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1.
A. A. Koronovskiĭ P. V. Popov A. E. Hramov 《Journal of Experimental and Theoretical Physics》2006,103(4):654-665
Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling between the systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed. 相似文献
2.
O. I. Moskalenko A. E. Hramov A. A. Koronovskii A. A. Ovchinnikov 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,82(1):69-82
The influence of noise on the generalized synchronization
regime in the chaotic systems with dissipative coupling is
considered. If attractors of the drive and response systems have an
infinitely large basin of attraction, generalized
synchronization is shown to possess a great stability with
respect to noise. The reasons of the revealed particularity are
explained by means of the modified system approach [A.E. Hramov,
A.A. Koronovskii, Phys. Rev. E 71, 067201 (2005)] and
confirmed by the results of numerical calculations and experimental
studies. The main results are illustrated using the examples of
unidirectionally coupled chaotic oscillators and discrete maps as
well as spatially extended dynamical systems. Different types of the
model noise are analyzed. Possible applications of the revealed
particularity are briefly discussed. 相似文献
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A way of data transmission using generalized chaotic synchronization is suggested. Since the characteristics of the valid signal are corrected by a noise generator with desired parameters, this way of data transmission offers a high degree of reliability. It is shown that noise in the method of generalized synchronization improves the privacy of the transmitted data. The basic ideas of the method are illustrated with unidirectionally coupled Ressler systems used as oscillators on the transmitter and receiver sides. 相似文献
5.
In this paper, complete synchronization and generalized synchronization between two unidirectionally coupled optical systems with multiple time delays and noise perturbation are investigated. Sufficient conditions for both complete synchronization and generalized synchronization are rigorously established. Numerical simulations fully support the theoretical results. The effect of parameter mismatch on the quality of synchronization is also explored. 相似文献
6.
Complete and generalized synchronization in a class of noise perturbed chaotic systems 总被引:1,自引:0,他引:1
In the paper, in light of the LaSalle-type invariance principle for stochastic differential equations, chaos synchronization is investigated for a class of chaotic systems dissatisfying a globally Lipschitz condition with noise perturbation. Sufficient criteria for both complete synchronization and generalized synchronization are rigorously established and thus successfully applied to realize chaos synchronization in the coupled unified chaotic systems. Furthermore, concrete examples as well as their numerical simulations are provided to illustrate the possible application of the established criteria. 相似文献
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This paper detects and characterizes the diverse roles played by
bounded noise in chaotic phase synchronization (CPS) of weakly
coupled nonlinear stochastic systems. Analysis of a paradigmatic
model of two bidirectional coupled three-level food chains is
carried out by various statistical measures such as Shannon entropy
and mutual information. The results indicate that inside the
synchronous regime, CPS is considerably reduced under the influence
of bounded noise; near the onset of phase synchronization, temporal
phase locking is diversely changed with the increase of noise, i.e.,
either weak or strong noise also degrades the degree of CPS, while
intermediate noise enhances CPS remarkably, and an optimal noise
intensity is detected that maximizes the enhancement. 相似文献
9.
The paper investigates synchronization in unidirectionally coupled dynamical systems wherein the influence of drive on response is cumulative: coupling signals are integrated over a time interval τ. A major consequence of integrative coupling is that the onset of the generalized and phase synchronization occurs at higher coupling compared to the instantaneous (τ?=?0) case. The critical coupling strength at which synchronization sets in is found to increase with τ. The systems explored are the chaotic Rössler and limit cycle (the Landau–Stuart model) oscillators. For coupled Rössler oscillators the region of generalized synchrony in the phase space is intercepted by an asynchronous region which corresponds to anomalous generalized synchronization. 相似文献
10.
研究了两个耦合格子动力系统的非线性相互作用。当两个耦合格子系统一样时,则导致完全同步化。而当两个耦合格子系统的参数不一样或者这两个系统不相同时,则导致广义同步化。计算了Lyapunov指数谱。 相似文献
11.
In this paper, we study the crucial impact of white noise on lag synchronous regime in a pair of time-delay unidirectionally coupled systems. Our result demonstrates that merely via white-noise-based coupling lag synchronization could be achieved between the coupled systems (chaotic or not). And it is also demonstrated that a conventional lag synchronous regime can be enhanced by white noise. Sufficient conditions are further proved mathematically for noise-inducing and noise-enhancing lag synchronization, respectively. Additionally, the influence of parameter mismatch on the proposed lag synchronous regime is studied, by which we announce the robustness and validity of the new strategy. Two numerical examples are provided to illustrate the validity and some possible applications of the theoretical result. 相似文献
12.
