressed for the first time as per our knowledge. To demonstrate the efficacy of the proposed strategy, simulation results are provided. PMID:29535622

Visibility graphlet approach to chaotic time series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mutua, Stephen; Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega; Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn

Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems.more » Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.« less

Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing

NASA Astrophysics Data System (ADS)

Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley

2017-08-01

At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such memristors into the hardware of a Hopfield computing network can greatly improve the efficiency and accuracy of converging to a solution for computationally difficult problems.

Synchronous, Alternating, and Phase-Locked Stridulation by a Tropical Katydid

NASA Astrophysics Data System (ADS)

Sismondo, Enrico

1990-07-01

In the field the chirps of neighboring Mecopoda sp. (Orthoptera, Tettigoniidae, and Mecopodinae) males are normally synchronized, but between more distant individuals the chirps are either synchronous or regularly alternating. The phase response to single-stimulus chirps depends on both the phase and the intensity of the stimulus. Iteration of the Poincare map of the phase response predicts a variety of phase-locked synchronization regimes, including period-doubling bifurcations, in close agreement with experimental observations. The versatile acoustic behavior of Mecopoda encompasses most of the phenomena found in other synchronizing insects and thus provides a general model of insect synchronization behavior.

Horizons of cybernetical physics

PubMed Central

2017-01-01

The subject and main areas of a new research field—cybernetical physics—are discussed. A brief history of cybernetical physics is outlined. The main areas of activity in cybernetical physics are briefly surveyed, such as control of oscillatory and chaotic behaviour, control of resonance and synchronization, control in thermodynamics, control of distributed systems and networks, quantum control. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115620

A novel image encryption algorithm based on synchronized random bit generated in cascade-coupled chaotic semiconductor ring lasers

NASA Astrophysics Data System (ADS)

Li, Jiafu; Xiang, Shuiying; Wang, Haoning; Gong, Junkai; Wen, Aijun

2018-03-01

In this paper, a novel image encryption algorithm based on synchronization of physical random bit generated in a cascade-coupled semiconductor ring lasers (CCSRL) system is proposed, and the security analysis is performed. In both transmitter and receiver parts, the CCSRL system is a master-slave configuration consisting of a master semiconductor ring laser (M-SRL) with cross-feedback and a solitary SRL (S-SRL). The proposed image encryption algorithm includes image preprocessing based on conventional chaotic maps, pixel confusion based on control matrix extracted from physical random bit, and pixel diffusion based on random bit stream extracted from physical random bit. Firstly, the preprocessing method is used to eliminate the correlation between adjacent pixels. Secondly, physical random bit with verified randomness is generated based on chaos in the CCSRL system, and is used to simultaneously generate the control matrix and random bit stream. Finally, the control matrix and random bit stream are used for the encryption algorithm in order to change the position and the values of pixels, respectively. Simulation results and security analysis demonstrate that the proposed algorithm is effective and able to resist various typical attacks, and thus is an excellent candidate for secure image communication application.

Synthesis and evaluation of phase detectors for active bit synchronizers

NASA Technical Reports Server (NTRS)

Mcbride, A. L.

1974-01-01

Self-synchronizing digital data communication systems usually use active or phase-locked loop (PLL) bit synchronizers. The three main elements of PLL synchronizers are the phase detector, loop filter, and the voltage controlled oscillator. Of these three elements, phase detector synthesis is the main source of difficulty, particularly when the received signals are demodulated square-wave signals. A phase detector synthesis technique is reviewed that provides a physically realizable design for bit synchronizer phase detectors. The development is based upon nonlinear recursive estimation methods. The phase detector portion of the algorithm is isolated and analyzed.

A new transiently chaotic flow with ellipsoid equilibria

NASA Astrophysics Data System (ADS)

Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan

2018-03-01

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

Cell Cycle Synchronization of HeLa Cells to Assay EGFR Pathway Activation.

PubMed

Wee, Ping; Wang, Zhixiang

2017-01-01

Progression through the cell cycle causes changes in the cell's signaling pathways that can alter EGFR signal transduction. Here, we describe drug-derived protocols to synchronize HeLa cells in various phases of the cell cycle, including G1 phase, S phase, G2 phase, and mitosis, specifically in the mitotic stages of prometaphase, metaphase, and anaphase/telophase. The synchronization procedures are designed to allow synchronized cells to be treated for EGF and collected for the purpose of Western blotting for EGFR signal transduction components.S phase synchronization is performed by thymidine block, G2 phase with roscovitine, prometaphase with nocodazole, metaphase with MG132, and anaphase/telophase with blebbistatin. G1 phase synchronization is performed by culturing synchronized mitotic cells obtained by mitotic shake-off. We also provide methods to validate the synchronization methods. For validation by Western blotting, we provide the temporal expression of various cell cycle markers that are used to check the quality of the synchronization. For validation of mitotic synchronization by microscopy, we provide a guide that describes the physical properties of each mitotic stage, using their cellular morphology and DNA appearance. For validation by flow cytometry, we describe the use of imaging flow cytometry to distinguish between the phases of the cell cycle, including between each stage of mitosis.

Determining the degree of synchronism for intermittent phase synchronization in human electroencephalography data

NASA Astrophysics Data System (ADS)

Koloskova, A. D.; Moskalenko, O. I.

2017-05-01

The phenomenon of intermittent phase synchronization during development of epileptic activity in human beings has been discovered based on EEG data. The presence of synchronous behavior phases has been detected both during spike-wave discharges and in the regions of background activity of the brain. The degree of synchronism in the intermittent phase-synchronization regime in both cases has been determined, and it has been established that spike-wave discharges are characterized by a higher degree of synchronism than exists in the regions of background activity of the brain. To determine the degree of synchronism, a modified method of evaluating zero conditional Lyapunov exponents from time series is proposed.

Detection of chaotic dynamics in human gait signals from mobile devices

NASA Astrophysics Data System (ADS)

DelMarco, Stephen; Deng, Yunbin

2017-05-01

The ubiquity of mobile devices offers the opportunity to exploit device-generated signal data for biometric identification, health monitoring, and activity recognition. In particular, mobile devices contain an Inertial Measurement Unit (IMU) that produces acceleration and rotational rate information from the IMU accelerometers and gyros. These signals reflect motion properties of the human carrier. It is well-known that the complexity of bio-dynamical systems gives rise to chaotic dynamics. Knowledge of chaotic properties of these systems has shown utility, for example, in detecting abnormal medical conditions and neurological disorders. Chaotic dynamics has been found, in the lab, in bio-dynamical systems data such as electrocardiogram (heart), electroencephalogram (brain), and gait data. In this paper, we investigate the following question: can we detect chaotic dynamics in human gait as measured by IMU acceleration and gyro data from mobile phones? To detect chaotic dynamics, we perform recurrence analysis on real gyro and accelerometer signal data obtained from mobile devices. We apply the delay coordinate embedding approach from Takens' theorem to reconstruct the phase space trajectory of the multi-dimensional gait dynamical system. We use mutual information properties of the signal to estimate the appropriate delay value, and the false nearest neighbor approach to determine the phase space embedding dimension. We use a correlation dimension-based approach together with estimation of the largest Lyapunov exponent to make the chaotic dynamics detection decision. We investigate the ability to detect chaotic dynamics for the different one-dimensional IMU signals, across human subject and walking modes, and as a function of different phone locations on the human carrier.

Precisely cyclic sand: self-organization of periodically sheared frictional grains.

PubMed

Royer, John R; Chaikin, Paul M

2015-01-06

The disordered static structure and chaotic dynamics of frictional granular matter has occupied scientists for centuries, yet there are few organizational principles or guiding rules for this highly hysteretic, dissipative material. We show that cyclic shear of a granular material leads to dynamic self-organization into several phases with different spatial and temporal order. Using numerical simulations, we present a phase diagram in strain-friction space that shows chaotic dispersion, crystal formation, vortex patterns, and most unusually a disordered phase in which each particle precisely retraces its unique path. However, the system is not reversible. Rather, the trajectory of each particle, and the entire frictional, many-degrees-of-freedom system, organizes itself into a limit cycle absorbing state. Of particular note is that fact that the cyclic states are spatially disordered, whereas the ordered states are chaotic.

Precisely cyclic sand: Self-organization of periodically sheared frictional grains

PubMed Central

Royer, John R.; Chaikin, Paul M.

2015-01-01

The disordered static structure and chaotic dynamics of frictional granular matter has occupied scientists for centuries, yet there are few organizational principles or guiding rules for this highly hysteretic, dissipative material. We show that cyclic shear of a granular material leads to dynamic self-organization into several phases with different spatial and temporal order. Using numerical simulations, we present a phase diagram in strain–friction space that shows chaotic dispersion, crystal formation, vortex patterns, and most unusually a disordered phase in which each particle precisely retraces its unique path. However, the system is not reversible. Rather, the trajectory of each particle, and the entire frictional, many–degrees-of-freedom system, organizes itself into a limit cycle absorbing state. Of particular note is that fact that the cyclic states are spatially disordered, whereas the ordered states are chaotic. PMID:25538298

Detection of Nonverbal Synchronization through Phase Difference in Human Communication.

PubMed

Kwon, Jinhwan; Ogawa, Ken-ichiro; Ono, Eisuke; Miyake, Yoshihiro

2015-01-01

Nonverbal communication is an important factor in human communication, and body movement synchronization in particular is an important part of nonverbal communication. Some researchers have analyzed body movement synchronization by focusing on changes in the amplitude of body movements. However, the definition of "body movement synchronization" is still unclear. From a theoretical viewpoint, phase difference is the most important factor in synchronization analysis. Therefore, there is a need to measure the synchronization of body movements using phase difference. The purpose of this study was to provide a quantitative definition of the phase difference distribution for detecting body movement synchronization in human communication. The phase difference distribution was characterized using four statistical measurements: density, mean phase difference, standard deviation (SD) and kurtosis. To confirm the effectiveness of our definition, we applied it to human communication in which the roles of speaker and listener were defined. Specifically, we examined the difference in the phase difference distribution between two different communication situations: face-to-face communication with visual interaction and remote communication with unidirectional visual perception. Participant pairs performed a task supposing lecture in the face-to-face communication condition and in the remote communication condition via television. Throughout the lecture task, we extracted a set of phase differences from the time-series data of the acceleration norm of head nodding motions between two participants. Statistical analyses of the phase difference distribution revealed the characteristics of head nodding synchronization. Although the mean phase differences in synchronized head nods did not differ significantly between the conditions, there were significant differences in the densities, the SDs and the kurtoses of the phase difference distributions of synchronized head nods. These results show the difference in nonverbal synchronization between different communication types. Our study indicates that the phase difference distribution is useful in detecting nonverbal synchronization in various human communication situations.

Nonlinear Analysis of Two-phase Circumferential Motion in the Ablation Circumstance

NASA Astrophysics Data System (ADS)

Xiao-liang, Xu; Hai-ming, Huang; Zi-mao, Zhang

2010-05-01

In aerospace craft reentry and solid rocket propellant nozzle, thermal chemistry ablation is a complex process coupling with convection, heat transfer, mass transfer and chemical reaction. Based on discrete vortex method (DVM), thermal chemical ablation model and particle kinetic model, a computational module dealing with the two-phase circumferential motion in ablation circumstance is designed, the ablation velocity and circumferential field can be thus calculated. The calculated nonlinear time series are analyzed in chaotic identification method: relative chaotic characters such as correlation dimension and the maximum Lyapunov exponent are calculated, fractal dimension of vortex bulbs and particles distributions are also obtained, thus the nonlinear ablation process can be judged as a spatiotemporal chaotic process.

Illusion optics in chaotic light

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang Suheng; Gan Shu; Xiong Jun

2010-08-15

The time-reversal process provides the possibility to counteract the time evolution of a physical system. Recent research has shown that such a process can occur in the first-order field correlation of chaotic light and result in the spatial interference and phase-reversal diffraction in an unbalanced interferometer. Here we report experimental investigations on the invisibility cloak and illusion phenomena in chaotic light. In an unbalanced interferometer illuminated by thermal light, we have observed the cloak effect and the optical transformation of one object into another object. The experimental results can be understood by the phase-reversal diffraction, and they demonstrate the theoreticalmore » proposal of similar effects in complementary media.« less

Dynamical phases of the Hindmarsh-Rose neuronal model: studies of the transition from bursting to spiking chaos.

PubMed

Innocenti, Giacomo; Morelli, Alice; Genesio, Roberto; Torcini, Alessandro

2007-12-01

The dynamical phases of the Hindmarsh-Rose neuronal model are analyzed in detail by varying the external current I. For increasing current values, the model exhibits a peculiar cascade of nonchaotic and chaotic period-adding bifurcations leading the system from the silent regime to a chaotic state dominated by bursting events. At higher I-values, this phase is substituted by a regime of continuous chaotic spiking and finally via an inverse period doubling cascade the system returns to silence. The analysis is focused on the transition between the two chaotic phases displayed by the model: one dominated by spiking dynamics and the other by bursts. At the transition an abrupt shrinking of the attractor size associated with a sharp peak in the maximal Lyapunov exponent is observable. However, the transition appears to be continuous and smoothed out over a finite current interval, where bursts and spikes coexist. The beginning of the transition (from the bursting side) is signaled from a structural modification in the interspike interval return map. This change in the map shape is associated with the disappearance of the family of solutions responsible for the onset of the bursting chaos. The successive passage from bursting to spiking chaos is associated with a progressive pruning of unstable long-lasting bursts.

Generalized Synchronization in AN Array of Nonlinear Dynamic Systems with Applications to Chaotic Cnn

NASA Astrophysics Data System (ADS)

Min, Lequan; Chen, Guanrong

This paper establishes some generalized synchronization (GS) theorems for a coupled discrete array of difference systems (CDADS) and a coupled continuous array of differential systems (CCADS). These constructive theorems provide general representations of GS in CDADS and CCADS. Based on these theorems, one can design GS-driven CDADS and CCADS via appropriate (invertible) transformations. As applications, the results are applied to autonomous and nonautonomous coupled Chen cellular neural network (CNN) CDADS and CCADS, discrete bidirectional Lorenz CNN CDADS, nonautonomous bidirectional Chua CNN CCADS, and nonautonomously bidirectional Chen CNN CDADS and CCADS, respectively. Extensive numerical simulations show their complex dynamic behaviors. These theorems provide new means for understanding the GS phenomena of complex discrete and continuously differentiable networks.

Impulse-induced localized control of chaos in starlike networks.

PubMed

Chacón, Ricardo; Palmero, Faustino; Cuevas-Maraver, Jesús

2016-06-01

Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e., all driving pulses transmit the same impulse, the networks display chaotic dynamics. It is found that the taming effect of decreasing the impulse transmitted by the pulses acting on particular nodes strongly depends on their number and degree of connectivity. A theoretical analysis is given explaining the basic physical mechanism as well as the main features of the chaos-control scenario.

Bistability and chaos in the Taylor-Green dynamo.

PubMed

Yadav, Rakesh K; Verma, Mahendra K; Wahi, Pankaj

2012-03-01

Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations.

PubMed

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, R e . Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

Cardiac phase-synchronized myocardial thallium-201 single-photon emission tomography using list mode data acquisition and iterative tomographic reconstruction.

PubMed

Vemmer, T; Steinbüchel, C; Bertram, J; Eschner, W; Kögler, A; Luig, H

1997-03-01

The purpose of this study was to determine whether data acquisition in the list mode and iterative tomographic reconstruction would render feasible cardiac phase-synchronized thallium-201 single-photon emission tomography (SPET) of the myocardium under routine conditions without modifications in tracer dose, acquisition time, or number of steps of the a gamma camera. Seventy non-selected patients underwent 201T1 SPET imaging according to a routine protocol (74 MBq/2 mCi 201T1, 180 degrees rotation of the gamma camera, 32 steps, 30 min). Gamma camera data, ECG, and a time signal were recorded in list mode. The cardiac cycle was divided into eight phases, the end-diastolic phase encompassing the QRS complex, and the end-systolic phase the T wave. Both phase- and non-phase-synchronized tomograms based on the same list mode data were reconstructed iteratively. Phase-synchronized and non-synchronized images were compared. Patients were divided into two groups depending on whether or not coronary artery disease had been definitely diagnosed prior to SPET imaging. The numbers of patients in both groups demonstrating defects visible on the phase-synchronized but not on the non-synchronized images were compared. It was found that both postexercise and redistribution phase tomograms were suited for interpretation. The changes from end-diastolic to end-systolic images allowed a comparative assessment of regional wall motility and tracer uptake. End-diastolic tomograms provided the best definition of defects. Additional defects not apparent on non-synchronized images were visible in 40 patients, six of whom did not show any defect on the non-synchronized images. Of 42 patients in whom coronary artery disease had been definitely diagnosed, 19 had additional defects not visible on the non-synchronized images, in comparison to 21 of 28 in whom coronary artery disease was suspected (P < 0.02; chi 2). It is concluded that cardiac phase-synchronized 201T1 SPET of the myocardium was made feasible by list mode data acquisition and iterative reconstruction. The additional findings on the phase-synchronized tomograms, not visible on the non-synchronized ones, represented genuine defects. Cardiac phase-synchronized 201T1 SPET is advantageous in allowing simultaneous assessment of regional wall motion and tracer uptake, and in visualizing smaller defects.

Effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks

NASA Astrophysics Data System (ADS)

Sun, Xiaojuan; Perc, Matjaž; Kurths, Jürgen

2017-05-01

In this paper, we study effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks. Our focus is on the impact of two parameters, namely the time delay τ and the probability of partial time delay pdelay, whereby the latter determines the probability with which a connection between two neurons is delayed. Our research reveals that partial time delays significantly affect phase synchronization in this system. In particular, partial time delays can either enhance or decrease phase synchronization and induce synchronization transitions with changes in the mean firing rate of neurons, as well as induce switching between synchronized neurons with period-1 firing to synchronized neurons with period-2 firing. Moreover, in comparison to a neuronal network where all connections are delayed, we show that small partial time delay probabilities have especially different influences on phase synchronization of neuronal networks.

Effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks.

PubMed

Sun, Xiaojuan; Perc, Matjaž; Kurths, Jürgen

2017-05-01

In this paper, we study effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks. Our focus is on the impact of two parameters, namely the time delay τ and the probability of partial time delay p delay , whereby the latter determines the probability with which a connection between two neurons is delayed. Our research reveals that partial time delays significantly affect phase synchronization in this system. In particular, partial time delays can either enhance or decrease phase synchronization and induce synchronization transitions with changes in the mean firing rate of neurons, as well as induce switching between synchronized neurons with period-1 firing to synchronized neurons with period-2 firing. Moreover, in comparison to a neuronal network where all connections are delayed, we show that small partial time delay probabilities have especially different influences on phase synchronization of neuronal networks.

Optical image cryptosystem using chaotic phase-amplitude masks encoding and least-data-driven decryption by compressive sensing

NASA Astrophysics Data System (ADS)

Lang, Jun; Zhang, Jing

2015-03-01

In our proposed optical image cryptosystem, two pairs of phase-amplitude masks are generated from the chaotic web map for image encryption in the 4f double random phase-amplitude encoding (DRPAE) system. Instead of transmitting the real keys and the enormous masks codes, only a few observed measurements intermittently chosen from the masks are delivered. Based on compressive sensing paradigm, we suitably refine the series expansions of web map equations to better reconstruct the underlying system. The parameters of the chaotic equations can be successfully calculated from observed measurements and then can be used to regenerate the correct random phase-amplitude masks for decrypting the encoded information. Numerical simulations have been performed to verify the proposed optical image cryptosystem. This cryptosystem can provide a new key management and distribution method. It has the advantages of sufficiently low occupation of the transmitted key codes and security improvement of information transmission without sending the real keys.

