Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators

Hramov, Alexander E.; Короновский, А. А.

doi:10.1209/epl/i2004-10488-6

Cited by 87 publications

(67 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The chaotic synchronization regime has been observed in a whole series of coupled physical, biological, physiological, chemical and other systems [1,[4][5][6][7]. At present, several different types of chaotic synchronization are known such as generalized synchronization [8], phase synchronization [4,9], lag synchronization [10], intermittent lag [11] and intermittent generalized [12] synchronization behaviour, noise-induced synchronization [13], complete synchronization [14] and time scale synchronization [15,16], which generalizes the above-listed types of chaotic synchronization [15,17,18]. The various methods of analysis should be used to detect the different synchronization regimes [9,10,15,16,[19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Chaotic synchronization in coupled spatially extended beam–plasma systems

2006

View full text Add to dashboard Cite

The appearance of the chaotic synchronization regimes has been discovered for the coupled spatially extended beam-plasma Pierce systems. The coupling was introduced only on the right bound of each subsystem. It has been shown that with coupling increase the spatially extended beam-plasma systems show the transition from asynchronous behavior to the phase synchronization and then to the complete synchronization regime. For the consideration of the chaotic synchronization we used the concept of time scale synchronization described in work [Chaos, 14, 3 (2004) 603-610] and based on the introduction of the continuous set of phases of chaotic signal. In case of unidirectional coupling the generalized synchronization regime has been observed in the spatially extended beam-plasma systems. The generalized synchronization appearance mechanism has been analyzed by means of the offered modified system approach [Phys. Rev. E, 71, 6 (2005) 067201].

show abstract

Section: Introductionmentioning

confidence: 99%

Chaotic synchronization in coupled spatially extended beam–plasma systems

2006

View full text Add to dashboard Cite

show abstract

“…Indeed, close to the threshold parameter values for which the coupled systems show synchronized dynamics, it is observed that the de-synchronization mechanism involves persistent intermittent time intervals during which the synchronized oscillations are interrupted by the non-synchronous behavior. These pre-transitional intermittencies have been described in details for the case of lag synchronization [5,6,7] and for generalized synchronization [8], and their main statistical properties (following those of the on-off intermittency) have been shown to be common to other relevant physical processes.As far as intermittency phenomena near the phase synchronization onset are concerned, two types of intermittent behavior have been observed so far [9,10,11,12], namely the type-I intermittency and the super-long laminar behavior (so called "eyelet intermittency" [13]). …”

mentioning

confidence: 99%

Ring Intermittency in Coupled Chaotic Oscillators at the Boundary of Phase Synchronization

et al. 2006

View full text Add to dashboard Cite

A new type of intermittent behavior is described to occur near the boundary of phase synchronization regime of coupled chaotic oscillators. This mechanism, called ring intermittency, arises for sufficiently high initial mismatches in the frequencies of the two coupled systems. The laws for both the distribution and the mean length of the laminar phases versus the coupling strength are analytically deduced. A very good agreement between the theoretical results and the numerically calculated data is shown. We discuss how this mechanism is expected to take place in other relevant physical circumstances. Intermittent behavior is an ubiquitous phenomenon in nonlinear science. Its arousal and main statistical properties have been studied and characterized already since long time ago, and different types of intermittency have been classified as types I-III [1, 2] or on-off intermittency [3,4]. One of the most general and interesting manifestations of the intermittent behavior can be observed near of the boundary of chaotic synchronization regimes. Indeed, close to the threshold parameter values for which the coupled systems show synchronized dynamics, it is observed that the de-synchronization mechanism involves persistent intermittent time intervals during which the synchronized oscillations are interrupted by the non-synchronous behavior. These pre-transitional intermittencies have been described in details for the case of lag synchronization [5,6,7] and for generalized synchronization [8], and their main statistical properties (following those of the on-off intermittency) have been shown to be common to other relevant physical processes.As far as intermittency phenomena near the phase synchronization onset are concerned, two types of intermittent behavior have been observed so far [9,10,11,12], namely the type-I intermittency and the super-long laminar behavior (so called "eyelet intermittency" [13]).In this Letter we report that a new type of intermittent behavior is observed near the phase synchronization boundary of two unidirectionally coupled chaotic oscillators, when the natural frequencies of the two oscillators are sufficiently different from one another. The system under study is represented by a pair of unidirectionally coupled Rössler systems, whose equations read aṡy r , z r )] are the cartesian coordinates of the drive (the response) oscillator, dots stand for temporal derivatives, and ε is a parameter ruling the coupling strength. The other control parameters of Eq. (1) have been set to a = 0.15, p = 0.2, c = 10.0, in analogy with previous studies [14,15]. The ω r -parameter (representing the natural frequency of the response system) has been selected to be ω r = 0.95; the analogous parameter for the drive system has been fixed to ω d = 1.0. For such a choice of parameter values, both chaotic attractors of the drive and response systems are, at zero coupling strength, phase coherent. Furthermore, the boundary of the phase synchronization regime occur around ε c ≈ 0.124.The instantaneous phase of the ch...

show abstract

“…In particular, the intermittent behavior is known to be revealed on the onset of GS [14,15] as well as in case of the lag [3,16,17] or phase [18][19][20] synchronization.…”

mentioning

confidence: 99%

Generalized synchronization onset

2005

Self Cite

View full text Add to dashboard Cite

Abstract. -The behavior of two unidirectionally coupled chaotic oscillators near the generalized synchronization onset has been considered. The character of the boundaries of the generalized synchronization regime has been explained by means of the modified system approach.Chaotic synchronization is one of the fundamental nonlinear phenomena actively studied recently [1]. Several different types of chaotic synchronization of coupled oscillators, i.e. There are also attempts to find unifying framework for chaotic synchronization of coupled dynamical systems [6][7][8][9].One of the interesting and intricate types of the synchronous behavior of unidirectionally coupled chaotic oscillators is the generalized synchronization. The presence of GS between the response x r (t) and drive x d (t) chaotic systems means that there is some functional relation x r (t) = F[x d (t)] between system states after the transient finished. This functional relation F[·] may be smooth or fractal. According to the properties of this relation, GS may be divided into the strong synchronization and weak synchronization, respectively [10]. There are several methods to detect the presence of GS between chaotic oscillators, such as the auxiliary system approach [11] or the method of nearest neighbors [2,12]. It is also possible to calculate the conditional Lyapunov exponents (CLEs) [10,13] to detect GS. The regimes of LS and CS are also the particular cases of GS.One of the interesting aspects of the generalized synchronization study is the analysis of the onset of this regime. In particular, the intermittent behavior is known to be revealed on the onset of GS [14,15] as well as in case of the lag [3,16,17] or phase [18][19][20] synchronization.At the same time, there are known examples of the unidirectionally coupled chaotic systems for which the location of the generalized synchronization onset on the "parameter mismatch -coupling strength" plane differs radically from the other synchronization types. Indeed, for two unidirectionally coupled Rössler oscillators with identical control parameters the value of the coupling strength corresponding to the onset of GS is twice as much as for the same

show abstract

Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators

Cited by 87 publications

References 37 publications

Chaotic synchronization in coupled spatially extended beam–plasma systems

Chaotic synchronization in coupled spatially extended beam–plasma systems

Ring Intermittency in Coupled Chaotic Oscillators at the Boundary of Phase Synchronization

Generalized synchronization onset

Contact Info

Product

Resources

About