时滞和噪声在复杂网络中普遍存在,而含有耦合时滞和噪声摄动的耦合网络同步的研究工作却极其稀少. 本文针对噪声环境下具有不同节点动力学、不同拓扑结构及不同节点数目的耦合时滞网络,提出了两个网络之间的广义投影滞后同步. 首先,构建了更加贴近现实的驱动-响应网络同步的理论框架;其次,基于随机时滞微分方程LaSalle不变性原理,严格证明了在合理的控制器作用下,驱动网络和响应网络在几乎必然渐近稳定性意义下能够取得广义投影滞后同步;最后,借助于计算机仿真,通过具体的网络模型验证了理论推理的有效性. 数值模拟结果表明,驱动网络与响应网络不但能够达到广义投影滞后同步,而且同步效果不依赖于耦合时滞和比例因子的选取,同时也揭示了更新增益和耦合时滞对同步收敛速度的显著性影响.
关键词:
复杂网络
广义投影滞后同步
随机噪声
时滞 相似文献
13.
In this paper we briefly report some recent developments on generalized synchronization. We discuss different methods of detecting generalized synchronization. We first consider two unidirectionally coupled systems and then two mutually coupled systems. We then extend the study to a network of coupled systems. In the study of generalized synchronization of coupled nonidentical systems we discuss the Master Stability Function (MSF) formalism for coupled nearly identical systems. Later we use this MSF to construct synchronized optimized networks. In the optimized networks the nodes which have parameter value at one extreme are chosen as hubs and the pair of nodes with larger difference in parameter are chosen to create links. 相似文献
14.
Generalized synchronization of chaos for secure communication: Remarkable stability to noise 总被引:1,自引:0,他引:1
A new method for secure information transmission based on generalized synchronization is proposed. The principal advantage of it is a remarkable stability to noise. To reveal this peculiarity of the proposed method the effectiveness of the detection of the information signal from the transmitted one in the presence of noise in the communication channel is examined both for the proposed scheme and for the schemes of chaotic communication known already. The main ideas of the proposed method are illustrated by the example of coupled Rössler systems used both transmitter and receiver. 相似文献
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A. A. Koronovskii O. I. Moskalenko P. V. Popov A. E. Hramov 《Bulletin of the Russian Academy of Sciences: Physics》2008,72(1):131-135
A method for secure data transmission is proposed on the basis of the phenomenon of generalized chaotic synchronization, which is characterized by extremely high stability to noise and fluctuations in a communication channel. The basic concepts of the method proposed are illustrated by numerical simulation of two unidirectionally coupled Róssler systems, chosen as a transmitter and a receiver. Fundamental advantages of the proposed method over the known ones are shown. 相似文献
17.
D.V. Senthilkumar M. Lakshmanan J. Kurths 《The European physical journal. Special topics》2008,161(1):35-44
Phase synchronization in unidirectionally coupled Ikeda time-delay systems
exhibiting non-phase-coherent hyperchaotic attractors of complex topology with
highly interwoven trajectories is studied. It is shown that in this set of
coupled systems phase synchronization (PS)does exist in a range of the
coupling strength which is preceded by a transition regime (approximate PS)and
a nonsynchronous regime. However, exact generalized synchronization does not seem
to occur in the coupled Ikeda systems (for the range of parameters we have
studied)even for large coupling strength, in contrast to our earlier studies in
coupled piecewise-linear and Mackey-Glass systems [27,28].
The above transitions are characterized in terms of recurrence based indices,
namely generalized autocorrelation function P(t), correlation of probability
of recurrence (CPR), joint probability of recurrence (JPR)and similarity of
probability of recurrence (SPR). The existence of phase synchronization is also
further confirmed by typical transitions in the Lyapunov exponents of the
coupled Ikeda time-delay systems and also using the concept of localized sets. 相似文献
18.
研究了一个时间混沌系统驱动多个时空混沌系统的并行同步问题.以单模激光Lorenz系统和一维耦合映像格子为例,在单模激光Lorenz系统中提取一个混沌序列,通过与一维耦合映像格子中的状态变量耦合使单模激光Lorenz系统和多个同结构一维耦合映像格子同时达到广义同步,并且多个一维耦合映像格子之间实现完全并行同步.通过计算条件Lyapunov指数,可以得到并行同步所需反馈系数的取值范围.数值模拟证明了此方法的可行性和有效性. 相似文献
19.
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piecewise linear and in coupled Mackey-Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from nonsynchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase-coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence-based indices, namely generalized autocorrelation function P(t), correlation of probability of recurrence, joint probability of recurrence, and similarity of probability of recurrence. We have quantified the different synchronization regimes in terms of these indices. The existence of phase synchronization is also characterized by typical transitions in the Lyapunov exponents of the coupled time-delay systems. 相似文献