A chaotic jerk system with non-hyperbolic equilibrium: Dynamics, effect of time delay and circuit realisation

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Pham, Viet-Thanh; Tahir, Fadhil Rahma; Akgul, Akif; Abdolmohammadi, Hamid Reza; Jafari, Sajad

2018-04-01

The literature on chaos has highlighted several chaotic systems with special features. In this work, a novel chaotic jerk system with non-hyperbolic equilibrium is proposed. The dynamics of this new system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, we investigate the time-delay effects on the proposed system. Realisation of such a system is presented to verify its feasibility.

Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime

NASA Astrophysics Data System (ADS)

Löck, Steffen; Bäcker, Arnd; Ketzmerick, Roland; Schlagheck, Peter

2010-03-01

We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. We give a qualitative recipe for identifying the relevance of nonlinear resonances in a given ℏ regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.

Network structure of multivariate time series.

PubMed

Lacasa, Lucas; Nicosia, Vincenzo; Latora, Vito

2015-10-21

Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range tools and techniques for time series analysis already exist, the increasing availability of massive data structures calls for new approaches for multidimensional signal processing. We present here a non-parametric method to analyse multivariate time series, based on the mapping of a multidimensional time series into a multilayer network, which allows to extract information on a high dimensional dynamical system through the analysis of the structure of the associated multiplex network. The method is simple to implement, general, scalable, does not require ad hoc phase space partitioning, and is thus suitable for the analysis of large, heterogeneous and non-stationary time series. We show that simple structural descriptors of the associated multiplex networks allow to extract and quantify nontrivial properties of coupled chaotic maps, including the transition between different dynamical phases and the onset of various types of synchronization. As a concrete example we then study financial time series, showing that a multiplex network analysis can efficiently discriminate crises from periods of financial stability, where standard methods based on time-series symbolization often fail.

Dynamics, Analysis and Implementation of a Multiscroll Memristor-Based Chaotic Circuit

NASA Astrophysics Data System (ADS)

Alombah, N. Henry; Fotsin, Hilaire; Ngouonkadi, E. B. Megam; Nguazon, Tekou

This article introduces a novel four-dimensional autonomous multiscroll chaotic circuit which is derived from the actual simplest memristor-based chaotic circuit. A fourth circuit element — another inductor — is introduced to generate the complex behavior observed. A systematic study of the chaotic behavior is performed with the help of some nonlinear tools such as Lyapunov exponents, phase portraits, and bifurcation diagrams. Multiple scroll attractors are observed in Matlab, Pspice environments and also experimentally. We also observe the phenomenon of antimonotonicity, periodic and chaotic bubbles, multiple periodic-doubling bifurcations, Hopf bifurcations, crises and the phenomenon of intermittency. The chaotic dynamics of this circuit is realized by laboratory experiments, Pspice simulations, numerical and analytical investigations. It is observed that the results from the three environments agree to a great extent. This topology is likely convenient to be used to intentionally generate chaos in memristor-based chaotic circuit applications, given the fact that multiscroll chaotic systems have found important applications as broadband signal generators, pseudorandom number generators for communication engineering and also in biometric authentication.

Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

NASA Astrophysics Data System (ADS)

Mobayen, Saleh; Kingni, Sifeu Takougang; Pham, Viet-Thanh; Nazarimehr, Fahimeh; Jafari, Sajad

2018-02-01

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

Detection of Nonverbal Synchronization through Phase Difference in Human Communication

PubMed Central

Kwon, Jinhwan; Ogawa, Ken-ichiro; Ono, Eisuke; Miyake, Yoshihiro

2015-01-01

Nonverbal communication is an important factor in human communication, and body movement synchronization in particular is an important part of nonverbal communication. Some researchers have analyzed body movement synchronization by focusing on changes in the amplitude of body movements. However, the definition of “body movement synchronization” is still unclear. From a theoretical viewpoint, phase difference is the most important factor in synchronization analysis. Therefore, there is a need to measure the synchronization of body movements using phase difference. The purpose of this study was to provide a quantitative definition of the phase difference distribution for detecting body movement synchronization in human communication. The phase difference distribution was characterized using four statistical measurements: density, mean phase difference, standard deviation (SD) and kurtosis. To confirm the effectiveness of our definition, we applied it to human communication in which the roles of speaker and listener were defined. Specifically, we examined the difference in the phase difference distribution between two different communication situations: face-to-face communication with visual interaction and remote communication with unidirectional visual perception. Participant pairs performed a task supposing lecture in the face-to-face communication condition and in the remote communication condition via television. Throughout the lecture task, we extracted a set of phase differences from the time-series data of the acceleration norm of head nodding motions between two participants. Statistical analyses of the phase difference distribution revealed the characteristics of head nodding synchronization. Although the mean phase differences in synchronized head nods did not differ significantly between the conditions, there were significant differences in the densities, the SDs and the kurtoses of the phase difference distributions of synchronized head nods. These results show the difference in nonverbal synchronization between different communication types. Our study indicates that the phase difference distribution is useful in detecting nonverbal synchronization in various human communication situations. PMID:26208100

The brain as a dynamic physical system.

PubMed

McKenna, T M; McMullen, T A; Shlesinger, M F

1994-06-01

The brain is a dynamic system that is non-linear at multiple levels of analysis. Characterization of its non-linear dynamics is fundamental to our understanding of brain function. Identifying families of attractors in phase space analysis, an approach which has proven valuable in describing non-linear mechanical and electrical systems, can prove valuable in describing a range of behaviors and associated neural activity including sensory and motor repertoires. Additionally, transitions between attractors may serve as useful descriptors for analysing state changes in neurons and neural ensembles. Recent observations of synchronous neural activity, and the emerging capability to record the spatiotemporal dynamics of neural activity by voltage-sensitive dyes and electrode arrays, provide opportunities for observing the population dynamics of neural ensembles within a dynamic systems context. New developments in the experimental physics of complex systems, such as the control of chaotic systems, selection of attractors, attractor switching and transient states, can be a source of powerful new analytical tools and insights into the dynamics of neural systems.

Dynamics of a grain-filled ball on a vibrating plate.

PubMed

Pacheco-Vázquez, F; Ludewig, F; Dorbolo, S

2014-09-12

We study experimentally how the bouncing dynamics of a hollow ball on a vibrating plate is modified when it is partially filled with liquid or grains. Whereas empty and liquid-filled balls display a dominant chaotic dynamics, a ball with grains exhibits a rich variety of stationary states, determined by the grain size and filling volume. In the collisional regime, i.e., when the energy injected to the system is mainly dissipated by interparticle collisions, an unexpected period-1 orbit appears independently of the vibration conditions, over a wide range. This is a self-regulated state driven by the formation and collapse of a granular gas within the ball during one cycle. In the frictional regime (dissipation dominated by friction), the grains move collectively and generate different patterns and steady modes: oscillons, waves, period doubling, etc. From a phase diagram and a geometrical analysis, we deduce that these modes are the result of a coupling (synchronization) between the vibrating plate frequency and the trajectory followed by the particles inside the cavity.

Dynamics of a Grain-Filled Ball on a Vibrating Plate

NASA Astrophysics Data System (ADS)

Pacheco-Vázquez, F.; Ludewig, F.; Dorbolo, S.

2014-09-01

We study experimentally how the bouncing dynamics of a hollow ball on a vibrating plate is modified when it is partially filled with liquid or grains. Whereas empty and liquid-filled balls display a dominant chaotic dynamics, a ball with grains exhibits a rich variety of stationary states, determined by the grain size and filling volume. In the collisional regime, i.e., when the energy injected to the system is mainly dissipated by interparticle collisions, an unexpected period-1 orbit appears independently of the vibration conditions, over a wide range. This is a self-regulated state driven by the formation and collapse of a granular gas within the ball during one cycle. In the frictional regime (dissipation dominated by friction), the grains move collectively and generate different patterns and steady modes: oscillons, waves, period doubling, etc. From a phase diagram and a geometrical analysis, we deduce that these modes are the result of a coupling (synchronization) between the vibrating plate frequency and the trajectory followed by the particles inside the cavity.

Synchronisation and Circuit Realisation of Chaotic Hartley System

NASA Astrophysics Data System (ADS)

Varan, Metin; Akgül, Akif; Güleryüz, Emre; Serbest, Kasım

2018-06-01

Hartley chaotic system is topologically the simplest, but its dynamical behaviours are very rich and its synchronisation has not been seen in literature. This paper aims to introduce a simple chaotic system which can be used as alternative to classical chaotic systems in synchronisation fields. Time series, phase portraits, and bifurcation diagrams reveal the dynamics of the mentioned system. Chaotic Hartley model is also supported with electronic circuit model simulations. Its exponential dynamics are hard to realise on circuit model; this paper is the first in literature that handles such a complex modelling problem. Modelling, synchronisation, and circuit realisation of the Hartley system are implemented respectively in MATLAB-Simulink and ORCAD environments. The effectiveness of the applied synchronisation method is revealed via numerical methods, and the results are discussed. Retrieved results show that this complex chaotic system can be used in secure communication fields.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

PubMed

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Controlling chaotic behavior in CO2 and other lasers

NASA Astrophysics Data System (ADS)

1993-06-01

Additional substantial experimental progress has been made, in the third month of the project, in setting up equipment and testing for producing chaotic behavior with a CO2 laser. The project goal is to synchronize and control chaos in CO2 and other lasers, and thereby increase the power in ensembles of coupled laser sources. Numerous investigations into the chaos regime have been made, a second CO2 laser has been brought on stream, and work is progressing in the fourth month toward coupling the two lasers and control of the first laser. It is also intended to submit at least two papers to the Second Experimental Chaos Conference which is supported by the Office of Naval Research. Abstracts to those two papers are attached. Last month's report discussed the experimental investigation of nonlinear dynamics of CO2 lasers which involved a new technique of inducing chaos. In this new technique, an acoustically modulated feedback of the laser light was used and led to chaotic dynamics at a very low modulation frequency of 375 Hz. Since then, new results have been obtained by an Electro-Optical Modulation (EOM) technique. In the new setup, the electro-optical modulator is placed in an external cavity outside the laser.

Chaotic oscillation and random-number generation based on nanoscale optical-energy transfer.

PubMed

Naruse, Makoto; Kim, Song-Ju; Aono, Masashi; Hori, Hirokazu; Ohtsu, Motoichi

2014-08-12

By using nanoscale energy-transfer dynamics and density matrix formalism, we demonstrate theoretically and numerically that chaotic oscillation and random-number generation occur in a nanoscale system. The physical system consists of a pair of quantum dots (QDs), with one QD smaller than the other, between which energy transfers via optical near-field interactions. When the system is pumped by continuous-wave radiation and incorporates a timing delay between two energy transfers within the system, it emits optical pulses. We refer to such QD pairs as nano-optical pulsers (NOPs). Irradiating an NOP with external periodic optical pulses causes the oscillating frequency of the NOP to synchronize with the external stimulus. We find that chaotic oscillation occurs in the NOP population when they are connected by an external time delay. Moreover, by evaluating the time-domain signals by statistical-test suites, we confirm that the signals are sufficiently random to qualify the system as a random-number generator (RNG). This study reveals that even relatively simple nanodevices that interact locally with each other through optical energy transfer at scales far below the wavelength of irradiating light can exhibit complex oscillatory dynamics. These findings are significant for applications such as ultrasmall RNGs.

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption.

PubMed

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2(1345). As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption

NASA Astrophysics Data System (ADS)

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 21345. As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

Missile Defense: European Phased Adaptive Approach Acquisitions Face Synchronization, Transparency, and Accountability Challenges

DTIC Science & Technology

2010-12-21

House of Representatives Subject: Missile Defense: European Phased Adaptive Approach Acquisitions Face Synchronization , Transparency, and...TITLE AND SUBTITLE Missile Defense: European Phased Adaptive Approach Acquisitions Face Synchronization , Transparency, and Accountability...However, we found that DOD has not fully implemented a management process that synchronizes EPAA acquisition activities and ensures transparency and

On the robustness of complex heterogeneous gene expression networks.

PubMed

Gómez-Gardeñes, Jesús; Moreno, Yamir; Floría, Luis M

2005-04-01

We analyze a continuous gene expression model on the underlying topology of a complex heterogeneous network. Numerical simulations aimed at studying the chaotic and periodic dynamics of the model are performed. The results clearly indicate that there is a region in which the dynamical and structural complexity of the system avoid chaotic attractors. However, contrary to what has been reported for Random Boolean Networks, the chaotic phase cannot be completely suppressed, which has important bearings on network robustness and gene expression modeling.

New type of chimera and mutual synchronization of spatiotemporal structures in two coupled ensembles of nonlocally interacting chaotic maps

NASA Astrophysics Data System (ADS)

Bukh, Andrei; Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim

2017-11-01

We study numerically the dynamics of a network made of two coupled one-dimensional ensembles of discrete-time systems. The first ensemble is represented by a ring of nonlocally coupled Henon maps and the second one by a ring of nonlocally coupled Lozi maps. We find that the network of coupled ensembles can realize all the spatio-temporal structures which are observed both in the Henon map ensemble and in the Lozi map ensemble while uncoupled. Moreover, we reveal a new type of spatiotemporal structure, a solitary state chimera, in the considered network. We also establish and describe the effect of mutual synchronization of various complex spatiotemporal patterns in the system of two coupled ensembles of Henon and Lozi maps.

A Tribute to J. C. Sprott

NASA Astrophysics Data System (ADS)

Nazarimehr, Fahimeh; Jafari, Sajad; Chen, Guanrong; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Li, Chunbiao; Wei, Zhouchao

2017-12-01

In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems, nonautonomous systems, partial differential equations, fractional-order systems, delay differential systems, spatiotemporal systems, artificial neural networks, and chaotic electrical circuits. He has also studied dynamical properties of complex systems such as bifurcations and basins of attraction. He has done work on generating fractal art. He has examined models of real-world systems that exhibit chaos. The second group of his works comprise control and synchronization of chaos. Finally, the third group is extracting dynamical properties of systems using time-series analysis. This paper highlights the impact of Sprott’s work on the promotion of nonlinear dynamics.

Assessing Chaos in Sickle Cell Anemia Crises

NASA Astrophysics Data System (ADS)

Harris, Wesley; Le Floch, Francois

2006-11-01

Recent developments in sickle cell research and blood flow modeling allow for new interpretations of the sickle cell crises. With an appropriate set of theoretical and empirical equations describing the dynamics of the red cells in their environment, and the response of the capillaries to major changes in the rheology, a complete mathematical system has been derived. This system of equations is believed to be of major importance to provide new and significant insight into the causes of the disease and related crises. With simulations, it has been proven that the system transition from a periodic solution to a chaotic one, which illustrates the onset of crises from a regular blood flow synchronized with the heart beat. Moreover, the analysis of the effects of various physiological parameters exposes the potential to control chaotic solutions, which, in turn, could lead to the creation of new and more effective treatments for sickle cell anemia. .

Connection adaption for control of networked mobile chaotic agents.

PubMed

Zhou, Jie; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Xiao, Gaoxi; Boccaletti, S

2017-11-22

In this paper, we propose a strategy for the control of mobile chaotic oscillators by adaptively rewiring connections between nearby agents with local information. In contrast to the dominant adaptive control schemes where coupling strength is adjusted continuously according to the states of the oscillators, our method does not request adaption of coupling strength. As the resulting interaction structure generated by this proposed strategy is strongly related to unidirectional chains, by investigating synchronization property of unidirectional chains, we reveal that there exists a certain coupling range in which the agents could be controlled regardless of the length of the chain. This feature enables the adaptive strategy to control the mobile oscillators regardless of their moving speed. Compared with existing adaptive control strategies for networked mobile agents, our proposed strategy is simpler for implementation where the resulting interaction networks are kept unweighted at all time.

Efficient biometric authenticated key agreements based on extended chaotic maps for telecare medicine information systems.

PubMed

Lou, Der-Chyuan; Lee, Tian-Fu; Lin, Tsung-Hung

2015-05-01

Authenticated key agreements for telecare medicine information systems provide patients, doctors, nurses and health visitors with accessing medical information systems and getting remote services efficiently and conveniently through an open network. In order to have higher security, many authenticated key agreement schemes appended biometric keys to realize identification except for using passwords and smartcards. Due to too many transmissions and computational costs, these authenticated key agreement schemes are inefficient in communication and computation. This investigation develops two secure and efficient authenticated key agreement schemes for telecare medicine information systems by using biometric key and extended chaotic maps. One scheme is synchronization-based, while the other nonce-based. Compared to related approaches, the proposed schemes not only retain the same security properties with previous schemes, but also provide users with privacy protection and have fewer transmissions and lower computational cost.

Temporal intermittency and the lifetime of chimera states in ensembles of nonlocally coupled chaotic oscillators

NASA Astrophysics Data System (ADS)

Semenova, N. I.; Strelkova, G. I.; Anishchenko, V. S.; Zakharova, A.

2017-06-01

We describe numerical results for the dynamics of networks of nonlocally coupled chaotic maps. Switchings in time between amplitude and phase chimera states have been first established and studied. It has been shown that in autonomous ensembles, a nonstationary regime of switchings has a finite lifetime and represents a transient process towards a stationary regime of phase chimera. The lifetime of the nonstationary switching regime can be increased to infinity by applying short-term noise perturbations.

Stability and Noise-induced Transitions in an Ensemble of Nonlocally Coupled Chaotic Maps

NASA Astrophysics Data System (ADS)

Bukh, Andrei V.; Slepnev, Andrei V.; Anishchenko, Vadim S.; Vadivasova, Tatiana E.

2018-05-01

The influence of noise on chimera states arising in ensembles of nonlocally coupled chaotic maps is studied. There are two types of chimera structures that can be obtained in such ensembles: phase and amplitude chimera states. In this work, a series of numerical experiments is carried out to uncover the impact of noise on both types of chimeras. The noise influence on a chimera state in the regime of periodic dynamics results in the transition to chaotic dynamics. At the same time, the transformation of incoherence clusters of the phase chimera to incoherence clusters of the amplitude chimera occurs. Moreover, it is established that the noise impact may result in the appearance of a cluster with incoherent behavior in the middle of a coherence cluster.

Three-dimensional information hierarchical encryption based on computer-generated holograms

NASA Astrophysics Data System (ADS)

Kong, Dezhao; Shen, Xueju; Cao, Liangcai; Zhang, Hao; Zong, Song; Jin, Guofan

2016-12-01

A novel approach for encrypting three-dimensional (3-D) scene information hierarchically based on computer-generated holograms (CGHs) is proposed. The CGHs of the layer-oriented 3-D scene information are produced by angular-spectrum propagation algorithm at different depths. All the CGHs are then modulated by different chaotic random phase masks generated by the logistic map. Hierarchical encryption encoding is applied when all the CGHs are accumulated one by one, and the reconstructed volume of the 3-D scene information depends on permissions of different users. The chaotic random phase masks could be encoded into several parameters of the chaotic sequences to simplify the transmission and preservation of the keys. Optical experiments verify the proposed method and numerical simulations show the high key sensitivity, high security, and application flexibility of the method.

