We developed two cases studies in which we coupled a lorenz system to a du ng system. Ho, adaptive stabilization and synchronization for chaotic lure systems with timevarying delay. Synchronization of coupled mechanical oscillators 115 figure 3 bifurcation diagram of three coupled dung oscillators 5. Global exponential synchronization for coupled switched delayed recurrent neural networks with stochastic perturbation. Furthermore, a novel delayrangedependent robust adaptive synchronization control approach for dealing with locally lipschitz nondelayed and delayed nonlinearities in the dynamics of chaotic oscillators is provided by employing an additional adaptation law for the nonlinearities. An adaptive coupling gain is realized by adopting an adaptive law to estimate the lipschitz constant of the chaotic system. Synchronization of pulsecoupled biological oscillators. Control of partial synchronization in chaotic oscillators. Synchronization in a population of globally coupled chaotic. Anishchenko, vladimir astakhov, alexander neiman, tatjana vadivasova, lutz schimanskygeier this book is a complete treatise on the theory of nonlinear dynamics of chaotic and stochastic systems. Several subdisciplines and cottage industries have emerged that have taken on bona fide lives of their own. Synchronization of chaotic oscillators is one of the fundamental phenomena of nonlinear dynamics. Coexistence of synchronization and antisynchronization for chaotic systems via feedback control 203 hammami sonia and benrejeb mohamed applications. We experimentally demonstrate and numerically simulate an adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and timevarying e.
Chapters 6 and 7 extend the chaos synchronization framework from a pair of coupled oscillators to a network of multicoupled oscillators. Pikovsky department of physics, university of potsdam. Adaptive techniques and the design of optimal networks by bhargava ravoori dissertation submitted to the faculty of the graduate school of the. To prove this numerically, we consider the chaotic lorenz system. This kind of synchronization has potential interest in several areas such as secure communication, biological oscillators and animal gaits. Synchronization of these timers to environmental lightdark cycles entrainment is crucial for an organisms fitness. Authors personal copy physica a 387 2008 6045 6056 contents lists available atsciencedirect. Different from the previous methods, in this paper, the following two questions are investigated. The synchronization of oscillators is a universal concept in nonlinear sciences 1,2. Synchronization of nondifferentiable chaotic oscillators. Adaptive coupled synchronization of coupled chaotic. We experimentally demonstrate and numerically simulate a new adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is.
Synchronization of coupled oscillators is a game huibing yin, prashant g. We present the results of both, theoretical and experimental investigations of synchronization between two, three and four almost identical oscillators. Synchronization of diffusively coupled oscillators. Existing coupled micromechanical oscillators suffer from limited range, neighborhood restriction and noncongurable coupling which limit the control, physical size and possible topologies of complex oscillator networks 1,2. Here, the equivalent master bpo is an external function. Nonlinear dynamics of chaotic and stochastic systems. The case of identical chaotic oscillators is studied in chapter 6, while the nonidentical setting is discussed in chapter 7. Hespanha, ieee transactions on automatic control, 60 32263241, 2015. The method of linear difference signal has been applied. Synchronization of coupled boolean phase oscillators. Two theorems for adaptive synchronization of unidirectional and mutual coupled nonautonomous chaotic systems are derived individually. In real coupling it is hard especially for multidimensional. In the case of two linearly coupled identical chaotic oscillators.
To give an example of the use of this function, we follow ref. These topics include temporal networks in which the entities andor their interactions change in time, stochastic and deterministic dynamical processes on networks. Timedelayed mutual information of the phase as a measure. Optimal control for synchronization with lower energy. Both oscillators remain chaotic what can be seen from their phase portraits. Synchronization and phase locking of two mutually coupled. Us8369377b2 us12507,111 us50711109a us8369377b2 us 8369377 b2 us8369377 b2 us 8369377b2 us 50711109 a us50711109 a us 50711109a us 8369377 b2 us8369377 b2 us 8369377b2 authority. Limits to detection of generalized synchronization in delay coupled chaotic oscillators hideyuki kato,1 miguel c. Synchronization is a general effect in coupled oscillator sys tems.
