Generalized synchronization in coupled Ginzburg-Landau equations and mechanisms of its arising

Hramov, Alexander E.; Короновский, А. А.; Popov, P. V.

doi:10.1103/physreve.72.037201

Cited by 46 publications

(43 citation statements)

References 37 publications

(53 reference statements)

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“…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 oscillators with parameters detuned sufficiently [21]. For two unidirectionally coupled onedimensional complex Ginzburg-Landau equations with sufficiently detuned control parameters the threshold of the GS regime onset does not depend on the value of the drive system parameter when the response system parameters are fixed [22]. Alternatively, for all other types of chaotic synchronization the dependence of the threshold of the synchronous regime arising on the value of the control parameter mismatch behaves in the different way, i.e.…”

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confidence: 99%

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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Generalized synchronization onset

2005

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“…In this work, we have used the auxiliary system approach as another alternative method to study synchronization, in the generalized sense, in our coupled system. A detailed formulation of the technique is presented by Rulkov et al (1995), and some examples of its use are presented in the work by Hramov et al (2005) and Hramov and Koronovskii (2005b). In that technique, we consider the dynamics of the master x m (t) and the slave x s (t) systems.…”

Section: Generalized Synchronization: the Auxiliary System Approachmentioning

confidence: 99%

Synchronization in a coupled two-layer quasigeostrophic model of baroclinic instability – Part 1: Master-slave configuration

Castrejón‐Pita¹,

Read

2009

Nonlin. Processes Geophys.

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Abstract. Synchronization is studied using a pair of diffusively-coupled, two-layer quasi-geostrophic systems each comprising a single baroclinic wave and a zonal flow. In particular, the coupling between the systems is in the well-known master-slave or one-way configuration. Nonlinear time series analysis, phase dynamics, and bifurcation diagrams are used to study the dynamics of the coupled system. Phase synchronization, imperfect synchronization (phase slips), or complete synchronization are found, depending upon the strength of coupling, when the systems are either in a periodic or a chaotic regime. The results of investigations when the dynamics of each system are in different regimes are also presented. These results also show evidence of phase synchronization and signs of chaos control.

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“…The concept of GS has also been extended to spatially extended chaotic systems such as coupled Ginzburg-Landau equations [16]. Recently, the terminology intermittent generalized synchronization (IGS) [17] was introduced in diffusively coupled Rössler systems in analogy with intermittent lag synchronization (ILS) [18,19] and intermittent phase synchronization (IPS) [20,21,22], and also experimentally in coupled Chua's circuit.…”

Section: Introductionmentioning

confidence: 99%

Intermittency transition to generalized synchronization in coupled time-delay systems

Senthilkumar

Lakshmanan

2007

Phys. Rev. E

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In this paper, we report the nature of transition to generalized synchronization (GS) in a system of two coupled scalar piecewise linear time-delay systems using the auxiliary system approach. We demonstrate that the transition to GS occurs via on-off intermittency route and also it exhibits characteristically distinct behaviors for different coupling configurations. In particular, the intermittency transition occurs in a rather broad range of coupling strength for error feedback coupling configuration and in a narrow range of coupling strength for direct feedback coupling configuration. It is also shown that the intermittent dynamics displays periodic bursts of period equal to the delay time of the response system in the former case, while they occur in random time intervals of finite duration in the latter case. The robustness of these transitions with system parameters and delay times has also been studied for both linear and nonlinear coupling configurations. The results are corroborated analytically by suitable stability conditions for asymptotically stable synchronized states and numerically by the probability of synchronization and by the transition of subLyapunov exponents of the coupled time-delay systems. We have also indicated the reason behind these distinct transitions by referring to unstable periodic orbit theory of intermittency synchronization in low-dimensional systems.

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Generalized synchronization in coupled Ginzburg-Landau equations and mechanisms of its arising

Cited by 46 publications

References 37 publications

Generalized synchronization onset

Generalized synchronization onset

Synchronization in a coupled two-layer quasigeostrophic model of baroclinic instability – Part 1: Master-slave configuration

Intermittency transition to generalized synchronization in coupled time-delay systems

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