Hierarchical structure in sharply divided phase space for the piecewise linear map

NASA Astrophysics Data System (ADS)

Akaishi, Akira; Aoki, Kazuki; Shudo, Akira

2017-05-01

We have studied a two-dimensional piecewise linear map to examine how the hierarchical structure of stable regions affects the slow dynamics in Hamiltonian systems. In the phase space there are infinitely many stable regions, each of which is polygonal-shaped, and the rest is occupied by chaotic orbits. By using symbolic representation of stable regions, a procedure to compute the edges of the polygons is presented. The stable regions are hierarchically distributed in phase space and the edges of the stable regions show the marginal instability. The cumulative distribution of the recurrence time obeys a power law as ˜t-2 , the same as the one for the system with phase space, which is composed of a single stable region and chaotic components. By studying the symbol sequence of recurrence trajectories, we show that the hierarchical structure of stable regions has no significant effect on the power-law exponent and that only the marginal instability on the boundary of stable regions is responsible for determining the exponent. We also discuss the relevance of the hierarchical structure to those in more generic chaotic systems.

Critical edge between frozen extinction and chaotic life

NASA Astrophysics Data System (ADS)

Monetti, Roberto A.; Albano, Ezequiel V.

1995-12-01

The cellular automata ``game of life'' (GL) proposed by J. Conway simulates the dynamic evolution of a society of living organisms. It has been extensively studied in order to understand the emergence of complexity and diversity from a set of local rules. More recently, the capability of GL to self-oranize into a critical state has opened an interesting debate. In this work we adopt a different approach: by introducing stochastic rules in the GL it is found that ``life'' exhibits a very rich critical behavior. Discontinuous (first-order) irreversible phase transitions (IPT's) between an extinct phase and a steady state supporting life are found. A precise location of the critical edge is achieved by means of an epidemic analysis, which also allows us to determine dynamic critical exponents. Furthermore, by means of a damage spreading study we conclude that the living phase is chaotic. The edge of the frozen-chaotic transition coincides with that of the IPT's life extinction. Close to the edge, fractal spreading of the damage is observed; however, deep inside the living phase such spreading becomes homogeneous. (c) 1995 The American Physical Society

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale.

PubMed

Maslennikov, Oleg V; Nekorkin, Vladimir I

2016-07-01

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.

Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches

PubMed Central

Lowet, Eric; Roberts, Mark J.; Bonizzi, Pietro; Karel, Joël; De Weerd, Peter

2016-01-01

Synchronization or phase-locking between oscillating neuronal groups is considered to be important for coordination of information among cortical networks. Spectral coherence is a commonly used approach to quantify phase locking between neural signals. We systematically explored the validity of spectral coherence measures for quantifying synchronization among neural oscillators. To that aim, we simulated coupled oscillatory signals that exhibited synchronization dynamics using an abstract phase-oscillator model as well as interacting gamma-generating spiking neural networks. We found that, within a large parameter range, the spectral coherence measure deviated substantially from the expected phase-locking. Moreover, spectral coherence did not converge to the expected value with increasing signal-to-noise ratio. We found that spectral coherence particularly failed when oscillators were in the partially (intermittent) synchronized state, which we expect to be the most likely state for neural synchronization. The failure was due to the fast frequency and amplitude changes induced by synchronization forces. We then investigated whether spectral coherence reflected the information flow among networks measured by transfer entropy (TE) of spike trains. We found that spectral coherence failed to robustly reflect changes in synchrony-mediated information flow between neural networks in many instances. As an alternative approach we explored a phase-locking value (PLV) method based on the reconstruction of the instantaneous phase. As one approach for reconstructing instantaneous phase, we used the Hilbert Transform (HT) preceded by Singular Spectrum Decomposition (SSD) of the signal. PLV estimates have broad applicability as they do not rely on stationarity, and, unlike spectral coherence, they enable more accurate estimations of oscillatory synchronization across a wide range of different synchronization regimes, and better tracking of synchronization-mediated information flow among networks. PMID:26745498

Symmetric encryption algorithms using chaotic and non-chaotic generators: A review

PubMed Central

Radwan, Ahmed G.; AbdElHaleem, Sherif H.; Abd-El-Hafiz, Salwa K.

2015-01-01

This paper summarizes the symmetric image encryption results of 27 different algorithms, which include substitution-only, permutation-only or both phases. The cores of these algorithms are based on several discrete chaotic maps (Arnold’s cat map and a combination of three generalized maps), one continuous chaotic system (Lorenz) and two non-chaotic generators (fractals and chess-based algorithms). Each algorithm has been analyzed by the correlation coefficients between pixels (horizontal, vertical and diagonal), differential attack measures, Mean Square Error (MSE), entropy, sensitivity analyses and the 15 standard tests of the National Institute of Standards and Technology (NIST) SP-800-22 statistical suite. The analyzed algorithms include a set of new image encryption algorithms based on non-chaotic generators, either using substitution only (using fractals) and permutation only (chess-based) or both. Moreover, two different permutation scenarios are presented where the permutation-phase has or does not have a relationship with the input image through an ON/OFF switch. Different encryption-key lengths and complexities are provided from short to long key to persist brute-force attacks. In addition, sensitivities of those different techniques to a one bit change in the input parameters of the substitution key as well as the permutation key are assessed. Finally, a comparative discussion of this work versus many recent research with respect to the used generators, type of encryption, and analyses is presented to highlight the strengths and added contribution of this paper. PMID:26966561

Effect of Parametric Dichotomic Markov Noise on the Properties of Chaotic Transitions in Dynamical Systems

NASA Astrophysics Data System (ADS)

Gac, J. M.; Żebrowski, J. J.

A chaotic transition occurs when a continuous change of one of the parameters of the system causes a discontinuous change in the properties of the chaotic attractor of the system. Such phenomena are present in many dynamical systems, in which a chaotic behavior occurs. The best known of these transitions are: the period-doubling bifurcation cascade, intermittency and crises. The effect of dichotomous Markov noise (DMN) on the properties of systems with chaotic transitions is discussed. DMN is a very simple two-valued stochastic process, with constant transition rates between the two states. In spite of its simplicity, this kind of noise is a very powerful tool to describe various phenomena present in many physical, chemical or biological systems. Many interesting phenomena induced by DMN are known. However, there is no research on the effect of this kind of noise on intermittency or crises. We present the change of the mean laminar phase length and of laminar phase length distribution caused by DMN modulating the parameters of a system with intermittency and the modification of the mean life time on the pre-crisis attractor in the case of a boundary crisis. The results obtained analytically are compared with numerical simulations for several simple dynamical systems.

Carrier phase synchronization system for improved amplitude modulation and television broadcast reception

DOEpatents

Smith, Stephen F [Loudon, TN; Moore, James A [Powell, TN

2011-02-01

Systems and methods are described for carrier phase synchronization for improved AM and TV broadcast reception. A method includes synchronizing the phase of a carrier frequency of a broadcast signal with the phase of a remote reference frequency. An apparatus includes a receiver to detect the phase of a reference signal; a phase comparator coupled to the reference signal-phase receiver; a voltage controlled oscillator coupled to the phase comparator; and a phase-controlled radio frequency output coupled to the voltage controlled oscillator.

Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses.

PubMed

Yu, Haitao; Wang, Jiang; Du, Jiwei; Deng, Bin; Wei, Xile

2015-02-01

Effects of time delay on the local and global synchronization in small-world neuronal networks with chemical synapses are investigated in this paper. Numerical results show that, for both excitatory and inhibitory coupling types, the information transmission delay can always induce synchronization transitions of spiking neurons in small-world networks. In particular, regions of in-phase and out-of-phase synchronization of connected neurons emerge intermittently as the synaptic delay increases. For excitatory coupling, all transitions to spiking synchronization occur approximately at integer multiples of the firing period of individual neurons; while for inhibitory coupling, these transitions appear at the odd multiples of the half of the firing period of neurons. More importantly, the local synchronization transition is more profound than the global synchronization transition, depending on the type of coupling synapse. For excitatory synapses, the local in-phase synchronization observed for some values of the delay also occur at a global scale; while for inhibitory ones, this synchronization, observed at the local scale, disappears at a global scale. Furthermore, the small-world structure can also affect the phase synchronization of neuronal networks. It is demonstrated that increasing the rewiring probability can always improve the global synchronization of neuronal activity, but has little effect on the local synchronization of neighboring neurons.

Chaotic simulated annealing by a neural network with a variable delay: design and application.

PubMed

Chen, Shyan-Shiou

2011-10-01

In this paper, we have three goals: the first is to delineate the advantages of a variably delayed system, the second is to find a more intuitive Lyapunov function for a delayed neural network, and the third is to design a delayed neural network for a quadratic cost function. For delayed neural networks, most researchers construct a Lyapunov function based on the linear matrix inequality (LMI) approach. However, that approach is not intuitive. We provide a alternative candidate Lyapunov function for a delayed neural network. On the other hand, if we are first given a quadratic cost function, we can construct a delayed neural network by suitably dividing the second-order term into two parts: a self-feedback connection weight and a delayed connection weight. To demonstrate the advantage of a variably delayed neural network, we propose a transiently chaotic neural network with variable delay and show numerically that the model should possess a better searching ability than Chen-Aihara's model, Wang's model, and Zhao's model. We discuss both the chaotic and the convergent phases. During the chaotic phase, we simply present bifurcation diagrams for a single neuron with a constant delay and with a variable delay. We show that the variably delayed model possesses the stochastic property and chaotic wandering. During the convergent phase, we not only provide a novel Lyapunov function for neural networks with a delay (the Lyapunov function is independent of the LMI approach) but also establish a correlation between the Lyapunov function for a delayed neural network and an objective function for the traveling salesman problem. © 2011 IEEE

Increased phase synchronization during continuous face integration measured simultaneously with EEG and fMRI.

PubMed

Kottlow, Mara; Jann, Kay; Dierks, Thomas; Koenig, Thomas

2012-08-01

Gamma zero-lag phase synchronization has been measured in the animal brain during visual binding. Human scalp EEG studies used a phase locking factor (trial-to-trial phase-shift consistency) or gamma amplitude to measure binding but did not analyze common-phase signals so far. This study introduces a method to identify networks oscillating with near zero-lag phase synchronization in human subjects. We presented unpredictably moving face parts (NOFACE) which - during some periods - produced a complete schematic face (FACE). The amount of zero-lag phase synchronization was measured using global field synchronization (GFS). GFS provides global information on the amount of instantaneous coincidences in specific frequencies throughout the brain. Gamma GFS was increased during the FACE condition. To localize the underlying areas, we correlated gamma GFS with simultaneously recorded BOLD responses. Positive correlates comprised the bilateral middle fusiform gyrus and the left precuneus. These areas may form a network of areas transiently synchronized during face integration, including face-specific as well as binding-specific regions and regions for visual processing in general. Thus, the amount of zero-lag phase synchronization between remote regions of the human visual system can be measured with simultaneously acquired EEG/fMRI. Copyright © 2012 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Emergence of synchronization induced by the interplay between two prisoner's dilemma games with volunteering in small-world networks

NASA Astrophysics Data System (ADS)

Chen, Yong; Qin, Shao-Meng; Yu, Lianchun; Zhang, Shengli

2008-03-01

We studied synchronization between prisoner’s dilemma games with voluntary participation in two Newman-Watts small-world networks. It was found that there are three kinds of synchronization: partial phase synchronization, total phase synchronization, and complete synchronization, for varied coupling factors. Besides, two games can reach complete synchronization for the large enough coupling factor. We also discussed the effect of the coupling factor on the amplitude of oscillation of cooperator density.

Intermittent and sustained periodic windows in networked chaotic Rössler oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Zhiwei; Sun, Yong; University of the Chinese Academy of Sciences, Beijing 100049

Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weakmore » coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators.« less

The integration of temporally shifted visual feedback in a synchronization task: The role of perceptual stability in a visuo-proprioceptive conflict situation.

PubMed

Ceux, Tanja; Montagne, Gilles; Buekers, Martinus J

2010-12-01

The present study examined whether the beneficial role of coherently grouped visual motion structures for performing complex (interlimb) coordination patterns can be generalized to synchronization behavior in a visuo-proprioceptive conflict situation. To achieve this goal, 17 participants had to synchronize a self-moved circle, representing the arm movement, with a visual target signal corresponding to five temporally shifted visual feedback conditions (0%, 25%, 50%, 75%, and 100% of the target cycle duration) in three synchronization modes (in-phase, anti-phase, and intermediate). The results showed that the perception of a newly generated perceptual Gestalt between the visual feedback of the arm and the target signal facilitated the synchronization performance in the preferred in-phase synchronization mode in contrast to the less stable anti-phase and intermediate mode. Our findings suggest that the complexity of the synchronization mode defines to what extent the visual and/or proprioceptive information source affects the synchronization performance in the present unimanual synchronization task. Copyright © 2010 Elsevier B.V. All rights reserved.

Scale-freeness or partial synchronization in neural mass phase oscillator networks: Pick one of two?

PubMed

Daffertshofer, Andreas; Ton, Robert; Pietras, Bastian; Kringelbach, Morten L; Deco, Gustavo

2018-04-04

Modeling and interpreting (partial) synchronous neural activity can be a challenge. We illustrate this by deriving the phase dynamics of two seminal neural mass models: the Wilson-Cowan firing rate model and the voltage-based Freeman model. We established that the phase dynamics of these models differed qualitatively due to an attractive coupling in the first and a repulsive coupling in the latter. Using empirical structural connectivity matrices, we determined that the two dynamics cover the functional connectivity observed in resting state activity. We further searched for two pivotal dynamical features that have been reported in many experimental studies: (1) a partial phase synchrony with a possibility of a transition towards either a desynchronized or a (fully) synchronized state; (2) long-term autocorrelations indicative of a scale-free temporal dynamics of phase synchronization. Only the Freeman phase model exhibited scale-free behavior. Its repulsive coupling, however, let the individual phases disperse and did not allow for a transition into a synchronized state. The Wilson-Cowan phase model, by contrast, could switch into a (partially) synchronized state, but it did not generate long-term correlations although being located close to the onset of synchronization, i.e. in its critical regime. That is, the phase-reduced models can display one of the two dynamical features, but not both. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Indirect synchronization control in a starlike network of phase oscillators

NASA Astrophysics Data System (ADS)

Kuptsov, Pavel V.; Kuptsova, Anna V.

2018-04-01

A starlike network of non-identical phase oscillators is considered that contains the hub and tree rays each having a single node. In such network effect of indirect synchronization control is reported: changing the natural frequency and the coupling strength of one of the peripheral oscillators one can switch on an off the synchronization of the others. The controlling oscillator at that is not synchronized with them and has a frequency that is approximately four time higher then the frequency of the synchronization. The parameter planes showing a corresponding synchronization tongue are represented and time dependencies of phase differences are plotted for points within and outside of the tongue.

Improved numerical solutions for chaotic-cancer-model

NASA Astrophysics Data System (ADS)

Yasir, Muhammad; Ahmad, Salman; Ahmed, Faizan; Aqeel, Muhammad; Akbar, Muhammad Zubair

2017-01-01

In biological sciences, dynamical system of cancer model is well known due to its sensitivity and chaoticity. Present work provides detailed computational study of cancer model by counterbalancing its sensitive dependency on initial conditions and parameter values. Cancer chaotic model is discretized into a system of nonlinear equations that are solved using the well-known Successive-Over-Relaxation (SOR) method with a proven convergence. This technique enables to solve large systems and provides more accurate approximation which is illustrated through tables, time history maps and phase portraits with detailed analysis.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munoz, Pablo R.; Rempel, Erico L.; Barroso, Joaquim J.

We study the chaotic dynamics of the Pierce diode, a simple spatially extended system for collisionless bounded plasmas, focusing on the concept of edge of chaos, the boundary that separates transient from asymptotic dynamics. We fully characterize an interior crisis at the end of a periodic window, thereby showing direct evidence of the collision between a chaotic attractor, a chaotic saddle, and the edge of chaos, formed by a period-3 unstable periodic orbit and its stable manifold. The edge of chaos persists after the interior crisis, when the global attractor of the system increases its size in the phase space.

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maslennikov, Oleg V.; Nekorkin, Vladimir I.

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basicmore » properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.« less

An authenticated image encryption scheme based on chaotic maps and memory cellular automata

NASA Astrophysics Data System (ADS)

Bakhshandeh, Atieh; Eslami, Ziba

2013-06-01

This paper introduces a new image encryption scheme based on chaotic maps, cellular automata and permutation-diffusion architecture. In the permutation phase, a piecewise linear chaotic map is utilized to confuse the plain-image and in the diffusion phase, we employ the Logistic map as well as a reversible memory cellular automata to obtain an efficient and secure cryptosystem. The proposed method admits advantages such as highly secure diffusion mechanism, computational efficiency and ease of implementation. A novel property of the proposed scheme is its authentication ability which can detect whether the image is tampered during the transmission or not. This is particularly important in applications where image data or part of it contains highly sensitive information. Results of various analyses manifest high security of this new method and its capability for practical image encryption.

Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks.

PubMed

Li, Chunguang; Chen, Luonan; Aihara, Kazuyuki

2008-06-01

Real systems are often subject to both noise perturbations and impulsive effects. In this paper, we study the stability and stabilization of systems with both noise perturbations and impulsive effects. In other words, we generalize the impulsive control theory from the deterministic case to the stochastic case. The method is based on extending the comparison method to the stochastic case. The method presented in this paper is general and easy to apply. Theoretical results on both stability in the pth mean and stability with disturbance attenuation are derived. To show the effectiveness of the basic theory, we apply it to the impulsive control and synchronization of chaotic systems with noise perturbations, and to the stability of impulsive stochastic neural networks. Several numerical examples are also presented to verify the theoretical results.

Quantifying chaotic dynamics from integrate-and-fire processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavlov, A. N.; Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov; Pavlova, O. N.

2015-01-15

Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periodsmore » of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.« less

Instrument to synchronize Thomson scattering diagnostic measurements with MHD acitivity in a tokamak

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wintenberg, A.L.

1985-04-01

An instrument to synchronize the firing of a ruby laser for a Thomson scattering diagnostic with plasma oscillations was designed, developed, and evaluated. The instrument will fire the laser at a user-selected phase of an input sine or sawtooth wave with an accuracy of +-15/sup 0/. Allowable frequencies range from 20 to 500 Hz for a sawtooth and from 1 to 30 kHz for a sine wave. The instrument also allows synchronization with a sine wave to be enabled by a preselected sawtooth phase. The instrument uses analog signal processing circuits to separate the signal components, remove unwanted components, andmore » produce zero-phase synchronization pulses. The instrument measures the period between zero-phase pulses in order to produce phase synchronization pulses delayed a fraction of the period from the zero-phase pulses. The laser is fired by the phase synchronization pulse. Unwanted signal components are attenuated by bandpass filters. A digitally controlled self-adjusting bandpass filter for sine processing. The instrument was used to investigate the variation of the electron temperature profile with the phase of the x-ray signal from an Impurity Studies Experiment (ISX-B) plasma exhibiting magnetohydrodynamic (MHD) activity.« less

[Present state in synchronization therapy of malignant tumors and acute leukemias (author's transl)].

PubMed

Sauer, H; Wilmanns, W

1976-03-01

Chemotherapy of malignant tumors can be made more effective by synchronization of the cell cycle. Synchronization therapy consists of a synchronizing step (phase I), an interval and a cytocidal step (phase II). Some regimens till now approved in clinical treatment are presented. The results are found to be encouraging. In all schedules three effects work together namely synchronization recruitment, summation.

Measures of Quantum Synchronization in Continuous Variable Systems

NASA Astrophysics Data System (ADS)

Mari, A.; Farace, A.; Didier, N.; Giovannetti, V.; Fazio, R.

2013-09-01

We introduce and characterize two different measures which quantify the level of synchronization of coupled continuous variable quantum systems. The two measures allow us to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is, in principle, unbounded; however, in the absence of quantum resources (e.g., squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum optomechanical systems.

