Generalized synchronization: A modified system approach

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

doi:10.1103/physreve.71.067201

Cited by 129 publications

(130 citation statements)

References 19 publications

Supporting

Mentioning

119

Contrasting

Unclassified

Order By: Relevance

“…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.…”

mentioning

confidence: 99%

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

et al. 2006

Self Cite

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

mentioning

confidence: 99%

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

et al. 2006

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hramov et.al. [11] proposed GS by a modified system approach in 2005. They investigated the physical reasons leading to GS appearance in unidirectionally coupled chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Generalized synchronization of bidirectionally coupled chaotic systems via linear transformations

Khan¹

2012

International Journal of Basic and Applied Sciences

View full text Add to dashboard Cite

Several important properties of chaos synchronization of bidirectionally coupled systems remain still unexplored. This paper designes a new synchronization scheme for generalized bidirectionally coupled chaotic systems via linear transformations. The proposed synchronization scheme of bidirectionally coupled chaotic systems are discussed taking coupled unified chaotic systems. In this method, we can predict the driven systems behavior in advance, knowing the driving systems behavior. Simulation results are presented to show the effectiveness of the proposed scheme.

show abstract

“…The main idea of the proposed approach is the following. Since the chaotic oscillator dynamics changed sufficiently when GS arises [3], one can expect that this transformation is also manifested in the power spectra modifications. To detect the qualitative changes in the power spectrum of the response system taking place with the increase of the coupling strength ε = 10 −Γ/20 (where Γ is the attenuation factor of the coupling microwave line) we propose the following characteristic…”

mentioning

confidence: 99%

“…Unless the dynamics of the response system is transformed cardinally the value σ(ε) is not supposed to be changed greatly. Since arising the GS regime means the major restructuring of the response system dynamics [3], one can expect that the noticeable variations in the evolution of the characteristic σ(ε) corresponding to the onset of the GS regime may be observed. Since the power spectra obtained in the experiment are represented by the discrete sets of data, the integral in (1) should be replaced by the sum and, therefore, Eq.…”

mentioning

confidence: 99%

“…One of the interesting and intricate types of the synchronous behavior of unidirectionally coupled chaotic oscillators is the generalized synchronization (GS) [2,3], which means the presence a functional relation between the dynamics of the drive and response chaotic systems, though this relation may be very complicated and its explicit form cannot be found in most cases. Remarkably, that practically all studies of the generalized synchronization phenomenon deal with the low-dimensional model systems or the low frequency oscillators.…”

mentioning

confidence: 99%

See 1 more Smart Citation

First Experimental Observation of Generalized Synchronization Phenomena in Microwave Oscillators

et al. 2009

Self Cite

View full text Add to dashboard Cite

In this Letter we report for the first time on the experimental observation of the generalized synchronization regime in the microwave electronic systems, namely, in the multicavity klystron generators. A new approach devoted to the generalized synchronization detection has been developed. The experimental observations are in the excellent agreement with the results of numerical simulation. The observed phenomena gives a strong potential for new applications requiring microwave chaotic signals. Chaotic synchronization is one of the fundamental phenomena, widely studied recently, having both theoretical and applied significance [1]. One of the interesting and intricate types of the synchronous behavior of unidirectionally coupled chaotic oscillators is the generalized synchronization (GS) [2,3], which means the presence a functional relation between the dynamics of the drive and response chaotic systems, though this relation may be very complicated and its explicit form cannot be found in most cases. Remarkably, that practically all studies of the generalized synchronization phenomenon deal with the low-dimensional model systems or the low frequency oscillators. Even if generalized synchronization in lasers is studied, the oscillations of the total intensity of the laser output are usually considered whose frequency is in the megahertz range, with the oscillator dynamics being described by the system of the ordinary differential equations [4]. The more complicated objects with the infinite dimensional phase space (such as spatially extended systems (see, e.g., [5]) or oscillators with the delayed feedback) are considered from the point of view of generalized synchronization rarely, and, practically always, numerically.In this Letter we report for the first time on the experimental revelation of generalized synchronization in the microwave systems with the infinite dimensional phase space, namely, in the multicavity klystron oscillators with the delayed feedback. Along with the theoretical interest this study is also important from the point of view of the practical purposes of communication, where the microwave range signals are used very widely.To detect the onset of generalized synchronization in the experiment a new approach being applicable to the microwave systems has been developed. Actually, there are various techniques for detecting the presence of GS between chaotic oscillators, such as the method of nearest neighbors [6] or the auxiliary system approach [2]. It is also possible to calculate the conditional Lyapunov exponents [7] to reveal the generalized synchronization regime. Unfortunately, these approaches are often difficult (or impossible) to implement in the experimental measurements (specifically, in the microwave range), due to the presence of noise and lack of the precisions. Therefore, in this Letter we propose the radically different approach which may deal with the chaotic oscillators of the microwave range to detect experimentally the onset of the generalized synchronization regime. Moreove...

show abstract

Generalized synchronization: A modified system approach

Cited by 129 publications

References 19 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

Generalized synchronization of bidirectionally coupled chaotic systems via linear transformations

First Experimental Observation of Generalized Synchronization Phenomena in Microwave Oscillators

Contact Info

Product

Resources

About