With this algorithm, chaos synchronization of colpitts circuits can be achieved and maintained in awgn channels. Synchronization of identical oscillators coupled through a symmetric network with dynamics. On common noiseinduced synchronization in complex networks with statedependent noise diffusion processes. We propose a timedelayed mutual information of the phase for detecting nonlinear synchronization in electrophysiological data such as meg. It seems to play an important role in the ability of biological oscillators, such as neurons, to act cooperatively, there are several different types of synchronization of coupled chaotic oscillators. Chaos synchronization of financial chaotic system with. This paper addresses the problem of optimization of the synchronization of a chaotic modified rayleigh system. We present the new effect of phase synchronization of weakly coupled selfsustained chaotic oscillators. The behavior of two unidirectionally coupled chaotic oscillators exhibited at the threshold of generalized chaotic synchronization is considered. Us7245723b2 us11270,502 us27050205a us7245723b2 us 7245723 b2 us7245723 b2 us 7245723b2 us 27050205 a us27050205 a us 27050205a us 7245723 b2 us7245723 b2 us 7245723b2 authority us united states prior art keywords chaotic circuit signal voltage receiver prior art date 19980717 legal status the legal status is an assumption and is not a legal conclusion. Synchronization and phase locking of two mutually coupled chaotic oscillators i. Although there are many studies regarding synchronization of chaotic oscillators and regarding numerical problems, as far as we know, no study deals with numerical problems in the synchronization of chaotic systems. This ranges from complete agreement of trajectories to locking of phases. The little book of semaphores is a free in both senses of the word textbook that introduces the principles of synchronization for concurrent programming.
As the simplest example of phase synchronization, we consider two coupled rossler. To obtain estimates on small datasets as reliably as possible, we adopt the numerical implementation as proposed by kraskov and colleagues 2. A classical feedback controller is first used to stabilize the system at its equilibrium. In this paper, synchronization of chaotic colpitts circuits using a particle filter pf to combat the additive white gaussian noise awgn channel effect is studied by numeric simulations.
This is relevant in situations 24,25 as explained using the example of foodweb model. Adaptive elimination of synchronization in coupled oscillator. Synchronization in coupled phase oscillators natasha cayco gajic november 1, 2007 abstract in a system of coupled oscillators, synchronization occurs when the oscillators spontaneously lock to a common frequency or phase. Desynchronization in an ensemble of globally coupled chaotic bursting neuronal oscillators by dynamic delayed feedback control. International journal of bifurcation and chaos vol 18, no 08. Particle filterbased synchronization of chaotic colpitts. On the synchronization techniques of chaotic oscillators and their. Synchronization of pulsecoupled oscillators with a refractory period and frequency distribution for a. This leads us to the study of the more complicated topic of coupled oscillations. This paper investigates the problem of two kinds of function projective synchronization of financial chaotic system with definite integration scaling function, which are not fully considered in the existing research. This letter addresses a nonlinear robust adaptive control that utilizes linear matrix inequalities for asymptotic synchronization of two coupled chaotic fitzhughnagumo neurons under unknown.
Furthermore, an adaptive synchronization scheme for a system of two coupled 4d hyperchaotic hyperjerk systems has been developed. Pdf targeting and control of synchronization in chaotic oscillators. This paper deals with the problem of control and synchronization of coupled secondorder oscillators showing a chaotic behavior. Injection locking and injection pulling are the frequency effects that can occur when a harmonic oscillator is disturbed by a second oscillator operating at a nearby frequency. Some realizations of chaotic oscillators with electronic circuits are presented in chapter ten. In this example, the impact of the stimulation u on the oscil. Communications system using chaotic synchronized circuits. Therefore, the methods used for controlling nonlinear systems can also be applied for synchronizing two or more coupled chaotic oscillators. Noiseenhanced phase synchronization in weakly coupled chaotic oscillators. An appropriate electronic circuit analog simulator is. Bifurcations and attractors in synchronization dynamics of. Theory of coupledmaster equations and transport equation of collective motion as repeatedly. In the present study, we investigate the dynamics of shunting inhibitory cellular neural networks sicnns with impulsive effects. We study the dynamics of an adaptive coupled array of phase oscillators.
Adaptation and selforganizing systems authorstitles may 20. Request pdf antisynchronization of chaotic oscillators we have observed anti synchronization phenomena in coupled identical chaotic oscillators. Sms is a form of referential behavior in which actions are timed relative to an external event, the referent pressing, 1999. Author links open overlay panel hilaire fotsin a c samuel bowong b. A novel fourdimensional noequilibrium hyperchaotic. Pdf adaptive synchronization of coupled chaotic oscillators. Synchrony suppression in ensembles of coupled oscillators via. The main areas of activity in cybernetical physics are brie. Circadian clocks are endogenous oscillators driving daily rhythms in physiology and behavior. Adaptive control strategy for projective synchronization of neural networks. Pdf a method of targeting synchronization and its control is reported in chaotic oscillators. Many different synchronization states of coupled chaotic systems have been. Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs hongwei zhang, member, ieee, frank l.