Measures of quantum synchronization in continuous variable systems.

PubMed

Mari, A; Farace, A; Didier, N; Giovannetti, V; Fazio, R

2013-09-06

We introduce and characterize two different measures which quantify the level of synchronization of coupled continuous variable quantum systems. The two measures allow us to extend to the quantum domain the notions of complete and phase synchronization. The Heisenberg principle sets a universal bound to complete synchronization. The measure of phase synchronization is, in principle, unbounded; however, in the absence of quantum resources (e.g., squeezing) the synchronization level is bounded below a certain threshold. We elucidate some interesting connections between entanglement and synchronization and, finally, discuss an application based on quantum optomechanical systems.

Current Trend Towards Using Soft Computing Approaches to Phase Synchronization in Communication Systems

NASA Technical Reports Server (NTRS)

Drake, Jeffrey T.; Prasad, Nadipuram R.

1999-01-01

This paper surveys recent advances in communications that utilize soft computing approaches to phase synchronization. Soft computing, as opposed to hard computing, is a collection of complementary methodologies that act in producing the most desirable control, decision, or estimation strategies. Recently, the communications area has explored the use of the principal constituents of soft computing, namely, fuzzy logic, neural networks, and genetic algorithms, for modeling, control, and most recently for the estimation of phase in phase-coherent communications. If the receiver in a digital communications system is phase-coherent, as is often the case, phase synchronization is required. Synchronization thus requires estimation and/or control at the receiver of an unknown or random phase offset.

Cross-entropy optimization for neuromodulation.

PubMed

Brar, Harleen K; Yunpeng Pan; Mahmoudi, Babak; Theodorou, Evangelos A

2016-08-01

This study presents a reinforcement learning approach for the optimization of the proportional-integral gains of the feedback controller represented in a computational model of epilepsy. The chaotic oscillator model provides a feedback control systems view of the dynamics of an epileptic brain with an internal feedback controller representative of the natural seizure suppression mechanism within the brain circuitry. Normal and pathological brain activity is simulated in this model by adjusting the feedback gain values of the internal controller. With insufficient gains, the internal controller cannot provide enough feedback to the brain dynamics causing an increase in correlation between different brain sites. This increase in synchronization results in the destabilization of the brain dynamics, which is representative of an epileptic seizure. To provide compensation for an insufficient internal controller an external controller is designed using proportional-integral feedback control strategy. A cross-entropy optimization algorithm is applied to the chaotic oscillator network model to learn the optimal feedback gains for the external controller instead of hand-tuning the gains to provide sufficient control to the pathological brain and prevent seizure generation. The correlation between the dynamics of neural activity within different brain sites is calculated for experimental data to show similar dynamics of epileptic neural activity as simulated by the network of chaotic oscillators.

Methods, systems and apparatus for synchronous current regulation of a five-phase machine

DOEpatents

Gallegos-Lopez, Gabriel; Perisic, Milun

2012-10-09

Methods, systems and apparatus are provided for controlling operation of and regulating current provided to a five-phase machine when one or more phases has experienced a fault or has failed. In one implementation, the disclosed embodiments can be used to synchronously regulate current in a vector controlled motor drive system that includes a five-phase AC machine, a five-phase inverter module coupled to the five-phase AC machine, and a synchronous current regulator.

Desynchronization of stochastically synchronized chemical oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Snari, Razan; Tinsley, Mark R., E-mail: mark.tinsley@mail.wvu.edu, E-mail: kshowalt@wvu.edu; Faramarzi, Sadegh

Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.

Synchronization of Oscillators: An Ideal Introduction to Phase Transitions

ERIC Educational Resources Information Center

English, L. Q.

2008-01-01

The spontaneous synchronization of phase-coupled, non-identical oscillators is explored numerically via the famous Kuramoto model. The conditions for synchronization are examined as a function of the coupling network. I argue that such a numerical exploration provides a feasible way to introduce the topic of phase transitions early in the physics…

G2 phase-specific proteins of HeLa cells.

PubMed Central

Al-Bader, A A; Orengo, A; Rao, P N

1978-01-01

The objective of this study was to determine if HeLa cells irreversibly arrested in G2 phase of the cell cycle by a brief exposure to a nitrosourea compound were deficient in certain proteins when compared with G2-synchronized cells. Total cellular proteins of G2-synchronized, G2-arrested, and S phase-synchronized cells were compared by two-dimensional polyacrylamide gel electrophoresis. The S phase cells differed from the G2-synchronized and G2-arrested cells by the absence of about 35 and 25 protein spots, respectively, of a total of nearly 150. At least nine protein spots in the molecular weight range of 4--5 X 10(4) that were present in the G2-synchronized cells were absent in both the G2-arrested and the S phase cells. Thus, these studies suggest that the missing proteins are probably necessary for the transition of cells from G2 phase to mitosis. Supplying the missing proteins to the G2-arrested cells by fusion with G2-synchronized cells facilitated the entry of the former into mitosis. Images PMID:282623

Synchronization of coupled metronomes on two layers

NASA Astrophysics Data System (ADS)

Zhang, Jing; Yu, Yi-Zhen; Wang, Xin-Gang

2017-12-01

Coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of complex dynamical systems, as well as a classical setup for classroom demonstrations of synchronization phenomena. Whereas previous studies of metronome synchronization have been concentrating on symmetric coupling schemes, here we consider the asymmetric case by adopting the scheme of layered metronomes. Specifically, we place two metronomes on each layer, and couple two layers by placing one on top of the other. By varying the initial conditions of the metronomes and adjusting the friction between the two layers, a variety of synchronous patterns are observed in experiment, including the splay synchronization (SS) state, the generalized splay synchronization (GSS) state, the anti-phase synchronization (APS) state, the in-phase delay synchronization (IPDS) state, and the in-phase synchronization (IPS) state. In particular, the IPDS state, in which the metronomes on each layer are synchronized in phase but are of a constant phase delay to metronomes on the other layer, is observed for the first time. In addition, a new technique based on audio signals is proposed for pattern detection, which is more convenient and easier to apply than the existing acquisition techniques. Furthermore, a theoretical model is developed to explain the experimental observations, and is employed to explore the dynamical properties of the patterns, including the basin distributions and the pattern transitions. Our study sheds new lights on the collective behaviors of coupled metronomes, and the developed setup can be used in the classroom for demonstration purposes.

Chaotic behavior of a spin-glass model on a Cayley tree

NASA Astrophysics Data System (ADS)

da Costa, F. A.; de Araújo, J. M.; Salinas, S. R.

2015-06-01

We investigate the phase diagram of a spin-1 Ising spin-glass model on a Cayley tree. According to early work of Thompson and collaborators, this problem can be formulated in terms of a set of nonlinear discrete recursion relations along the branches of the tree. Physically relevant solutions correspond to the attractors of these mapping equations. In the limit of infinite coordination of the tree, and for some choices of the model parameters, we make contact with findings for the phase diagram of more recently investigated versions of the Blume-Emery-Griffiths spin-glass model. In addition to the anticipated phases, we numerically characterize the existence of modulated and chaotic structures.

Double-well chimeras in 2D lattice of chaotic bistable elements

NASA Astrophysics Data System (ADS)

Shepelev, I. A.; Bukh, A. V.; Vadivasova, T. E.; Anishchenko, V. S.; Zakharova, A.

2018-01-01

We investigate spatio-temporal dynamics of a 2D ensemble of nonlocally coupled chaotic cubic maps in a bistability regime. In particular, we perform a detailed study on the transition ;coherence - incoherence; for varying coupling strength for a fixed interaction radius. For the 2D ensemble we show the appearance of amplitude and phase chimera states previously reported for 1D ensembles of nonlocally coupled chaotic systems. Moreover, we uncover a novel type of chimera state, double-well chimera, which occurs due to the interplay of the bistability of the local dynamics and the 2D ensemble structure. Additionally, we find double-well chimera behavior for steady states which we call double-well chimera death. A distinguishing feature of chimera patterns observed in the lattice is that they mainly combine clusters of different chimera types: phase, amplitude and double-well chimeras.

Denoising of chaotic signal using independent component analysis and empirical mode decomposition with circulate translating

NASA Astrophysics Data System (ADS)

Wen-Bo, Wang; Xiao-Dong, Zhang; Yuchan, Chang; Xiang-Li, Wang; Zhao, Wang; Xi, Chen; Lei, Zheng

2016-01-01

In this paper, a new method to reduce noises within chaotic signals based on ICA (independent component analysis) and EMD (empirical mode decomposition) is proposed. The basic idea is decomposing chaotic signals and constructing multidimensional input vectors, firstly, on the base of EMD and its translation invariance. Secondly, it makes the independent component analysis on the input vectors, which means that a self adapting denoising is carried out for the intrinsic mode functions (IMFs) of chaotic signals. Finally, all IMFs compose the new denoised chaotic signal. Experiments on the Lorenz chaotic signal composed of different Gaussian noises and the monthly observed chaotic sequence on sunspots were put into practice. The results proved that the method proposed in this paper is effective in denoising of chaotic signals. Moreover, it can correct the center point in the phase space effectively, which makes it approach the real track of the chaotic attractor. Project supported by the National Science and Technology, China (Grant No. 2012BAJ15B04), the National Natural Science Foundation of China (Grant Nos. 41071270 and 61473213), the Natural Science Foundation of Hubei Province, China (Grant No. 2015CFB424), the State Key Laboratory Foundation of Satellite Ocean Environment Dynamics, China (Grant No. SOED1405), the Hubei Provincial Key Laboratory Foundation of Metallurgical Industry Process System Science, China (Grant No. Z201303), and the Hubei Key Laboratory Foundation of Transportation Internet of Things, Wuhan University of Technology, China (Grant No.2015III015-B02).

Application of Soft Computing in Coherent Communications Phase Synchronization

NASA Technical Reports Server (NTRS)

Drake, Jeffrey T.; Prasad, Nadipuram R.

2000-01-01

The use of soft computing techniques in coherent communications phase synchronization provides an alternative to analytical or hard computing methods. This paper discusses a novel use of Adaptive Neuro-Fuzzy Inference Systems (ANFIS) for phase synchronization in coherent communications systems utilizing Multiple Phase Shift Keying (MPSK) modulation. A brief overview of the M-PSK digital communications bandpass modulation technique is presented and it's requisite need for phase synchronization is discussed. We briefly describe the hybrid platform developed by Jang that incorporates fuzzy/neural structures namely the, Adaptive Neuro-Fuzzy Interference Systems (ANFIS). We then discuss application of ANFIS to phase estimation for M-PSK. The modeling of both explicit, and implicit phase estimation schemes for M-PSK symbols with unknown structure are discussed. Performance results from simulation of the above scheme is presented.

Analysis of the Multiple-Solution Response of a Flexible Rotor Supported on Non-Linear Squeeze Film Dampers

NASA Astrophysics Data System (ADS)

ZHU, C. S.; ROBB, D. A.; EWINS, D. J.

2002-05-01

The multiple-solution response of rotors supported on squeeze film dampers is a typical non-linear phenomenon. The behaviour of the multiple-solution response in a flexible rotor supported on two identical squeeze film dampers with centralizing springs is studied by three methods: synchronous circular centred-orbit motion solution, numerical integration method and slow acceleration method using the assumption of a short bearing and cavitated oil film; the differences of computational results obtained by the three different methods are compared in this paper. It is shown that there are three basic forms for the multiple-solution response in the flexible rotor system supported on the squeeze film dampers, which are the resonant, isolated bifurcation and swallowtail bifurcation multiple solutions. In the multiple-solution speed regions, the rotor motion may be subsynchronous, super-subsynchronous, almost-periodic and even chaotic, besides synchronous circular centred, even if the gravity effect is not considered. The assumption of synchronous circular centred-orbit motion for the journal and rotor around the static deflection line can be used only in some special cases; the steady state numerical integration method is very useful, but time consuming. Using the slow acceleration method, not only can the multiple-solution speed regions be detected, but also the non-synchronous response regions.

Audio signal encryption using chaotic Hénon map and lifting wavelet transforms

NASA Astrophysics Data System (ADS)

Roy, Animesh; Misra, A. P.

2017-12-01

We propose an audio signal encryption scheme based on the chaotic Hénon map. The scheme mainly comprises two phases: one is the preprocessing stage where the audio signal is transformed into data by the lifting wavelet scheme and the other in which the transformed data is encrypted by chaotic data set and hyperbolic functions. Furthermore, we use dynamic keys and consider the key space size to be large enough to resist any kind of cryptographic attacks. A statistical investigation is also made to test the security and the efficiency of the proposed scheme.

Some new surprises in chaos.

PubMed

Bunimovich, Leonid A; Vela-Arevalo, Luz V

2015-09-01

"Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.

Effect of Noise on the Relaxation to an Invariant Probability Measure of Nonhyperbolic Chaotic Attractors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anishchenko, Vadim S.; Vadivasova, Tatjana E.; Kopeikin, Andrey S.

2001-07-30

We study the influence of external noise on the relaxation to an invariant probability measure for two types of nonhyperbolic chaotic attractors, a spiral (or coherent) and a noncoherent one. We find that for the coherent attractor the rate of mixing changes under the influence of noise, although the largest Lyapunov exponent remains almost unchanged. A mechanism of the noise influence on mixing is presented which is associated with the dynamics of the instantaneous phase of chaotic trajectories. This also explains why the noncoherent regime is robust against the presence of external noise.

Note: A phase synchronization photography method for AC discharge.

PubMed

Wu, Zhicheng; Zhang, Qiaogen; Ma, Jingtan; Pang, Lei

2018-05-01

To research discharge physics under AC voltage, a phase synchronization photography method is presented. By using a permanent-magnet synchronous motor to drive a photography mask synchronized with a discharge power supply, discharge images in a specific phase window can be recorded. Some examples of discharges photographed by this method, including the corona discharge in SF 6 and the corona discharge along the air/epoxy surface, demonstrate the feasibility of this method. Therefore, this method provides an effective tool for discharge physics researchers.

Note: A phase synchronization photography method for AC discharge

NASA Astrophysics Data System (ADS)

Wu, Zhicheng; Zhang, Qiaogen; Ma, Jingtan; Pang, Lei

2018-05-01

To research discharge physics under AC voltage, a phase synchronization photography method is presented. By using a permanent-magnet synchronous motor to drive a photography mask synchronized with a discharge power supply, discharge images in a specific phase window can be recorded. Some examples of discharges photographed by this method, including the corona discharge in SF6 and the corona discharge along the air/epoxy surface, demonstrate the feasibility of this method. Therefore, this method provides an effective tool for discharge physics researchers.

Desktop chaotic systems: Intuition and visualization

NASA Technical Reports Server (NTRS)

Bright, Michelle M.; Melcher, Kevin J.; Qammar, Helen K.; Hartley, Tom T.

1993-01-01

This paper presents a dynamic study of the Wildwood Pendulum, a commercially available desktop system which exhibits a strange attractor. The purpose of studying this chaotic pendulum is twofold: to gain insight in the paradigmatic approach of modeling, simulating, and determining chaos in nonlinear systems; and to provide a desktop model of chaos as a visual tool. For this study, the nonlinear behavior of this chaotic pendulum is modeled, a computer simulation is performed, and an experimental performance is measured. An assessment of the pendulum in the phase plane shows the strange attractor. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined for both the model and the experimental pendulum systems. Correlation dimension results indicate that the pendulum and the model are chaotic and their fractal dimensions are similar.

Stability of the phase motion in race-track microtrons

NASA Astrophysics Data System (ADS)

Kubyshin, Yu. A.; Larreal, O.; Ramírez-Ros, R.; Seara, T. M.

2017-06-01

We model the phase oscillations of electrons in race-track microtrons by means of an area preserving map with a fixed point at the origin, which represents the synchronous trajectory of a reference particle in the beam. We study the nonlinear stability of the origin in terms of the synchronous phase -the phase of the synchronous particle at the injection. We estimate the size and shape of the stability domain around the origin, whose main connected component is enclosed by an invariant curve. We describe the evolution of the stability domain as the synchronous phase varies. We also clarify the role of the stable and unstable invariant curves of some hyperbolic (fixed or periodic) points.

Distributed Synchronization in Communication Networks

DTIC Science & Technology

2018-01-24

synchronization. Secondly, it is known that identical oscillators with sin() coupling functions are guaranteed to synchronize in phase on a complete...provide sufficient conditions for phase- locking , i.e., convergence to a stable equilibrium almost surely. We additionally find conditions when the

Self-organized synchronization of digital phase-locked loops with delayed coupling in theory and experiment

PubMed Central

Wetzel, Lucas; Jörg, David J.; Pollakis, Alexandros; Rave, Wolfgang; Fettweis, Gerhard; Jülicher, Frank

2017-01-01

Self-organized synchronization occurs in a variety of natural and technical systems but has so far only attracted limited attention as an engineering principle. In distributed electronic systems, such as antenna arrays and multi-core processors, a common time reference is key to coordinate signal transmission and processing. Here we show how the self-organized synchronization of mutually coupled digital phase-locked loops (DPLLs) can provide robust clocking in large-scale systems. We develop a nonlinear phase description of individual and coupled DPLLs that takes into account filter impulse responses and delayed signal transmission. Our phase model permits analytical expressions for the collective frequencies of synchronized states, the analysis of stability properties and the time scale of synchronization. In particular, we find that signal filtering introduces stability transitions that are not found in systems without filtering. To test our theoretical predictions, we designed and carried out experiments using networks of off-the-shelf DPLL integrated circuitry. We show that the phase model can quantitatively predict the existence, frequency, and stability of synchronized states. Our results demonstrate that mutually delay-coupled DPLLs can provide robust and self-organized synchronous clocking in electronic systems. PMID:28207779

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape.

PubMed

Gilpin, William; Feldman, Marcus W

2017-07-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the "edge of chaos" while creating a wide distribution of opportunities for speciation during epochs of disruptive selection-a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.

On the estimation of phase synchronization, spurious synchronization and filtering

NASA Astrophysics Data System (ADS)

Rios Herrera, Wady A.; Escalona, Joaquín; Rivera López, Daniel; Müller, Markus F.

2016-12-01

Phase synchronization, viz., the adjustment of instantaneous frequencies of two interacting self-sustained nonlinear oscillators, is frequently used for the detection of a possible interrelationship between empirical data recordings. In this context, the proper estimation of the instantaneous phase from a time series is a crucial aspect. The probability that numerical estimates provide a physically relevant meaning depends sensitively on the shape of its power spectral density. For this purpose, the power spectrum should be narrow banded possessing only one prominent peak [M. Chavez et al., J. Neurosci. Methods 154, 149 (2006)]. If this condition is not fulfilled, band-pass filtering seems to be the adequate technique in order to pre-process data for a posterior synchronization analysis. However, it was reported that band-pass filtering might induce spurious synchronization [L. Xu et al., Phys. Rev. E 73, 065201(R), (2006); J. Sun et al., Phys. Rev. E 77, 046213 (2008); and J. Wang and Z. Liu, EPL 102, 10003 (2013)], a statement that without further specification causes uncertainty over all measures that aim to quantify phase synchronization of broadband field data. We show by using signals derived from different test frameworks that appropriate filtering does not induce spurious synchronization. Instead, filtering in the time domain tends to wash out existent phase interrelations between signals. Furthermore, we show that measures derived for the estimation of phase synchronization like the mean phase coherence are also useful for the detection of interrelations between time series, which are not necessarily derived from coupled self-sustained nonlinear oscillators.

Digital phase shifter synchronizes local oscillators

NASA Technical Reports Server (NTRS)

Ali, S. M.

