Transition from intermittency to periodicity in lag synchronization in coupled Rössler oscillators

Zhan, Meng; Wei, Guannan; Lai, Choy Heng

doi:10.1103/physreve.65.036202

Cited by 74 publications

(51 citation statements)

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“…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]). …”

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

et al. 2006

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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...

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

et al. 2006

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“…Close to the threshold parameter value the coupled chaotic systems demonstrate synchronized dynamics most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous behavior. These pretransitional intermittencies have been described in [6,22,23] for the case of lag synchronization and in [24][25][26] for phase synchronization, respectively.Due to the existence of unifying framework of coupled chaotic oscillators synchronization one can also expect the intermitted behavior at the threshold of the generalized synchronization appearance. In this work we consider the behavior of coupled chaotic oscillators close to the coupling parameter value corresponding to the onset of generalized synchronization regime.…”

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Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators

Hramov

Короновский

2005

Europhys. Lett.

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Abstract. -A new behavior type of unidirectionally coupled chaotic oscillators near the generalized synchronization transition has been detected. It has been shown that the generalized synchronization appearance is preceded by the intermitted behavior: close to threshold parameter value the coupled chaotic systems demonstrate the generalized synchronization most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous bursts. This type of the system behavior has been called intermitted generalized synchronization (IGS) by analogy with intermitted lag synchronization (ILS) [Phys. Rev. E 62, 7497 (2000)].Synchronization [1,2] of interacting chaotic oscillators is one of the fundamental phenomena of nonlinear dynamics. Recently several types of chaotic synchronization have been observed in coupled nonlinear oscillators. These are phase synchronization (PS) [3][4][5], lag synchronization (LS) [6][7][8], complete synchronization (CS) [9][10][11][12] and generalized synchronization (GS) [13][14][15]. It is important to note that GS may also takes place in the non-oscillatory chaotic systems (see [16] for detail). All synchronization types are interrelated (see for detail [7,13,17]), but the relationship between them is not completely clarified yet. In recent works [18][19][20][21] it has been shown that all these synchronization types may be considered from the common point of view as different manifestations of one universal phenomenon.It has also been found that onsets of phase and lag synchronization types are preceded by intermittent behavior. Close to the threshold parameter value the coupled chaotic systems demonstrate synchronized dynamics most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous behavior. These pretransitional intermittencies have been described in [6,22,23] for the case of lag synchronization and in [24][25][26] for phase synchronization, respectively.Due to the existence of unifying framework of coupled chaotic oscillators synchronization one can also expect the intermitted behavior at the threshold of the generalized synchronization appearance. In this work we consider the behavior of coupled chaotic oscillators close to the coupling parameter value corresponding to the onset of generalized synchronization regime. As it will be shown below the generalized synchronization appearance is also preceded by the intermitted behavior in the same way as the phase synchronization and lag c EDP Sciences

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“…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.…”

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Generalized synchronization onset

2005

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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

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Transition from intermittency to periodicity in lag synchronization in coupled Rössler oscillators

Cited by 74 publications

References 33 publications

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

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

Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators

Generalized synchronization onset

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