Antisynchronization of chaotic oscillators request pdf. Lyapunov, adaptive, and optimal design techniques for. Performance evaluation of chaotic spreading sequences on softwaredefined radio. The study of synchronization in coupled oscillators is of fundamental importance with applications in various. The oscillators in a system are not restricted to pure forms. Here, we demonstrate the synchronization of two dissimilar micromechanical oscillators using the. Ryskinb a institute of electronics and mechanical engineering, yuri gagarin state technical university. Illustration of phase synchronization in two coupled roessler systems. Development of structural correlations and synchronization from. Synchronization transition in neuronal networks composed. The proposed scheme enhances the synchronization and achieves a more reasonable coupling dynamics for the network of oscillators with different. To study phase synchronization of coupled chaotic oscillators, we calculate the phases of the oscillators and then check whether the weak locking condition jnf 1 2 mf 2j, const is satis. Coupling governs entrainment range of circadian clocks. The liyorke definition of chaos is used in our theoretical discussions.
Adaptive synchronization of globally coupled chaotic. Noiseenhanced phase synchronization of chaotic oscillators. We give a mathematical description of the chaos for the multidimensional dynamics of impulsive sicnns, and prove its existence rigorously by taking advantage of the external inputs. Analog circuit design and optimal synchronization of a. Us7245723b2 chaotic communication system and method. Performance evaluation of chaotic spreading sequences on. Shanbhag abstractthe purpose of this paper is to understand phase transition in noncooperative dynamic games with a large number of agents. In this letter, we restrict ourselves to the case m n 1. Mathematical frameworks for oscillatory network dynamics. Consensus of multiagent systems and synchronization of. Control of functional connectivity in cerebral cortex by. Geometry, dynamics, and regulation in biological questions. In these chapters, network synchronization is presented by numerical simulations. The modifiedsystem approach is applied to explain physical mechanisms of formation of this regime in the cases of large and small mismatches of interacting systems.
Comparing the results of adaptive active control and optimal control. Dew as inventors, the entire disclosure of which is hereby incorporated by reference. When the coupling is strong enough and the frequencies near enough, the second oscillator can capture the first oscillator, causing it to have essentially identical frequency as the second. Adaptive coupling and enhanced synchronization in coupled. Adaptive synchronization of coupled chaotic oscillators arxiv. Soriano, 2ernesto pereda,3 ingo fischer,2 and claudio r. A prevalent example of adaptation in connectivity takes place in. To characterize this phenomenon, we use the analytic signal approach based on the hilbert. I briefly survey several fascinating topics in networks and nonlinearity. Our principal result is that there are parameter regimes of positive measure for which eq. This method can avoid estimating the value of coupling coefficient. Designing identification and control modules completely independently. This coupling scheme is further explored, in this paper, to control partial synchronization in coupled chaotic systems. In this paper complete synchronization of diffusively coupled oscillators is considered.
Synchronization of nondifferentiable chaotic oscillators chapter 1. Time scale synchronization of chaotic oscillators, physica. Computation free fulltext analysis, synchronization. Synchronization of a set of coupled chaotic fitzhughnagumo and hindmarshrose neurons with external electrical stimulation. Chuas circuit and chuas equation eecs at uc berkeley. In addition to keeping the two systems isochronally synchronized in the presence of a priori unknown timevarying coupling strength, the. We report a general phenomenon concerning the effect of noise on phase synchronization in coupled chaotic oscillators. This paper investigates the problem of synchronization of fractionalorder complexvariable chaotic systems foccs with unknown complex parameters. It has been reported in 7, and conjectured as the simplest possible for a chaotic oscillator. Dincon2017 synchronization on the accuracy of chaotic. A simple model for synchronous firing of biological oscillators based on peskins model of the cardiac pacemaker mathematical aspects of heart physiology, courant institute of mathematical sciences. We first introduce a fourdimensional autonomous chaotic system which is obtained by the modification of a twodimensional rayleigh system. Little is known about which oscillator qualities determine entrainment, i.
Limits to detection of generalized synchronization in delay. The subject and main areas of a new research fieldcybernetical physicsare discussed. A novel pf algorithm suitable for chaos synchronization is proposed. There is a long tradition of studying sms in laboratory tasks that require participants to produce simple movements such as finger taps in time with events in computercontrolled pacing sequences e. The adaptive law is designed in such a way that the coupling grows stronger for the pairs which have larger phase incoherence. Fundamentals of synchronization in chaotic systems. The field of chaotic synchronization has grown considerably since its advent in 1990. Synchronization of chaos is a phenomenon that may occur when two, or more, dissipative chaotic systems are coupled because of the exponential divergence of the nearby trajectories of chaotic systems, having two chaotic systems evolving in synchrony might appear surprising. Synchronization of two coupled fractionalorder chaotic. Adaptive synchronization of unidirectional and mutual. A new approach to detect the synchronized behaviour of chaotic oscillators has been proposed. Based on the complexvariable inequality and stability theory for fractionalorder complexvalued system, a new scheme is presented for adaptive synchronization of foccs with unknown complex parameters. Chaotic synchronization of two optical cavity modes in. Synchronization in a population of globally coupled chaotic oscillators a.