1978-01-01

Digital phase-shifting network is used as synchronous frequency multiplier for applications such as phase-locking two signals that may differ in frequency. Circuit has various phase-shift capability. Possible applications include data-communication systems and hybrid digital/analog phase-locked loops.

Chaos-on-a-chip secures data transmission in optical fiber links.

PubMed

Argyris, Apostolos; Grivas, Evangellos; Hamacher, Michael; Bogris, Adonis; Syvridis, Dimitris

2010-03-01

Security in information exchange plays a central role in the deployment of modern communication systems. Besides algorithms, chaos is exploited as a real-time high-speed data encryption technique which enhances the security at the hardware level of optical networks. In this work, compact, fully controllable and stably operating monolithic photonic integrated circuits (PICs) that generate broadband chaotic optical signals are incorporated in chaos-encoded optical transmission systems. Data sequences with rates up to 2.5 Gb/s with small amplitudes are completely encrypted within these chaotic carriers. Only authorized counterparts, supplied with identical chaos generating PICs that are able to synchronize and reproduce the same carriers, can benefit from data exchange with bit-rates up to 2.5Gb/s with error rates below 10(-12). Eavesdroppers with access to the communication link experience a 0.5 probability to detect correctly each bit by direct signal detection, while eavesdroppers supplied with even slightly unmatched hardware receivers are restricted to data extraction error rates well above 10(-3).

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

NASA Astrophysics Data System (ADS)

Zverev, V. V.; Rubinstein, B. Ya.

1991-04-01

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.

Chaotic diffusion in the Gliese-876 planetary system

NASA Astrophysics Data System (ADS)

Martí, J. G.; Cincotta, P. M.; Beaugé, C.

2016-07-01

Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disc, and a natural consequence of irregular motion. In this paper, we show that resonant multiplanetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and may still survive virtually unchanged over time-scales comparable to their age. Using the GJ-876 system as an example, we analyse the chaotic diffusion of the outermost (and less massive) planet. We construct a set of stability maps in the surrounding regions of the Laplace resonance. We numerically integrate ensembles of close initial conditions, compute Poincaré maps and estimate the chaotic diffusion present in this system. Our results show that, the Laplace resonance contains two different regions: an inner domain characterized by low chaoticity and slow diffusion, and an outer one displaying larger values of dynamical indicators. In the outer resonant domain, the stochastic borders of the Laplace resonance seem to prevent the complete destruction of the system. We characterize the diffusion for small ensembles along the parameters of the outermost planet. Finally, we perform a stability analysis of the inherent chaotic, albeit stable Laplace resonance, by linking the behaviour of the resonant variables of the configurations to the different sub-structures inside the three-body resonance.

A Simple Model for Complex Dynamical Transitions in Epidemics

NASA Astrophysics Data System (ADS)

Earn, David J. D.; Rohani, Pejman; Bolker, Benjamin M.; Grenfell, Bryan T.

2000-01-01

Dramatic changes in patterns of epidemics have been observed throughout this century. For childhood infectious diseases such as measles, the major transitions are between regular cycles and irregular, possibly chaotic epidemics, and from regionally synchronized oscillations to complex, spatially incoherent epidemics. A simple model can explain both kinds of transitions as the consequences of changes in birth and vaccination rates. Measles is a natural ecological system that exhibits different dynamical transitions at different times and places, yet all of these transitions can be predicted as bifurcations of a single nonlinear model.

Communication scheme using a hyperchaotic semiconductor laser model: Chaos shift key revisited

NASA Astrophysics Data System (ADS)

Fataf, N. A. A.; Palit, Sanjay Kumar; Mukherjee, Sayan; Said, M. R. M.; Son, Doan Hoai; Banerjee, Santo

2017-11-01

Based on the Maxwell-Bloch equations, we considered a five-dimensional ODE system, describing the dynamics of a semiconductor laser. The system has rich dynamics with multi-periodic, chaotic and hyperchaotic states. In this analysis, we have investigated the hyperchaotic nature of the aforesaid model and proposed a communication scheme, the generalized form of chaos shift keys, where the coupled systems do not need to be in the synchronized state. The results are implemented with the hyperchaotic laser model followed by a comprehensive security analysis.

Statistical physics of interacting neural networks

NASA Astrophysics Data System (ADS)

Kinzel, Wolfgang; Metzler, Richard; Kanter, Ido

2001-12-01

Recent results on the statistical physics of time series generation and prediction are presented. A neural network is trained on quasi-periodic and chaotic sequences and overlaps to the sequence generator as well as the prediction errors are calculated numerically. For each network there exists a sequence for which it completely fails to make predictions. Two interacting networks show a transition to perfect synchronization. A pool of interacting networks shows good coordination in the minority game-a model of competition in a closed market. Finally, as a demonstration, a perceptron predicts bit sequences produced by human beings.

Classification of attractors for systems of identical coupled Kuramoto oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 asmore » 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.« less

The dynamical structure of the MEO region: long-term stability, chaos, and transport

NASA Astrophysics Data System (ADS)

Daquin, Jérôme; Rosengren, Aaron J.; Alessi, Elisa Maria; Deleflie, Florent; Valsecchi, Giovanni B.; Rossi, Alessandro

2016-04-01

It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Recent studies have shown that the occurrence and nature of the resonances driving these dynamics depend chiefly on the frequencies of nodal and apsidal precession and the rate of regression of the Moon's nodes. Woven throughout the inclination and eccentricity phase space is an exceedingly complicated web-like structure of lunisolar secular resonances, which become particularly dense near the inclinations of the navigation satellite orbits. A clear picture of the physical significance of these resonances is of considerable practical interest for the design of disposal strategies for the four constellations. Here we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions, and trace the topological organization of the manifolds on which the chaotic motions take place. We present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. As the semi-major axis of the satellite is receding, we observe a transition from stable Nekhoroshev-like structures at three Earth radii, where regular orbits dominate, to a Chirikov regime where resonances overlap at five Earth radii. From a numerical estimation of the Lyapunov times, we find that many of the inclined, nearly circular orbits of the navigation satellites are strongly chaotic and that their dynamics are unpredictable on decadal timescales.

Performance prediction of a synchronization link for distributed aerospace wireless systems.

PubMed

Wang, Wen-Qin; Shao, Huaizong

2013-01-01

For reasons of stealth and other operational advantages, distributed aerospace wireless systems have received much attention in recent years. In a distributed aerospace wireless system, since the transmitter and receiver placed on separated platforms which use independent master oscillators, there is no cancellation of low-frequency phase noise as in the monostatic cases. Thus, high accurate time and frequency synchronization techniques are required for distributed wireless systems. The use of a dedicated synchronization link to quantify and compensate oscillator frequency instability is investigated in this paper. With the mathematical statistical models of phase noise, closed-form analytic expressions for the synchronization link performance are derived. The possible error contributions including oscillator, phase-locked loop, and receiver noise are quantified. The link synchronization performance is predicted by utilizing the knowledge of the statistical models, system error contributions, and sampling considerations. Simulation results show that effective synchronization error compensation can be achieved by using this dedicated synchronization link.

Steady-State Visual Evoked Potentials and Phase Synchronization in Migraine Patients

NASA Astrophysics Data System (ADS)

Angelini, L.; Tommaso, M. De; Guido, M.; Hu, K.; Ivanov, P. Ch.; Marinazzo, D.; Nardulli, G.; Nitti, L.; Pellicoro, M.; Pierro, C.; Stramaglia, S.

2004-07-01

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in the presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli.

Effects of frustration on explosive synchronization

NASA Astrophysics Data System (ADS)

Huang, Xia; Gao, Jian; Sun, Yu-Ting; Zheng, Zhi-Gang; Xu, Can

2016-12-01

In this study, we consider the emergence of explosive synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and frustration is included in the system. This assumption can enhance or delay the explosive transition to synchronization. Interestingly, a de-synchronization phenomenon occurs and the type of phase transition is also changed. Furthermore, we provide an analytical treatment based on a star graph, which resembles that obtained in scale-free networks. Finally, a self-consistent approach is implemented to study the de-synchronization regime. Our findings have important implications for controlling synchronization in complex networks because frustration is a controllable parameter in experiments and a discontinuous abrupt phase transition is always dangerous in engineering in the real world.

Thermodynamics aspects of noise-induced phase synchronization

NASA Astrophysics Data System (ADS)

Pinto, Pedro D.; Oliveira, Fernando A.; Penna, André L. A.

2016-05-01

In this article, we present an approach for the thermodynamics of phase oscillators induced by an internal multiplicative noise. We analytically derive the free energy, entropy, internal energy, and specific heat. In this framework, the formulation of the first law of thermodynamics requires the definition of a synchronization field acting on the phase oscillators. By introducing the synchronization field, we have consistently obtained the susceptibility and analyzed its behavior. This allows us to characterize distinct phases in the system, which we have denoted as synchronized and parasynchronized phases, in analogy with magnetism. The system also shows a rich complex behavior, exhibiting ideal gas characteristics for low temperatures and susceptibility anomalies that are similar to those present in complex fluids such as water.

Thermodynamics aspects of noise-induced phase synchronization.

PubMed

Pinto, Pedro D; Oliveira, Fernando A; Penna, André L A

2016-05-01

In this article, we present an approach for the thermodynamics of phase oscillators induced by an internal multiplicative noise. We analytically derive the free energy, entropy, internal energy, and specific heat. In this framework, the formulation of the first law of thermodynamics requires the definition of a synchronization field acting on the phase oscillators. By introducing the synchronization field, we have consistently obtained the susceptibility and analyzed its behavior. This allows us to characterize distinct phases in the system, which we have denoted as synchronized and parasynchronized phases, in analogy with magnetism. The system also shows a rich complex behavior, exhibiting ideal gas characteristics for low temperatures and susceptibility anomalies that are similar to those present in complex fluids such as water.

Chaotic dynamics of Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions

NASA Astrophysics Data System (ADS)

Blessy, B. S. Gnana; Latha, M. M.

2017-10-01

We investigate the chaotic dynamics of one dimensional Heisenberg ferromagnetic spin chain by constructing the Hamiltonian equations of motion. We present the trajectory and phase plots of the system with bilinear and also biquadratic interactions. The stability of the system is analysed in both cases by constructing the Jacobian matrix and by measuring the Lyapunov exponents. The results are illustrated graphically.

Design and implementation of grid multi-scroll fractional-order chaotic attractors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Liping, E-mail: lip-chenhut@126.com; Pan, Wei; Wu, Ranchao

2016-08-15

This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most.more » Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.« less

Digital synchronization and communication techniques

NASA Technical Reports Server (NTRS)

Lindsey, William C.

1992-01-01

Information on digital synchronization and communication techniques is given in viewgraph form. Topics covered include phase shift keying, modems, characteristics of open loop digital synchronizers, an open loop phase and frequency estimator, and a digital receiver structure using an open loop estimator in a decision directed architecture.

Phase locked loop synchronization for direct detection optical PPM communication systems

NASA Technical Reports Server (NTRS)

Chen, C. C.; Gardner, C. S.

1985-01-01

Receiver timing synchronization of an optical pulse position modulation (PPM) communication system can be achieved using a phase locked loop (PLL) if the photodetector output is properly processed. The synchronization performance is shown to improve with increasing signal power and decreasing loop bandwidth. Bit error rate (BER) of the PLL synchronized PPM system is analyzed and compared to that for the perfectly synchronized system. It is shown that the increase in signal power needed to compensate for the imperfect synchronization is small (less than 0.1 dB) for loop bandwidths less than 0.1% of the slot frequency.

A novel grid multiwing chaotic system with only non-hyperbolic equilibria

NASA Astrophysics Data System (ADS)

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-05-01

The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil'nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.

Cooling of a magmatic system under thermal chaotic mixing

NASA Astrophysics Data System (ADS)

Petrelli, Maurizio; El Omari, Kamal; Le Guer, Yves; Perugini, Diego

2015-04-01

The cooling of a melt undergoing chaotic advection is studied numerically for a magma with a temperature-dependent viscosity in a 2D cavity with moving boundary. Different statistical mixing and energy indicators are used to characterize the efficiency of cooling by thermal chaotic mixing. We show that different cooling rates can be obtained during the thermal mixing even of a single basaltic magmatic batch undergoing chaotic advection. This process can induce complex temperature patterns inside the magma chamber. The emergence of chaotic dynamics strongly affects the temperature field during time and greatly increases the cooling rates. This mechanism has implications for the lifetime of a magmatic body and may favor the appearance of chemical heterogeneities in igneous systems as a result of different crystallization rates. Results from this study also highlight that even a single magma batch can develop, under chaotic thermal advection, complex thermal and therefore compositional patterns resulting from different cooling rates, which can account for some natural features that, to date, have received unsatisfactory explanations. Among them, the production of magmatic enclaves showing completely different cooling histories compared with the host magma, compositional zoning in mineral phases, and the generation of large-scale compositionally zoning observed in many plutons worldwide.

High-frequency chaotic dynamics enabled by optical phase-conjugation

PubMed Central

Mercier, Émeric; Wolfersberger, Delphine; Sciamanna, Marc

2016-01-01

Wideband chaos is of interest for applications such as random number generation or encrypted communications, which typically use optical feedback in a semiconductor laser. Here, we show that replacing conventional optical feedback with phase-conjugate feedback improves the chaos bandwidth. In the range of achievable phase-conjugate mirror reflectivities, the bandwidth increase reaches 27% when compared with feedback from a conventional mirror. Experimental measurements of the time-resolved frequency dynamics on nanosecond time-scales show that the bandwidth enhancement is related to the onset of self-pulsing solutions at harmonics of the external-cavity frequency. In the observed regime, the system follows a chaotic itinerancy among these destabilized high-frequency external-cavity modes. The recorded features are unique to phase-conjugate feedback and distinguish it from the long-standing problem of time-delayed feedback dynamics. PMID:26739806

Experimental Demonstration of Coherent Control in Quantum Chaotic Systems

NASA Astrophysics Data System (ADS)

Bitter, M.; Milner, V.

2017-01-01

We experimentally demonstrate coherent control of a quantum system, whose dynamics is chaotic in the classical limit. Interaction of diatomic molecules with a periodic sequence of ultrashort laser pulses leads to the dynamical localization of the molecular angular momentum, a characteristic feature of the chaotic quantum kicked rotor. By changing the phases of the rotational states in the initially prepared coherent wave packet, we control the rotational distribution of the final localized state and its total energy. We demonstrate the anticipated sensitivity of control to the exact parameters of the kicking field, as well as its disappearance in the classical regime of excitation.

Effect of collision duration on the chaotic dynamics of a ball bouncing on a vertically vibrating plate

NASA Astrophysics Data System (ADS)

Jiang, Z. H.; Liang, Z. J.; Wu, A. C.; Zheng, R. H.

2018-03-01

Experiments have been performed to study the chaotic dynamics of a ball bouncing on a vertically vibrating plate. The velocity dependence of collision duration and coefficient of restitution is determined, and phase portraits of chaotic structures for the flight time and the relative collision velocities are obtained. Numerical calculations are carried out to examine the effects of velocity-dependent collision duration on the ball dynamics. It is revealed that when the collision is instantaneous, sticking solutions are always observed, whereas when the collision duration is taken into account, sticking solutions are destroyed and thereby chaos behaviors are induced.

Chaotic Ising-like dynamics in traffic signals

PubMed Central

Suzuki, Hideyuki; Imura, Jun-ichi; Aihara, Kazuyuki

2013-01-01

The green and red lights of a traffic signal can be viewed as the up and down states of an Ising spin. Moreover, traffic signals in a city interact with each other, if they are controlled in a decentralised way. In this paper, a simple model of such interacting signals on a finite-size two-dimensional lattice is shown to have Ising-like dynamics that undergoes a ferromagnetic phase transition. Probabilistic behaviour of the model is realised by chaotic billiard dynamics that arises from coupled non-chaotic elements. This purely deterministic model is expected to serve as a starting point for considering statistical mechanics of traffic signals. PMID:23350034

Fast angular synchronization for phase retrieval via incomplete information

NASA Astrophysics Data System (ADS)

Viswanathan, Aditya; Iwen, Mark

2015-08-01

We consider the problem of recovering the phase of an unknown vector, x ∈ ℂd, given (normalized) phase difference measurements of the form xjxk*/|xjxk*|, j,k ∈ {1,...,d}, and where xj* denotes the complex conjugate of xj. This problem is sometimes referred to as the angular synchronization problem. This paper analyzes a linear-time-in-d eigenvector-based angular synchronization algorithm and studies its theoretical and numerical performance when applied to a particular class of highly incomplete and possibly noisy phase difference measurements. Theoretical results are provided for perfect (noiseless) measurements, while numerical simulations demonstrate the robustness of the method to measurement noise. Finally, we show that this angular synchronization problem and the specific form of incomplete phase difference measurements considered arise in the phase retrieval problem - where we recover an unknown complex vector from phaseless (or magnitude) measurements.

Noncoherent DTTLs for Symbol Synchronization

NASA Technical Reports Server (NTRS)

Simon, Marvin; Tkacenko, Andre

2007-01-01

Noncoherent data-transition tracking loops (DTTLs) have been proposed for use as symbol synchronizers in digital communication receivers. [Communication- receiver subsystems that can perform their assigned functions in the absence of synchronization with the phases of their carrier signals ( carrier synchronization ) are denoted by the term noncoherent, while receiver subsystems that cannot function without carrier synchronization are said to be coherent. ] The proposal applies, more specifically, to receivers of binary phase-shift-keying (BPSK) signals generated by directly phase-modulating binary non-return-to-zero (NRZ) data streams onto carrier signals having known frequencies but unknown phases. The proposed noncoherent DTTLs would be modified versions of traditional DTTLs, which are coherent. The symbol-synchronization problem is essentially the problem of recovering symbol timing from a received signal. In the traditional, coherent approach to symbol synchronization, it is necessary to establish carrier synchronization in order to recover symbol timing. A traditional DTTL effects an iterative process in which it first generates an estimate of the carrier phase in the absence of symbol-synchronization information, then uses the carrier-phase estimate to obtain an estimate of the symbol-synchronization information, then feeds the symbol-synchronization estimate back to the carrier-phase-estimation subprocess. In a noncoherent symbol-synchronization process, there is no need for carrier synchronization and, hence, no need for iteration between carrier-synchronization and symbol- synchronization subprocesses. The proposed noncoherent symbolsynchronization process is justified theoretically by a mathematical derivation that starts from a maximum a posteriori (MAP) method of estimation of symbol timing utilized in traditional, coherent DTTLs. In that MAP method, one chooses the value of a variable of interest (in this case, the offset in the estimated symbol timing) that causes a likelihood function of symbol estimates over some number of symbol periods to assume a maximum value. In terms that are necessarily oversimplified to fit within the space available for this article, it can be said that the mathematical derivation involves a modified interpretation of the likelihood function that lends itself to noncoherent DTTLs. The proposal encompasses both linear and nonlinear noncoherent DTTLs. The performances of both have been computationally simulated; for comparison, the performances of linear and nonlinear coherent DTTLs have also been computationally simulated. The results of these simulations show that, among other things, the expected mean-square timing errors of coherent and noncoherent DTTLs are relatively insensitive to window width. The results also show that at high signal-to-noise ratios (SNRs), the performances of the noncoherent DTTLs approach those of their coherent counterparts at, while at low SNRs, the noncoherent DTTLs incur penalties of the order of 1.5 to 2 dB.

Synchronization of multi-phase oscillators: an Axelrod-inspired model

NASA Astrophysics Data System (ADS)

Kuperman, M. N.; Zanette, D. H.

2009-07-01

Inspired by Axelrod’s model of culture dissemination, we introduce and analyze a model for a population of coupled oscillators where different levels of synchronization can be assimilated to different degrees of cultural organization. The state of each oscillator is represented by a set of phases, and the interaction - which occurs between homologous phases - is weighted by a decreasing function of the distance between individual states. Both ordered arrays and random networks are considered. We find that the transition between synchronization and incoherent behaviour is mediated by a clustering regime with rich organizational structure, where any two oscillators can be synchronized in some of their phases, while their remain unsynchronized in the others.

High Speed Turbo-Generator: Test Stand Simulator Including Turbine Engine Emulator

DTIC Science & Technology

2010-07-30

15% Shaft Power 4% 8% Our model of the six-phase synchronous machine was based on work by Schiferl and Ong [1]. The six-phase synchronous machine is...develop and submit to ONR a follow-on proposal to address these open issues. 27 REFERENCES [1] R. F. Schiferl and C. M. Ong, "Six phase...at 32 References [Al] R. F. Schiferl and C. M. Ong, "Six phase synchronous machine with ac and dc stator connections, Part I: Equivalent Circuit

Onset of chaos in helical vortex breakdown at low Reynolds number

NASA Astrophysics Data System (ADS)

Pasche, S.; Avellan, F.; Gallaire, F.

2018-06-01

The nonlinear dynamics of a swirling wake flow stemming from a Graboswksi-Berger vortex [Grabowski and Berger, J. Fluid Mech. 75, 525 (1976), 10.1017/S0022112076000360] in a semi-infinite domain is addressed at low Reynolds numbers for a fixed swirl number S =1.095 , defined as the ratio between the characteristic tangential velocity and the centerline axial velocity. In this system, only pure hydrodynamic instabilities develop and interact through the quadratic nonlinearities of the Navier-Stokes equations. Such interactions lead to the onset of chaos at a Reynolds value of Re=220 . This chaotic state is reached by following a Ruelle-Takens-Newhouse scenario, which is initiated by a Hopf bifurcation (the spiral vortex breakdown) as the Reynolds number increases. At larger Reynolds value, a frequency synchronization regime appears followed by a chaotic state again. This scenario is corroborated by nonlinear time series analyses. Stability analysis around the time-average flow and temporal-azimuthal Fourier decomposition of the nonlinear flow distributions both identify successfully the developing vortices and provide deeper insight into the development of the flow patterns leading to this route to chaos. Three single-helical vortices are involved: the primary spiral associated with the spiral vortex breakdown, a downstream spiral, and a near-wake spiral. As the Reynolds number increases, the frequencies of these vortices become closer, increasing their interactions by nonlinearity to eventually generate a strong chaotic axisymmetric oscillation.

Phase synchronization between tropospheric radio refractivity and rainfall amount in a tropical region

NASA Astrophysics Data System (ADS)

Fuwape, Ibiyinka A.; Ogunjo, Samuel T.; Dada, Joseph B.; Ashidi, Gabriel A.; Emmanuel, Israel

2016-11-01

This study investigated linear and nonlinear relationship between the amount of rainfall and radio refractivity in a tropical country, Nigeria using forty seven locations scattered across the country. Correlation and Phase synchronization measures were used for the linear and nonlinear relationship respectively. Weak correlation and phase synchronization was observed between seasonal mean rainfall amount and radio refractivity while strong phase synchronization was found for the detrended data suggesting similar underlying dynamics between rainfall amount and radio refractivity. Causation between rainfall and radio refractivity in a tropical location was studied using Granger causality test. In most of the Southern locations, rainfall was found to Granger cause radio refractivity. Furthermore, it was observed that there is strong correlation between mean rainfall amount and the phase synchronization index over Nigeria. Coupling between rainfall and radio refractivity has been found to be due to water vapour in the atmosphere. Frequency planning and budgeting for microwave propagation during periods of high rainfall should take into consideration this nonlinear relationship.

Analysis of an all-digital maximum likelihood carrier phase and clock timing synchronizer for eight phase-shift keying modulation

NASA Astrophysics Data System (ADS)

Degaudenzi, Riccardo; Vanghi, Vieri

1994-02-01

In all-digital Trellis-Coded 8PSK (TC-8PSK) demodulator well suited for VLSI implementation, including maximum likelihood estimation decision-directed (MLE-DD) carrier phase and clock timing recovery, is introduced and analyzed. By simply removing the trellis decoder the demodulator can efficiently cope with uncoded 8PSK signals. The proposed MLE-DD synchronization algorithm requires one sample for the phase and two samples per symbol for the timing loop. The joint phase and timing discriminator characteristics are analytically derived and numerical results checked by means of computer simulations. An approximated expression for steady-state carrier phase and clock timing mean square error has been derived and successfully checked with simulation findings. Synchronizer deviation from the Cramer Rao bound is also discussed. Mean acquisition time for the digital synchronizer has also been computed and checked, using the Monte Carlo simulation technique. Finally, TC-8PSK digital demodulator performance in terms of bit error rate and mean time to lose lock, including digital interpolators and synchronization loops, is presented.

Abnormal auditory synchronization in stuttering: A magnetoencephalographic study.

PubMed

Kikuchi, Yoshikazu; Okamoto, Tsuyoshi; Ogata, Katsuya; Hagiwara, Koichi; Umezaki, Toshiro; Kenjo, Masamutsu; Nakagawa, Takashi; Tobimatsu, Shozo

2017-02-01

In a previous magnetoencephalographic study, we showed both functional and structural reorganization of the right auditory cortex and impaired left auditory cortex function in people who stutter (PWS). In the present work, we reevaluated the same dataset to further investigate how the right and left auditory cortices interact to compensate for stuttering. We evaluated bilateral N100m latencies as well as indices of local and inter-hemispheric phase synchronization of the auditory cortices. The left N100m latency was significantly prolonged relative to the right N100m latency in PWS, while healthy control participants did not show any inter-hemispheric differences in latency. A phase-locking factor (PLF) analysis, which indicates the degree of local phase synchronization, demonstrated enhanced alpha-band synchrony in the right auditory area of PWS. A phase-locking value (PLV) analysis of inter-hemispheric synchronization demonstrated significant elevations in the beta band between the right and left auditory cortices in PWS. In addition, right PLF and PLVs were positively correlated with stuttering frequency in PWS. Taken together, our data suggest that increased right hemispheric local phase synchronization and increased inter-hemispheric phase synchronization are electrophysiological correlates of a compensatory mechanism for impaired left auditory processing in PWS. Published by Elsevier B.V.

Quantum Synchronization of three-level atoms

NASA Astrophysics Data System (ADS)

He, Peiru; Rey, Ana Maria; Holland, Murray

2015-05-01

Recent studies show that quantum synchronization, the spontaneous alignment of the quantum phase between different oscillators, can be used to build superradiant lasers with ultranarrow linewidth. We theoretically investigate the effect of quantum synchronization on many coupled three-level atoms where there are richer phase diagrams than the standard two-level system. This three-level model allows two-color ultranarrow coherent light to be produced where more than one phase must be simultaneously synchronized. Of particular interest, we study the V-type geometry that is relevant to current 87 Sr experiments in JILA. As well as the synchronization phenomenon, we explore other quantum effects such as photon correlations and squeezing. This work is supported by the DARPA QuASAR program, the NSF, and NIST.

A quantitative theory of gamma synchronization in macaque V1.

PubMed

Lowet, Eric; Roberts, Mark J; Peter, Alina; Gips, Bart; De Weerd, Peter

2017-08-31

Gamma-band synchronization coordinates brief periods of excitability in oscillating neuronal populations to optimize information transmission during sensation and cognition. Commonly, a stable, shared frequency over time is considered a condition for functional neural synchronization. Here, we demonstrate the opposite: instantaneous frequency modulations are critical to regulate phase relations and synchronization. In monkey visual area V1, nearby local populations driven by different visual stimulation showed different gamma frequencies. When similar enough, these frequencies continually attracted and repulsed each other, which enabled preferred phase relations to be maintained in periods of minimized frequency difference. Crucially, the precise dynamics of frequencies and phases across a wide range of stimulus conditions was predicted from a physics theory that describes how weakly coupled oscillators influence each other's phase relations. Hence, the fundamental mathematical principle of synchronization through instantaneous frequency modulations applies to gamma in V1 and is likely generalizable to other brain regions and rhythms.

Competing role of Interactions in Synchronization of Exciton-Polariton condensates

NASA Astrophysics Data System (ADS)

Khan, Saeed; Tureci, Hakan E.

We present a theoretical study of synchronization dynamics in incoherently pumped exciton-polariton condensates in coupled traps. Our analysis is based on an expansion in non-Hermitian modes that take into account the trapping potential and the pump-induced complex-valued potential. We find that polariton-polariton and reservoir-polariton interactions play competing roles in the emergence of a synchronized phase as pumping power is increased, leading to qualitatively different synchronized phases. Crucially, these interactions can also act against each other to hinder synchronization. We present a phase diagram and explain the general characteristics of these phases using a generalized Adler equation. Our work sheds light on dynamics strongly influenced by competing interactions particular to incoherently pumped exciton-polariton condensates, which can lead to interesting features in recently engineered polariton lattices. This work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering.

A quantitative theory of gamma synchronization in macaque V1

PubMed Central

Roberts, Mark J; Peter, Alina; Gips, Bart; De Weerd, Peter

2017-01-01

Gamma-band synchronization coordinates brief periods of excitability in oscillating neuronal populations to optimize information transmission during sensation and cognition. Commonly, a stable, shared frequency over time is considered a condition for functional neural synchronization. Here, we demonstrate the opposite: instantaneous frequency modulations are critical to regulate phase relations and synchronization. In monkey visual area V1, nearby local populations driven by different visual stimulation showed different gamma frequencies. When similar enough, these frequencies continually attracted and repulsed each other, which enabled preferred phase relations to be maintained in periods of minimized frequency difference. Crucially, the precise dynamics of frequencies and phases across a wide range of stimulus conditions was predicted from a physics theory that describes how weakly coupled oscillators influence each other’s phase relations. Hence, the fundamental mathematical principle of synchronization through instantaneous frequency modulations applies to gamma in V1 and is likely generalizable to other brain regions and rhythms. PMID:28857743

Analysis of remote synchronization in complex networks

NASA Astrophysics Data System (ADS)

Gambuzza, Lucia Valentina; Cardillo, Alessio; Fiasconaro, Alessandro; Fortuna, Luigi; Gómez-Gardeñes, Jesus; Frasca, Mattia

2013-12-01

A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs [Bergner et al., Phys. Rev. E 85, 026208 (2012)]. We show the existence of a more general dynamical state of remote synchronization in arbitrary networks of coupled oscillators. This state is characterized by the synchronization of pairs of nodes that are not directly connected via a physical link or any sequence of synchronized nodes. This phenomenon is almost negligible in networks of phase oscillators as its underlying mechanism is the modulation of the amplitude of those intermediary nodes between the remotely synchronized units. Our findings thus show the ubiquity and robustness of these states and bridge the gap from their recent observation in simple toy graphs to complex networks.

Chaotic Motifs in Gene Regulatory Networks

PubMed Central

Zhang, Zhaoyang; Ye, Weiming; Qian, Yu; Zheng, Zhigang; Huang, Xuhui; Hu, Gang

2012-01-01

Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs. PMID:22792171

Cardiorespiratory phase synchronization during normal rest and inward-attention meditation.

PubMed

Wu, Shr-Da; Lo, Pei-Chen

2010-06-11

The cardiac and respiratory systems can be viewed as two self-sustained oscillators with various interactions between them. In this study, the cardiorespiratory phase synchronization (CRPS) quantified by synchrogram was investigated to explore the phase synchronization between these two systems. The synchrogram scheme was applied to electrocardiogram (ECG) and respiration signals. Particular focus was the distinct cardiac-respiratory regulation phenomena intervened by inward-attention meditation and normal relaxation. Four synchronization parameters were measured: frequency ratio, lasting length, number of epochs, and total length. The results showed that normal rest resulted in much weaker CRPS. Statistical analysis reveals that the number of synchronous epochs and the total synchronization length significantly increase (p=0.024 and 0.034 respectively) during meditation. Furthermore, a predominance of 4:1 and 5:1 rhythm-ratio synchronizations was observed during meditation. Consequently, this study concludes that CRPS can be enhanced during meditation, compared with normal relaxation, and reveals a predominance of specific frequency ratios. Copyright (c) 2008 Elsevier Ireland Ltd. All rights reserved.

Investigation of phase synchronization of interictal EEG in right temporal lobe epilepsy

NASA Astrophysics Data System (ADS)

Yu, Haitao; Cai, Lihui; Wu, Xinyu; Song, Zhenxi; Wang, Jiang; Xia, Zijie; Liu, Jing; Cao, Yibin

2018-02-01

Epilepsy is commonly associated with abnormally synchronous activity of neurons located in epileptogenic zones. In this study, we investigated the synchronization characteristic of right temporal lobe epilepsy (RTLE). Multichannel electroencephalography (EEG) data were recorded from the RTLE patients during interictal period and normal controls. Power spectral density was first used to analyze the EEG power for two groups of subjects. It was found that the power of epileptics is increased in the whole brain compared with that of the control. We calculated phase lag index (PLI) to measure the phase synchronization between each pair of EEG signals. A higher degree of synchronization was observed in the epileptics especially between distant channels. In particular, the regional synchronization degree was negatively correlated with power spectral density and the correlation was weaker for epileptics. Moreover, the synchronization degree decayed with the increase of relative distance of channels for both the epilepsy and control, but the dependence was weakened in the former. The obtained results may provide new insights into the generation mechanism of epilepsy.

Performance Prediction of a Synchronization Link for Distributed Aerospace Wireless Systems

PubMed Central

Shao, Huaizong

2013-01-01

For reasons of stealth and other operational advantages, distributed aerospace wireless systems have received much attention in recent years. In a distributed aerospace wireless system, since the transmitter and receiver placed on separated platforms which use independent master oscillators, there is no cancellation of low-frequency phase noise as in the monostatic cases. Thus, high accurate time and frequency synchronization techniques are required for distributed wireless systems. The use of a dedicated synchronization link to quantify and compensate oscillator frequency instability is investigated in this paper. With the mathematical statistical models of phase noise, closed-form analytic expressions for the synchronization link performance are derived. The possible error contributions including oscillator, phase-locked loop, and receiver noise are quantified. The link synchronization performance is predicted by utilizing the knowledge of the statistical models, system error contributions, and sampling considerations. Simulation results show that effective synchronization error compensation can be achieved by using this dedicated synchronization link. PMID:23970828

A network of networks model to study phase synchronization using structural connection matrix of human brain

NASA Astrophysics Data System (ADS)

Ferrari, F. A. S.; Viana, R. L.; Reis, A. S.; Iarosz, K. C.; Caldas, I. L.; Batista, A. M.

2018-04-01

The cerebral cortex plays a key role in complex cortical functions. It can be divided into areas according to their function (motor, sensory and association areas). In this paper, the cerebral cortex is described as a network of networks (cortex network), we consider that each cortical area is composed of a network with small-world property (cortical network). The neurons are assumed to have bursting properties with the dynamics described by the Rulkov model. We study the phase synchronization of the cortex network and the cortical networks. In our simulations, we verify that synchronization in cortex network is not homogeneous. Besides, we focus on the suppression of neural phase synchronization. Synchronization can be related to undesired and pathological abnormal rhythms in the brain. For this reason, we consider the delayed feedback control to suppress the synchronization. We show that delayed feedback control is efficient to suppress synchronous behavior in our network model when an appropriate signal intensity and time delay are defined.

Genetic drift and collective dispersal can result in chaotic genetic patchiness.

PubMed

Broquet, Thomas; Viard, Frédérique; Yearsley, Jonathan M

2013-06-01

Chaotic genetic patchiness denotes unexpected patterns of genetic differentiation that are observed at a fine scale and are not stable in time. These patterns have been described in marine species with free-living larvae, but are unexpected because they occur at a scale below the dispersal range of pelagic larvae. At the scale where most larvae are immigrants, theory predicts spatially homogeneous, temporally stable genetic variation. Empirical studies have suggested that genetic drift interacts with complex dispersal patterns to create chaotic genetic patchiness. Here we use a co-ancestry model and individual-based simulations to test this idea. We found that chaotic genetic patterns (qualified by global FST and spatio-temporal variation in FST's between pairs of samples) arise from the combined effects of (1) genetic drift created by the small local effective population sizes of the sessile phase and variance in contribution among breeding groups and (2) collective dispersal of related individuals in the larval phase. Simulations show that patchiness levels qualitatively comparable to empirical results can be produced by a combination of strong variance in reproductive success and mild collective dispersal. These results call for empirical studies of the effective number of breeders producing larval cohorts, and population genetics at the larval stage. © 2012 The Author(s). Evolution © 2012 The Society for the Study of Evolution.

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

PubMed Central

2017-01-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the “edge of chaos” while creating a wide distribution of opportunities for speciation during epochs of disruptive selection—a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies. PMID:28678792

White noise and synchronization shaping the age structure of the human population

NASA Astrophysics Data System (ADS)

Cebrat, Stanislaw; Biecek, Przemyslaw; Bonkowska, Katarzyna; Kula, Mateusz

2007-06-01

We have modified the standard diploid Penna model of ageing in such a way that instead of threshold of defective loci resulting in genetic death of individuals, the fluctuation of environment and "personal" fluctuations of individuals were introduced. The sum of the both fluctuations describes the health status of the individual. While environmental fluctuations are the same for all individuals in the population, the personal component of fluctuations is composed of fluctuations corresponding to each physiological function (gene, genetic locus). It is rather accepted hypothesis that physiological parameters of any organism fluctuate highly nonlinearly. Transition to the synchronized behaviors could be a very strong diagnostic signal of the life threatening disorder. Thus, in our model, mutations of genes change the chaotic fluctuations representing the function of a wild gene to the synchronized signals generated by mutated genes. Genes are switched on chronologically, like in the standard Penna model. Accumulation of defective genes predicted by Medawar's theory of ageing leads to the replacement of uncorrelated white noise corresponding to the healthy organism by the correlated signals of defective functions. As a result we have got the age distribution of population corresponding to the human demographic data.

Spin-orbit coupling for tidally evolving super-Earths

NASA Astrophysics Data System (ADS)

Rodríguez, A.; Callegari, N.; Michtchenko, T. A.; Hussmann, H.

2012-12-01

We investigate the spin behaviour of close-in rocky planets and the implications for their orbital evolution. Considering that the planet rotation evolves under simultaneous actions of the torque due to the equatorial deformation and the tidal torque, both raised by the central star, we analyse the possibility of temporary captures in spin-orbit resonances. The results of the numerical simulations of the exact equations of motions indicate that, whenever the planet rotation is trapped in a resonant motion, the orbital decay and the eccentricity damping are faster than the ones in which the rotation follows the so-called pseudo-synchronization. Analytical results obtained through the averaged equations of the spin-orbit problem show a good agreement with the numerical simulations. We apply the analysis to the cases of the recently discovered hot super-Earths Kepler-10 b, GJ 3634 b and 55 Cnc e. The simulated dynamical history of these systems indicates the possibility of capture in several spin-orbit resonances; particularly, GJ 3634 b and 55 Cnc e can currently evolve under a non-synchronous resonant motion for suitable values of the parameters. Moreover, 55 Cnc e may avoid a chaotic rotation behaviour by evolving towards synchronization through successive temporary resonant trappings.

Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans.

PubMed Central

Stokes, C L; Rinzel, J

1993-01-01

Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet. Images FIGURE 1 PMID:8218890

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1996-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

Linking Chaotic Advection with Subsurface Biogeochemical Processes

NASA Astrophysics Data System (ADS)

Mays, D. C.; Freedman, V. L.; White, S. K.; Fang, Y.; Neupauer, R.