Mirasso 1center for simulation sciences, ochanomizu university, 211 ohtsuka bunkyoku, 1128610 tokyo, japan. Effect of common noise on phase synchronization in coupled. For example, odd cell dynamics can lead to antisynchrony as well as. Introduction chaos synchronization is an interesting topic, which has been widely studied the last few years. Some basic dynamical properties and behaviors of this system are investigated. The notation of synchronization has been extended to include a variety of phenomena in the context of interacting chaotic oscillators, such as complete synchronization cs 2, generalized synchronization 3, and phase syn. Synchronization of coupled oscillators in matlab youtube. Synchronization of coupled mechanical oscillators in the. Chaotic dynamical systems are ubiquitous in nature and most of them does not have an explicit dynamical equation and can be only understood through the available time series. This application is a continuation of commonowned, u. Impulsive sicnns with chaotic postsynaptic currents.
Selecting this option will search all publications across the scitation platform selecting this option will search all publications for the publishersociety in context. From huygens clocks to chaotic systems and large ensembles a. In order to synchronize two chaotic oscillators, the output from, at least, one of the coupled differential equations of the master chaotic oscillator. Us8369377b2 adaptive link communications using adaptive. We study the dynamics of two mutually coupled identical electric circuits, which are in a chaotic state before coupling. Synchronization of two coupled multimode oscillators with. The technique is applied to optoelectronic feedback loops.
It has been observed in both nature 2 and social activities 1,2,3, and also promises important applications in. Adaptive synchronization of coupled chaotic oscillators. Consensus of multiagent systems and synchronization of complex networks. Such a control of partial synchronization may be necessary, particularly, in the case of limited measurements accessibility. The technique is applied to optoelectronic feedback loops exhibiting high dimensional chaotic dynamics. In most computer science curricula, synchronization is a module in an operating systems class. This option allows users to search by publication, volume and page selecting this option will search the current publication in context. Amplitude envelope synchronization in coupled chaotic oscillators. Stouboulos physics department aristotle university of thessaloniki thessaloniki, gr 54006 greece abstract. The threshold of generalized synchronization of chaotic. It takes place in many physical,,, and biological, processes. This principle has been exploited as a means for decomposing a potentially chaotic time. The phases of oscillators are shifted but remain adjusted middle panel while the amplitudes are nearly uncorrelated.
Highlights a modular adaptive algorithm for synchronization of differentorder chaotic system. Synchronization of coupled optomechanical oscillators. A brief history of cybernetical physics is outlined. I highlight a few methods and ideas, including several of personal interest, that i anticipate to be especially important during the next several years. Synchronization of two coupled fractional order chaotic oscillators the model studied in this paper is an electronic chaotic oscillator of canonical structure, and one control parameter. We experimentally demonstrate and numerically simulate a new adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and timevarying e.
Adaptive control and synchronization of chaotic systems. Time scale synchronization of chaotic oscillators time scale synchronization of chaotic oscillators hramov, alexander e koronovskii, alexey a. H luo, ke yao, adaptive coupled synchronization among three coupled chaos systems and its application to secure communications. Antiphase synchronization in symmetrically coupled selfoscillators 851 a b fig. By using a simple state feedback control technique and introducing two new nonlinear functions into a modified sprott b system, a novel fourdimensional 4d noequilibrium hyperchaotic system with grid multiwing hyperchaotic hidden attractors is proposed in this paper. We test the locking capabilities of the bpo with an external driving signal of frequencies f m. Synchronization of nonidentical oscillators coupled through complex networks. Mathematical frameworks for oscillatory network dynamics in neuroscience. Adaptive synchronization of chaotic systems with nonlinear.
In networks of nonchaotic oscillators, when g is between 10. Palus already introduced the mutual information as a measure of synchronization 1. Introduction the dynamics of two coupled, chaotic oscillators is an. Synchronization of pulsecoupled biological oscillators siam. In fact, three coupled oscillators are sufficient to produce chaos. Adaptive mechanism for synchronization of chaotic oscillators. In this contribution we present a brief introduction to the theory of synchronization of selfsustained oscillators.
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