2017-12-01

This work investigates the extent to which groundwater flow kinematics drive subsurface biogeochemical processes. In terms of groundwater flow kinematics, we consider chaotic advection, whose essential ingredient is stretching and folding of plumes. Chaotic advection is appealing within the context of groundwater remediation because it has been shown to optimize plume spreading in the laminar flows characteristic of aquifers. In terms of subsurface biogeochemical processes, we consider an existing model for microbially-mediated reduction of relatively mobile uranium(VI) to relatively immobile uranium(IV) following injection of acetate into a floodplain aquifer beneath a former uranium mill in Rifle, Colorado. This model has been implemented in the reactive transport code eSTOMP, the massively parallel version of STOMP (Subsurface Transport Over Multiple Phases). This presentation will report preliminary numerical simulations in which the hydraulic boundary conditions in the eSTOMP model are manipulated to simulate chaotic advection resulting from engineered injection and extraction of water through a manifold of wells surrounding the plume of injected acetate. This approach provides an avenue to simulate the impact of chaotic advection within the existing framework of the eSTOMP code.

Chaotic Dynamical Ferromagnetic Phase Induced by Nonequilibrium Quantum Fluctuations

NASA Astrophysics Data System (ADS)

Lerose, Alessio; Marino, Jamir; Žunkovič, Bojan; Gambassi, Andrea; Silva, Alessandro

2018-03-01

We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbor spin interaction in one spatial dimension on the nonequilibrium dynamical phase diagram of the fully connected quantum Ising model. In particular, we focus on the transient dynamics after a quantum quench and study the prethermal state via a combination of analytic time-dependent spin wave theory and numerical methods based on matrix product states. We find that, upon increasing the strength of the quantum fluctuations, the dynamical critical point fans out into a chaotic dynamical phase within which the asymptotic ordering is characterized by strong sensitivity to the parameters and initial conditions. We argue that such a phenomenon is general, as it arises from the impact of quantum fluctuations on the mean-field out of equilibrium dynamics of any system which exhibits a broken discrete symmetry.

Chaotic Dynamical Ferromagnetic Phase Induced by Nonequilibrium Quantum Fluctuations.

PubMed

Lerose, Alessio; Marino, Jamir; Žunkovič, Bojan; Gambassi, Andrea; Silva, Alessandro

2018-03-30

We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbor spin interaction in one spatial dimension on the nonequilibrium dynamical phase diagram of the fully connected quantum Ising model. In particular, we focus on the transient dynamics after a quantum quench and study the prethermal state via a combination of analytic time-dependent spin wave theory and numerical methods based on matrix product states. We find that, upon increasing the strength of the quantum fluctuations, the dynamical critical point fans out into a chaotic dynamical phase within which the asymptotic ordering is characterized by strong sensitivity to the parameters and initial conditions. We argue that such a phenomenon is general, as it arises from the impact of quantum fluctuations on the mean-field out of equilibrium dynamics of any system which exhibits a broken discrete symmetry.

Inhibition of chaotic escape from a potential well by incommensurate escape-suppressing excitations.

PubMed

Chacón, R; Martínez, J A

2002-03-01

Theoretical results are presented concerning the reduction of chaotic escape from a potential well by means of a harmonic parametric excitation that satisfies an ultrasubharmonic resonance condition with the escape-inducing excitation. The possibility of incommensurate escape-suppressing excitations is demonstrated by studying rational approximations to the irrational escape-suppressing frequency. The analytical predictions for the suitable amplitudes and initial phases of the escape-suppressing excitation are tested against numerical simulations based on a high-resolution grid of initial conditions. These numerical results indicate that the reduction of escape is reliably achieved for small amplitudes and at, and only at, the predicted initial phases. For the case of irrational escape-suppressing frequencies, the effective escape-reducing initial phases are found to lie close to the accumulation points of the set of suitable initial phases that are associated with the complete series of convergents up to the convergent giving the chosen rational approximation.

EEG synchronization and migraine

NASA Astrophysics Data System (ADS)

Stramaglia, Sebastiano; Angelini, Leonardo; Pellicoro, Mario; Hu, Kun; Ivanov, Plamen Ch.

2004-03-01

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli.

Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

NASA Astrophysics Data System (ADS)

Hajipour, Ahmad; Tavakoli, Hamidreza

2017-12-01

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of 2.15. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

Chaotic behaviour of the Rossler model and its analysis by using bifurcations of limit cycles and chaotic attractors

NASA Astrophysics Data System (ADS)

Ibrahim, K. M.; Jamal, R. K.; Ali, F. H.

2018-05-01

The behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems’ variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osovski, Shmuel; Moiseyev, Nimrod

The recent pioneering experiments of the [Nature 412, 52 (2001)] and [Science, 293, 274 (2001)] groups have demonstrated the dynamical tunneling of cold atoms interacting with standing electromagnetic waves. It has been shown [Phys. Rev. Lett. 89, 253201 (2002)], that the tunneling oscillations observed in these experiments correspondingly stems from two- and three-Floquet quantum state mechanism and can be controlled by varying the experimental parameters. The question where are the fingerprints of the classical chaotic dynamics in a quantum dynamical process which is controlled by 2 or 3 quantum states remains open. Our calculations show that although the effective ({Dirac_h}/2{pi})more » associated with the two experiments is large, and the quantum system is far from its semiclassical limit, the quantum Floquet-Bloch quasienergy states still can be classified as regular and chaotic states. In both experiments the quantum and the classical phase-space entropies are quite similar, although the classical phase space is a mixed regular-chaotic space. It is also shown that as the wave packet which is initially localized at one of the two inner regular islands oscillates between them through the chaotic sea, it accumulates a random phase which causes the decay of the amplitude of the oscillating mean momentum, , as measured in both experiments. The extremely high sensitivity of the rate of decay of the oscillations of to the very small changes in the population of different Floquet-Bloch states, is another type of fingerprint of chaos in quantum dynamics that presumably was measured in the NIST and AUSTIN experiments for the first time.« less

Synchronization properties of heterogeneous neuronal networks with mixed excitability type

NASA Astrophysics Data System (ADS)

Leone, Michael J.; Schurter, Brandon N.; Letson, Benjamin; Booth, Victoria; Zochowski, Michal; Fink, Christian G.

2015-03-01

We study the synchronization of neuronal networks with dynamical heterogeneity, showing that network structures with the same propensity for synchronization (as quantified by master stability function analysis) may develop dramatically different synchronization properties when heterogeneity is introduced with respect to neuronal excitability type. Specifically, we investigate networks composed of neurons with different types of phase response curves (PRCs), which characterize how oscillating neurons respond to excitatory perturbations. Neurons exhibiting type 1 PRC respond exclusively with phase advances, while neurons exhibiting type 2 PRC respond with either phase delays or phase advances, depending on when the perturbation occurs. We find that Watts-Strogatz small world networks transition to synchronization gradually as the proportion of type 2 neurons increases, whereas scale-free networks may transition gradually or rapidly, depending upon local correlations between node degree and excitability type. Random placement of type 2 neurons results in gradual transition to synchronization, whereas placement of type 2 neurons as hubs leads to a much more rapid transition, showing that type 2 hub cells easily "hijack" neuronal networks to synchronization. These results underscore the fact that the degree of synchronization observed in neuronal networks is determined by a complex interplay between network structure and the dynamical properties of individual neurons, indicating that efforts to recover structural connectivity from dynamical correlations must in general take both factors into account.

Cooling of a Magmatic System Under Thermal Chaotic Mixing

NASA Astrophysics Data System (ADS)

El Omari, Kamal; Le Guer, Yves; Perugini, Diego; Petrelli, Maurizio

2015-07-01

The cooling of a basaltic melt undergoing chaotic advection is studied numerically for a magma with a temperature-dependent viscosity in a two-dimensional (2D) cavity with moving boundary. Different statistical mixing and energy indicators are used to characterize the efficiency of cooling by thermal chaotic mixing. We show that different cooling rates can be obtained during the thermal mixing of a single basaltic magmatic batch undergoing chaotic advection. This process can induce complex temperature patterns inside the magma chamber. The emergence of chaotic dynamics strongly modulates the temperature fields over time and greatly increases the cooling rates. This mechanism has implications for the thermal lifetime of the magmatic body and may favor the appearance of chemical heterogeneities in the igneous system as a result of different crystallization rates. Results from this study also highlight that even a single magma batch can develop, under chaotic thermal advection, complex thermal and therefore compositional patterns resulting from different cooling rates, which can account for some natural features that, to date, have received unsatisfactory explanations, including the production of magmatic enclaves showing completely different cooling histories compared with the host magma, compositional zoning in mineral phases, and the generation of large-scale compositional zoning observed in many plutons worldwide.

Quantum internet using code division multiple access

PubMed Central

Zhang, Jing; Liu, Yu-xi; Özdemir, Şahin Kaya; Wu, Re-Bing; Gao, Feifei; Wang, Xiang-Bin; Yang, Lan; Nori, Franco

2013-01-01

A crucial open problem inS large-scale quantum networks is how to efficiently transmit quantum data among many pairs of users via a common data-transmission medium. We propose a solution by developing a quantum code division multiple access (q-CDMA) approach in which quantum information is chaotically encoded to spread its spectral content, and then decoded via chaos synchronization to separate different sender-receiver pairs. In comparison to other existing approaches, such as frequency division multiple access (FDMA), the proposed q-CDMA can greatly increase the information rates per channel used, especially for very noisy quantum channels. PMID:23860488

Symmetries of Chimera States

NASA Astrophysics Data System (ADS)

Kemeth, Felix P.; Haugland, Sindre W.; Krischer, Katharina

2018-05-01

Symmetry broken states arise naturally in oscillatory networks. In this Letter, we investigate chaotic attractors in an ensemble of four mean-coupled Stuart-Landau oscillators with two oscillators being synchronized. We report that these states with partially broken symmetry, so-called chimera states, have different setwise symmetries in the incoherent oscillators, and in particular, some are and some are not invariant under a permutation symmetry on average. This allows for a classification of different chimera states in small networks. We conclude our report with a discussion of related states in spatially extended systems, which seem to inherit the symmetry properties of their counterparts in small networks.

Locally optimal extracellular stimulation for chaotic desynchronization of neural populations.

PubMed

Wilson, Dan; Moehlis, Jeff

2014-10-01

We use optimal control theory to design a methodology to find locally optimal stimuli for desynchronization of a model of neurons with extracellular stimulation. This methodology yields stimuli which lead to positive Lyapunov exponents, and hence desynchronizes a neural population. We analyze this methodology in the presence of interneuron coupling to make predictions about the strength of stimulation required to overcome synchronizing effects of coupling. This methodology suggests a powerful alternative to pulsatile stimuli for deep brain stimulation as it uses less energy than pulsatile stimuli, and could eliminate the time consuming tuning process.

Memristor emulator causes dissimilarity on a coupled memristive systems

NASA Astrophysics Data System (ADS)

Sabarathinam, S.; Prasad, Awadhesh

2018-04-01

The memristor is known as abasic fourth passive solid state circuit element. Itgaining increasing attention to create the next generation electronic devices commonly used as fundamental chaotic circuit although often arbitrary (typically piecewise linear or cubic) fluxcharge characteristics. In thispresent work, the causes of the memristor emulator studied in a coupled memristive chaoticoscillator for the first time. We confirm that the emulator that allows synchronization between theoscillators and cause the dissimilarity between the systems when increasing the couplingstrength, and co-efficient of the memristor emulator. The detailed statistical analysis was performed to confirm such phenomenon.

Remote Synchronization Reveals Network Symmetries and Functional Modules

NASA Astrophysics Data System (ADS)

Nicosia, Vincenzo; Valencia, Miguel; Chavez, Mario; Díaz-Guilera, Albert; Latora, Vito

2013-04-01

We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result, and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.

The properties of borderlines in discontinuous conservative systems

NASA Astrophysics Data System (ADS)

Wang, X.-M.; Fang, Z.-J.

2006-02-01

The properties of the set of borderline images in discontinuous conservative systems are commonly investigated. The invertible system in which a stochastic web was found in 1999 is re-discussed here. The result shows that the set of images of the borderline actually forms the same stochastic web. The web has two typical local fine structures. Firstly, in some parts of the web the borderline crosses the manifold of hyperbolic points so that the chaotic diffusion is damped greatly; secondly, in other parts of phase space many holes and elliptic islands appear in the stochastic layer. This local structure shows infinite self-similarity. The noninvertible system in which the so-called chaotic quasi-attractor was found in [X.-M. Wang et al., Eur. Phys. J. D 19, 119 (2002)] is also studied here. The numerical investigation shows that such a chaotic quasi-attractor is confined by the preceding lower order images of the borderline. The mechanism of this confinement is revealed: a forbidden zone exists that any orbit can not visit, which is the sub-phase space of one side of the first image of the borderline. Each order of the images of the forbidden zone can be qualitatively divided into two sub-phase regions: one is the so-called escaping region that provides the orbit with an escaping channel, the other is the so-called dissipative region where the contraction of phase space occurs.

Simulations of submonolayer Xe on Pt(111): The case for a chaotic low temperature phase

NASA Astrophysics Data System (ADS)

Novaco, Anthony D.; Bavaresco, Jessica

2018-04-01

Molecular dynamics simulations are reported for the structural and thermodynamic properties of submonolayer xenon adsorbed on the (111) surface of platinum for temperatures up to the (apparently incipient) triple point and beyond. While the motion of the atoms in the surface plane is treated with a standard two-dimensional molecular dynamics simulation, the model takes into consideration the thermal excitation of quantum states associated with surface-normal dynamics in an attempt to describe the apparent smoothing of the corrugation with increasing temperature. We examine the importance of this thermal smoothing to the relative stability of several observed and proposed low-temperature structures. Structure factor calculations are compared to experimental results in an attempt to determine the low temperature structure of this system. These calculations provide strong evidence that, at very low temperatures, the domain wall structure of a xenon monolayer adsorbed on a Pt(111) substrate possesses a chaotic-like nature, exhibiting long-lived meta-stable states with pinned domain walls, these walls having narrow widths and irregular shapes. This result is contrary to the standard wisdom regarding this system, namely, that the very low temperature phase of this system is a striped incommensurate phase. We present the case for further experimental investigation of this and similar systems as possible examples of chaotic low temperature phases in two dimensions.

Phase synchronization of neuronal noise in mouse hippocampal epileptiform dynamics.

PubMed

Serletis, Demitre; Carlen, Peter L; Valiante, Taufik A; Bardakjian, Berj L

2013-02-01

Organized brain activity is the result of dynamical, segregated neuronal signals that may be used to investigate synchronization effects using sophisticated neuroengineering techniques. Phase synchrony analysis, in particular, has emerged as a promising methodology to study transient and frequency-specific coupling effects across multi-site signals. In this study, we investigated phase synchronization in intracellular recordings of interictal and ictal epileptiform events recorded from pairs of cells in the whole (intact) mouse hippocampus. In particular, we focused our analysis on the background noise-like activity (NLA), previously reported to exhibit complex neurodynamical properties. Our results show evidence for increased linear and nonlinear phase coupling in NLA across three frequency bands [theta (4-10 Hz), beta (12-30 Hz) and gamma (30-80 Hz)] in the ictal compared to interictal state dynamics. We also present qualitative and statistical evidence for increased phase synchronization in the theta, beta and gamma frequency bands from paired recordings of ictal NLA. Overall, our results validate the use of background NLA in the neurodynamical study of epileptiform transitions and suggest that what is considered "neuronal noise" is amenable to synchronization effects in the spatiotemporal domain.

Conditional Lyapunov exponents and transfer entropy in coupled bursting neurons under excitation and coupling mismatch

NASA Astrophysics Data System (ADS)

Soriano, Diogo C.; Santos, Odair V. dos; Suyama, Ricardo; Fazanaro, Filipe I.; Attux, Romis

2018-03-01

This work has a twofold aim: (a) to analyze an alternative approach for computing the conditional Lyapunov exponent (λcmax) aiming to evaluate the synchronization stability between nonlinear oscillators without solving the classical variational equations for the synchronization error dynamical system. In this first framework, an analytic reference value for λcmax is also provided in the context of Duffing master-slave scenario and precisely evaluated by the proposed numerical approach; (b) to apply this technique to the study of synchronization stability in chaotic Hindmarsh-Rose (HR) neuronal models under uni- and bi-directional resistive coupling and different excitation bias, which also considered the root mean square synchronization error, information theoretic measures and asymmetric transfer entropy in order to offer a better insight of the synchronization phenomenon. In particular, statistical and information theoretical measures were able to capture similarity increase between the neuronal oscillators just after a critical coupling value in accordance to the largest conditional Lyapunov exponent behavior. On the other hand, transfer entropy was able to detect neuronal emitter influence even in a weak coupling condition, i.e. under the increase of conditional Lyapunov exponent and apparently desynchronization tendency. In the performed set of numerical simulations, the synchronization measures were also evaluated for a two-dimensional parameter space defined by the neuronal coupling (emitter to a receiver neuron) and the (receiver) excitation current. Such analysis is repeated for different feedback couplings as well for different (emitter) excitation currents, revealing interesting characteristics of the attained synchronization region and conditions that facilitate the emergence of the synchronous behavior. These results provide a more detailed numerical insight of the underlying behavior of a HR in the excitation and coupling space, being in accordance with some general findings concerning HR coupling topologies. As a perspective, besides the synchronization overview from different standpoints, we hope that the proposed numerical approach for conditional Lyapunov exponent evaluation could outline a valuable strategy for studying neuronal stability, especially when realistic models are considered, in which analytical or even Jacobian evaluation could define a laborious or impracticable task.

Analysis of structural patterns in the brain with the complex network approach

NASA Astrophysics Data System (ADS)

Maksimenko, Vladimir A.; Makarov, Vladimir V.; Kharchenko, Alexander A.; Pavlov, Alexey N.; Khramova, Marina V.; Koronovskii, Alexey A.; Hramov, Alexander E.

2015-03-01

In this paper we study mechanisms of the phase synchronization in a model network of Van der Pol oscillators and in the neural network of the brain by consideration of macroscopic parameters of these networks. As the macroscopic characteristics of the model network we consider a summary signal produced by oscillators. Similar to the model simulations, we study EEG signals reflecting the macroscopic dynamics of neural network. We show that the appearance of the phase synchronization leads to an increased peak in the wavelet spectrum related to the dynamics of synchronized oscillators. The observed correlation between the phase relations of individual elements and the macroscopic characteristics of the whole network provides a way to detect phase synchronization in the neural networks in the cases of normal and pathological activity.

More About the Phase-Synchronized Enhancement Method

NASA Technical Reports Server (NTRS)

Jong, Jen-Yi

2004-01-01

A report presents further details regarding the subject matter of "Phase-Synchronized Enhancement Method for Engine Diagnostics" (MFS-26435), NASA Tech Briefs, Vol. 22, No. 1 (January 1998), page 54. To recapitulate: The phase-synchronized enhancement method (PSEM) involves the digital resampling of a quasi-periodic signal in synchronism with the instantaneous phase of one of its spectral components. This resampling transforms the quasi-periodic signal into a periodic one more amenable to analysis. It is particularly useful for diagnosis of a rotating machine through analysis of vibration spectra that include components at the fundamental and harmonics of a slightly fluctuating rotation frequency. The report discusses the machinery-signal-analysis problem, outlines the PSEM algorithms, presents the mathematical basis of the PSEM, and presents examples of application of the PSEM in some computational simulations.

Bistable synchronization modes in hydrodynamically coupled micro-rotors

NASA Astrophysics Data System (ADS)

Guo, Hanliang; Kanale, Anup; Fuerthauer, Sebastian; Kanso, Eva

2017-11-01

Cilia often beat in synchrony, and they may transition between different synchronization modes in the same cell type. For example, cilia in the mammalian brain ventricles are reported to periodically change their collective beat orientation, providing a cilia-based switch for redirecting the transport of cerebrospinal fluid. Experimental and theoretical evidences suggest that phase coordinations can be achieved solely via hydrodynamical interactions. However, the exact mechanisms responsible for transitioning between various synchronization modes remain illusive. Here, we use a theoretical model where each cilium is represented by a bead moving along a closed trajectory close to a no-slip surface. We investigate the emergent synchronization modes and their stability for various cilia-inspired force profiles. We observe distinct stable synchronization modes between two rotors, including a bistable regime where both in-phase and anti-phase synchronizations are stable. We then extend this analysis to an array of rotors where we demonstrate the dynamical formations of metachronal waves. These findings may help us to understand the origin of synchrony in biological and bio-inspired systems, and the mechanisms underlying transitions between different synchronization modes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Stephen F; Moore, James A

Systems and methods are described for carrier phase synchronization for improved AM and TV broadcast reception. A method includes synchronizing the phase of a carrier frequency of a broadcast signal with the phase of a remote reference frequency. An apparatus includes a receiver to detect the phase of a reference signal; a phase comparator coupled to the reference signal-phase receiver; a voltage controlled oscillator coupled to the phase comparator; and a phase-controlled radio frequency output coupled to the voltage controlled oscillator.

An Intelligent Fingerprint-Biometric Image Scrambling Scheme

NASA Astrophysics Data System (ADS)

Khan, Muhammad Khurram; Zhang, Jiashu

To obstruct the attacks, and to hamper with the liveness and retransmission issues of biometrics images, we have researched on the challenge/response-based biometrics scrambled image transmission. We proposed an intelligent biometrics sensor, which has computational power to receive challenges from the authentication server and generate response against the challenge with the encrypted biometric image. We utilized the FRT for biometric image encryption and used its scaling factors and random phase mask as the additional secret keys. In addition, we chaotically generated the random phase masks by a chaotic map to further improve the encryption security. Experimental and simulation results have shown that the presented system is secure, robust, and deters the risks of attacks of biometrics image transmission.

Color image encryption using random transforms, phase retrieval, chaotic maps, and diffusion

NASA Astrophysics Data System (ADS)

Annaby, M. H.; Rushdi, M. A.; Nehary, E. A.

2018-04-01

The recent tremendous proliferation of color imaging applications has been accompanied by growing research in data encryption to secure color images against adversary attacks. While recent color image encryption techniques perform reasonably well, they still exhibit vulnerabilities and deficiencies in terms of statistical security measures due to image data redundancy and inherent weaknesses. This paper proposes two encryption algorithms that largely treat these deficiencies and boost the security strength through novel integration of the random fractional Fourier transforms, phase retrieval algorithms, as well as chaotic scrambling and diffusion. We show through detailed experiments and statistical analysis that the proposed enhancements significantly improve security measures and immunity to attacks.

A Two-Phase Time Synchronization-Free Localization Algorithm for Underwater Sensor Networks.

PubMed

Luo, Junhai; Fan, Liying

2017-03-30

Underwater Sensor Networks (UWSNs) can enable a broad range of applications such as resource monitoring, disaster prevention, and navigation-assistance. Sensor nodes location in UWSNs is an especially relevant topic. Global Positioning System (GPS) information is not suitable for use in UWSNs because of the underwater propagation problems. Hence, some localization algorithms based on the precise time synchronization between sensor nodes that have been proposed for UWSNs are not feasible. In this paper, we propose a localization algorithm called Two-Phase Time Synchronization-Free Localization Algorithm (TP-TSFLA). TP-TSFLA contains two phases, namely, range-based estimation phase and range-free evaluation phase. In the first phase, we address a time synchronization-free localization scheme based on the Particle Swarm Optimization (PSO) algorithm to obtain the coordinates of the unknown sensor nodes. In the second phase, we propose a Circle-based Range-Free Localization Algorithm (CRFLA) to locate the unlocalized sensor nodes which cannot obtain the location information through the first phase. In the second phase, sensor nodes which are localized in the first phase act as the new anchor nodes to help realize localization. Hence, in this algorithm, we use a small number of mobile beacons to help obtain the location information without any other anchor nodes. Besides, to improve the precision of the range-free method, an extension of CRFLA achieved by designing a coordinate adjustment scheme is updated. The simulation results show that TP-TSFLA can achieve a relative high localization ratio without time synchronization.

A Two-Phase Time Synchronization-Free Localization Algorithm for Underwater Sensor Networks

PubMed Central

Luo, Junhai; Fan, Liying

2017-01-01

Underwater Sensor Networks (UWSNs) can enable a broad range of applications such as resource monitoring, disaster prevention, and navigation-assistance. Sensor nodes location in UWSNs is an especially relevant topic. Global Positioning System (GPS) information is not suitable for use in UWSNs because of the underwater propagation problems. Hence, some localization algorithms based on the precise time synchronization between sensor nodes that have been proposed for UWSNs are not feasible. In this paper, we propose a localization algorithm called Two-Phase Time Synchronization-Free Localization Algorithm (TP-TSFLA). TP-TSFLA contains two phases, namely, range-based estimation phase and range-free evaluation phase. In the first phase, we address a time synchronization-free localization scheme based on the Particle Swarm Optimization (PSO) algorithm to obtain the coordinates of the unknown sensor nodes. In the second phase, we propose a Circle-based Range-Free Localization Algorithm (CRFLA) to locate the unlocalized sensor nodes which cannot obtain the location information through the first phase. In the second phase, sensor nodes which are localized in the first phase act as the new anchor nodes to help realize localization. Hence, in this algorithm, we use a small number of mobile beacons to help obtain the location information without any other anchor nodes. Besides, to improve the precision of the range-free method, an extension of CRFLA achieved by designing a coordinate adjustment scheme is updated. The simulation results show that TP-TSFLA can achieve a relative high localization ratio without time synchronization. PMID:28358342

Wirelessly Networked Digital Phased Array: Analysis and Development of a Phase Synchronization Concept

DTIC Science & Technology

2007-09-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS Approved for public release; distribution is unlimited WIRELESSLY NETWORKED...DIGITAL PHASED ARRAY: ANALYSIS AND DEVELOPMENT OF A PHASE SYNCHRONIZATION CONCEPT by Micael Grahn September 2007 Thesis Advisor...September 2007 3. REPORT TYPE AND DATES COVERED Master’s Thesis 4. TITLE AND SUBTITLE Wirelessly Networked Digital Phased Array: Analysis and

State observer for synchronous motors

DOEpatents

Lang, Jeffrey H.

1994-03-22

A state observer driven by measurements of phase voltages and currents for estimating the angular orientation of a rotor of a synchronous motor such as a variable reluctance motor (VRM). Phase voltages and currents are detected and serve as inputs to a state observer. The state observer includes a mathematical model of the electromechanical operation of the synchronous motor. The characteristics of the state observer are selected so that the observer estimates converge to the actual rotor angular orientation and velocity, winding phase flux linkages or currents.

Anticipated and zero-lag synchronization in motifs of delay-coupled systems

NASA Astrophysics Data System (ADS)

Mirasso, Claudio R.; Carelli, Pedro V.; Pereira, Tiago; Matias, Fernanda S.; Copelli, Mauro

2017-11-01

Anticipated and zero-lag synchronization have been observed in different scientific fields. In the brain, they might play a fundamental role in information processing, temporal coding and spatial attention. Recent numerical work on anticipated and zero-lag synchronization studied the role of delays. However, an analytical understanding of the conditions for these phenomena remains elusive. In this paper, we study both phenomena in systems with small delays. By performing a phase reduction and studying phase locked solutions, we uncover the functional relation between the delay, excitation and inhibition for the onset of anticipated synchronization in a sender-receiver-interneuron motif. In the case of zero-lag synchronization in a chain motif, we determine the stability conditions. These analytical solutions provide an excellent prediction of the phase-locked regimes of Hodgkin-Huxley models and Roessler oscillators.

Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution.

PubMed

Sasaki, Takuma; Kakesu, Izumi; Mitsui, Yusuke; Rontani, Damien; Uchida, Atsushi; Sunada, Satoshi; Yoshimura, Kazuyuki; Inubushi, Masanobu

2017-10-16

We experimentally achieve common-signal-induced synchronization in two photonic integrated circuits with short external cavities driven by a constant-amplitude random-phase light. The degree of synchronization can be controlled by changing the optical feedback phase of the two photonic integrated circuits. The change in the optical feedback phase leads to a significant redistribution of the spectral energy of optical and RF spectra, which is a unique characteristic of PICs with the short external cavity. The matching of the RF and optical spectra is necessary to achieve synchronization between the two PICs, and stable synchronization can be obtained over an hour in the presence of optical feedback. We succeed in generating information-theoretic secure keys and achieving the final key generation rate of 184 kb/s using the PICs.

A dynamical systems approach for estimating phase interactions between rhythms of different frequencies from experimental data.

PubMed

Onojima, Takayuki; Goto, Takahiro; Mizuhara, Hiroaki; Aoyagi, Toshio

2018-01-01

Synchronization of neural oscillations as a mechanism of brain function is attracting increasing attention. Neural oscillation is a rhythmic neural activity that can be easily observed by noninvasive electroencephalography (EEG). Neural oscillations show the same frequency and cross-frequency synchronization for various cognitive and perceptual functions. However, it is unclear how this neural synchronization is achieved by a dynamical system. If neural oscillations are weakly coupled oscillators, the dynamics of neural synchronization can be described theoretically using a phase oscillator model. We propose an estimation method to identify the phase oscillator model from real data of cross-frequency synchronized activities. The proposed method can estimate the coupling function governing the properties of synchronization. Furthermore, we examine the reliability of the proposed method using time-series data obtained from numerical simulation and an electronic circuit experiment, and show that our method can estimate the coupling function correctly. Finally, we estimate the coupling function between EEG oscillation and the speech sound envelope, and discuss the validity of these results.

Sub-nanosecond clock synchronization and trigger management in the nuclear physics experiment AGATA

NASA Astrophysics Data System (ADS)

Bellato, M.; Bortolato, D.; Chavas, J.; Isocrate, R.; Rampazzo, G.; Triossi, A.; Bazzacco, D.; Mengoni, D.; Recchia, F.

2013-07-01

The new-generation spectrometer AGATA, the Advanced GAmma Tracking Array, requires sub-nanosecond clock synchronization among readout and front-end electronics modules that may lie hundred meters apart. We call GTS (Global Trigger and Synchronization System) the infrastructure responsible for precise clock synchronization and for the trigger management of AGATA. It is made of a central trigger processor and nodes, connected in a tree structure by means of optical fibers operated at 2Gb/s. The GTS tree handles the synchronization and the trigger data flow, whereas the trigger processor analyses and eventually validates the trigger primitives centrally. Sub-nanosecond synchronization is achieved by measuring two different types of round-trip times and by automatically correcting for phase-shift differences. For a tree of depth two, the peak-to-peak clock jitter at each leaf is 70 ps; the mean phase difference is 180 ps, while the standard deviation over such phase difference, namely the phase equalization repeatability, is 20 ps. The GTS system has run flawlessly for the two-year long AGATA campaign, held at the INFN Legnaro National Laboratories, Italy, where five triple clusters of the AGATA sub-array were coupled with a variety of ancillary detectors.

Evidence for Chaotic Edge Turbulence in the Alcator C-Mod Tokamak

NASA Astrophysics Data System (ADS)

Zhu, Ziyan; White, Anne; Carter, Troy; Terry, Jim; Baek, Seung Gyou

2016-10-01

Turbulence greatly reduces the confinement time of magnetic-confined plasmas; understanding the nature of this turbulence and the associated transport is therefore of great importance. This research seeks to establish whether turbulent fluctuations in Alcator C-Mod are chaotic or stochastic. This has an important impact on transport caused by turbulence in C-Mod: stochastic fluctuations sample all of phase space and can lead to diffusive transport, whereas chaotic fluctuations live in a restricted phase space (e.g. on attractors) and a diffusive description may not be valid. By analyzing the time series from an O-Mode reflectometer, turbulent edge density fluctuations in Ohmic plasmas and L-mode plasmas in the Alcator C-Mod tokamak are shown to be chaotic. Supporting evidence for chaos in the edge region includes: the observation of an exponential power spectra (which is associated with Lorentzian-shaped pulses in the time series) and the location of the signal in the Complexity-Entropy plane (C-H plane) and its corresponding Brandt-Pompe (BP) probability distribution. These analysis techniques will be briefly introduced along with a discussion of the analysis results. Different diagnostic techniques, such as Gas Puff Imaging (GPI), could be used to confirm the results. Work supported by the U.S. Department of Energy Office of Science under Agreement DE-FC02-99ER54512 and DE-FC02-07ER54918:011.

Synchronization of EEG activity in patients with bipolar disorder

NASA Astrophysics Data System (ADS)

Panischev, O. Yu; Demin, S. A.; Muhametshin, I. G.; Demina, N. Yu

2015-12-01

In paper we apply the method based on the Flicker-Noise Spectroscopy (FNS) to determine the differences in frequency-phase synchronization of the cortical electroencephalographic (EEG) activities in patients with bipolar disorder (BD). We found that for healthy subjects the frequency-phase synchronization of EEGs from long-range electrodes was significantly better for BD patients. In BD patients a high synchronization of EEGs was observed only for short-range electrodes. Thus, the FNS is a simple graphical method for qualitative analysis can be applied to identify the synchronization effects in EEG activity and, probably, may be used for the diagnosis of this syndrome.

High-throughput synchronization of mammalian cell cultures by spiral microfluidics.

PubMed

Lee, Wong Cheng; Bhagat, Ali Asgar S; Lim, Chwee Teck

2014-01-01

The development of mammalian cell cycle synchronization techniques has greatly advanced our understanding of many cellular regulatory events and mechanisms specific to different phases of the cell cycle. In this chapter, we describe a high-throughput microfluidic-based approach for cell cycle synchronization. By exploiting the relationship between cell size and its phase in the cell cycle, large numbers of synchronized cells can be obtained by size fractionation in a spiral microfluidic channel. Protocols for the synchronization of primary cells such as mesenchymal stem cells, and immortal cell lines such as Chinese hamster ovarian cells (CHO-CD36) and HeLa cells are provided as examples.

An Efficient Method for Studying the Stability and Dynamics of the Rotational Motions of Celestial Bodies

NASA Astrophysics Data System (ADS)

Pavlov, A. I.; Maciejewski, A. J.

2003-08-01

We use the alternative MEGNO (Mean Exponential Growth of Nearby Orbits) technique developed by Cincotta and Simo to study the stability of orbital-rotational motions for plane oscillations and three-dimensional rotations. We present a detailed numerical-analytical study of a rigid body in the case where the proper rotation of the body is synchronized with its orbital motion as 3: 2 (Mercurian-type synchronism). For plane rotations, the loss of stability of the periodic solution that corresponds to a 3: 2 resonance is shown to be soft, which should be taken into account to estimate the upper limit for the ellipticity of Mercury. In studying stable and chaotic translational-rotational motions, we point out that the MEGNO criterion can be effectively used. This criterion gives a clear picture of the resonant structures and allows the calculations to be conveniently presented in the form of the corresponding MEGNO stability maps for multidimensional systems. We developed an appropriate software package.

Arnold Tongues in Cell Dynamics

NASA Astrophysics Data System (ADS)

Jensen, Mogens

In a recent work with Leo Kadanoff we studied the synchronization between an internal and an external frequency. One obtains a highly structured diagram with details that in essence are related to the difference between rational and irrational number. The synchronized regions appear as Arnold tongues that widen as the coupling between the frequencies increases. Such tongues have been observed in many physical systems, like in the Libchaber convective cell in the basement of the University of Chicago. In biological systems, where oscillators appear in in a broad variety, very little research on Arnold tongues has been performed. We discuss single cell oscillating dynamics triggered by an external cytokine signal. When this signal is overlaid by an oscillating variation, the two oscillators might couple leading to Arnold tongue diagram. When the tongues overlap, the cell dynamics can shift between the tongues eventually leading to a chaotic response. We quantify such switching in single cell experiments and in model systems based on Gillespie simulations. Kadanoff session.

Chaoticity parameter λ in two-pion interferometry in an expanding boson gas model

DOE PAGES

Liu, Jie; Ru, Peng; Zhang, Wei-Ning; ...

2014-10-15

We investigate the chaoticity parameter λ in two-pion interferometry in an expanding boson gas model. The degree of Bose-Einstein condensation of identical pions, density distributions, and Hanbury-Brown-Twiss (HBT) correlation functions are calculated for the expanding gas within the mean-field description with a harmonic oscillator potential. The results indicate that a sources with thousands of identical pions may exhibit a degree of Bose-Einstein condensation at the temperatures during the hadronic phase in relativistic heavy-ion collisions. This finite condensation may decrease the chaoticity parameter λ in the two-pion interferometry measurements at low pion pair momenta, but influence only slightly the λ valuemore » at high pion pair momentum.« less

Chaotic map clustering algorithm for EEG analysis

NASA Astrophysics Data System (ADS)

Bellotti, R.; De Carlo, F.; Stramaglia, S.

2004-03-01

The non-parametric chaotic map clustering algorithm has been applied to the analysis of electroencephalographic signals, in order to recognize the Huntington's disease, one of the most dangerous pathologies of the central nervous system. The performance of the method has been compared with those obtained through parametric algorithms, as K-means and deterministic annealing, and supervised multi-layer perceptron. While supervised neural networks need a training phase, performed by means of data tagged by the genetic test, and the parametric methods require a prior choice of the number of classes to find, the chaotic map clustering gives a natural evidence of the pathological class, without any training or supervision, thus providing a new efficient methodology for the recognition of patterns affected by the Huntington's disease.

Robust PRNG based on homogeneously distributed chaotic dynamics

NASA Astrophysics Data System (ADS)

Garasym, Oleg; Lozi, René; Taralova, Ina

2016-02-01

This paper is devoted to the design of new chaotic Pseudo Random Number Generator (CPRNG). Exploring several topologies of network of 1-D coupled chaotic mapping, we focus first on two dimensional networks. Two topologically coupled maps are studied: TTL rc non-alternate, and TTL SC alternate. The primary idea of the novel maps has been based on an original coupling of the tent and logistic maps to achieve excellent random properties and homogeneous /uniform/ density in the phase plane, thus guaranteeing maximum security when used for chaos base cryptography. In this aim two new nonlinear CPRNG: MTTL 2 sc and NTTL 2 are proposed. The maps successfully passed numerous statistical, graphical and numerical tests, due to proposed ring coupling and injection mechanisms.

Foraging at the Edge of Chaos: Internal Clock versus External Forcing

NASA Astrophysics Data System (ADS)

Nicolis, S. C.; Fernández, J.; Pérez-Penichet, C.; Noda, C.; Tejera, F.; Ramos, O.; Sumpter, D. J. T.; Altshuler, E.

2013-06-01

Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from “autocatalytic” mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos. The model suggests that a wide range of temporal structures and irregularities seen in the activity of animal and human groups might be accounted for by the coupling between collectively generated internal clocks and external forcings.

Parametric Identification of Nonlinear Dynamical Systems

NASA Technical Reports Server (NTRS)

Feeny, Brian

2002-01-01

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.