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1.
The present paper is mainly concerned with the issues of synchronization dynamics of complex delayed dynamical networks with impulsive effects. A general model of complex delayed dynamical networks with impulsive effects is formulated, which can well describe practical architectures of more realistic complex networks related to impulsive effects. Based on impulsive stability theory on delayed dynamical systems, some simple but less conservative criterion are derived for global synchronization of such dynamical network. It is shown that synchronization of the networks is heavily dependent on impulsive effects of connecting configuration in the networks. Furthermore, the theoretical results are applied to a typical SF network composing of impulsive coupled chaotic delayed Hopfield neural network nodes, and are also illustrated by numerical simulations. 相似文献
2.
In this Letter, singular hybrid coupled systems are introduced to describe complex networks with a special class of constraints. The synchronization problem of singular hybrid coupled systems with time-varying nonlinear perturbation is investigated. A sufficient condition for global synchronization is derived based on the Lyapunov stability theory. The singular system is regular and impulse free. Finally, a numerical example is provided to illustrate the effectiveness of the proposal conditions. 相似文献
3.
Measure synchronization in coupled Hamiltonian systems is a novel
synchronization phenomenon. The measure synchronization on symplectic map is
observed numerically, for identical coupled systems with different
parameters. We have found the properties of the characteristic frequency and
the amplitude of phase locking in regular motion when the measure
synchronization of coupled systems is obtained. The relations between the
change of the largest Lyapunov exponent and the course of phase
desynchronization are also discussed in coupled systems, some useful results
are obtained. A new approach is proposed for describing the measure
synchronization of coupled systems numerically, which is
advantage in judging the measure synchronization, especially for the coupled
systems in nonregular region. 相似文献
4.
Synchronization phenomena, an emergent property in networks of interacting dynamical elements, are widely observed in nature, and have become the subject of intense research. Here we will investigate the synchronization rate problem in coupled limit-cycle and chaotic oscillators. Based on the mode decomposition method and Gershgörin's discs theorem, some sufficient conditions for synchronization of coupled systems are obtained, and a synchronization rate is then derived. Such a synchronization rate indicates that the error functions between state variables of underlying individual systems tend to zero in the exponential form as time tends to the infinity. Several numerical examples are also given to validate the theoretical results. 相似文献
5.
Voss HU 《Chaos (Woodbury, N.Y.)》2003,13(1):327-334
The problem of constructing synchronizing systems to observed signals is approached from a data driven perspective, in which it is assumed that neither the drive nor the response systems are known explicitly but have to be derived from the observations. The response systems are modeled by utilizing standard methods of nonlinear time series analysis applied to sections of the driving signals. As a result, synchronization is more robust than what might be expected, given that the reconstructed systems are only approximations of the unknown true systems. Successful synchronization also may be accomplished in cases where the driving signals result from nonlinearly transformed chaotic states. The method is readily extended and applied to limited real-time predictions of chaotic signals. 相似文献
6.
Synchronization processes in populations of locally interacting elements are the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understanding synchronization phenomena in natural systems now take advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also take an overview of the new emergent features coming out from the interplay between the structure and the function of the underlying patterns of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences. 相似文献
7.
本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程. 相似文献
8.
9.
A. E. Hramov A. A. Koronovskii Yu. I. Levin 《Journal of Experimental and Theoretical Physics》2005,100(4):784-794
We consider chaotic oscillator synchronization and propose a new approach for detecting the synchronized behavior of chaotic oscillators. This approach is based on analysis of different time scales in the time series generated by coupled chaotic oscillators. We show that complete synchronization, phase synchronization, lag synchronization, and generalized synchronization are particular cases of the synchronized behavior called time-scale synchronization. A quantitative measure of chaotic oscillator synchronous behavior is proposed. This approach is applied to coupled Rössler systems. 相似文献
10.
声光双稳系统的混沌同步 总被引:6,自引:0,他引:6
首先给出布拉格型声光双稳系统耦合驱动的混沌同步化方案,用最大条件Lyapunov指数分析方法得出耦合驱动下系统混沌输出同步化条件,发现通过适当比例的耦合驱动可以使两组混沌系统达到同步的混沌输出。分析此混沌同步化方案可以抵抗噪声的干扰,并且在两系统出现偏差时仍可以实现混沌同步,找到了实用的单变量延时微分系统非Pecora-Carroll规则的混沌同步化方案。最后做了实验验证。 相似文献
11.
Fumito Mori 《Physica D: Nonlinear Phenomena》2009,238(14):1180-1185
We investigate the synchronous dynamics of Kuramoto oscillators and van der Pol oscillators on Watts-Strogatz type small-world networks. The order parameters to characterize macroscopic synchronization are calculated by numerical integration. We focus on the difference between frequency synchronization and phase synchronization. In both oscillator systems, the critical coupling strength of the phase order is larger than that of the frequency order for the small-world networks. The critical coupling strength for the phase and frequency synchronization diverges as the network structure approaches the regular one. For the Kuramoto oscillators, the behavior can be described by a power-law function and the exponents are obtained for the two synchronizations. The separation of the critical point between the phase and frequency synchronizations is found only for small-world networks in the theoretical models studied. 相似文献
12.
LI Yang LIAO Xiao-Feng LI Chuan-Dong CHEN Guo 《理论物理通讯》2007,47(6):1067-1072
The issue of impulsive synchronization of the coupled chaotic laser plasma system is investigated. A new framework for impulsive synchronization of such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. We derive some sufficient conditions for the synchronization of a laser plasma system via impulsive control with the varying impulsive intervals, which allows us to derive the impulsive synchronization law easily. To illustrate the effectiveness of the proposed results, two numerical examples are given. 相似文献
13.
A dynamical variable feedback scheme is proposed to synchronize chaotic motion of two identical and nearly identical laser systems with an injected signal. The feedback synchronization method works well while the conventional variable-replacement synchronization methods are not realizable. Various practical situations for synchronizing two chaotic laser systems located distance away from each other are taken into account. The application of this synchronization approach to wide range of practical systems is emphasized. 相似文献
14.
Synchronization criteria for complex dynamical networks with neutral-type coupling delay 总被引:1,自引:0,他引:1
A generalized complex dynamical networks model with neutral-type coupling delay is proposed, which is an extension for the systems without time delay and with the retarded delay. By some transformation, the synchronization problem of the complex networks is transferred equally into the asymptotical stability problem of a group of uncorrelated neutral delay functional differential equations. Furthermore, the less conservative sufficient conditions for both delay-independent and delay-dependent asymptotical synchronization stability criteria are derived in the form of linear matrix inequalities based on the free weighting matrix strategy. Numerical examples are given to illustrate the theoretical results. 相似文献
15.
In this paper, the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied. Firstly, the definition of combination projection synchronization of fractional-order complex dynamic networks is given, and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system. In addition, time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal. Then, based on Lyapunov stability theory and fractional inequality theory, the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors. The controller is easier to realize because there is no time-delay term in the controller. At last, the corresponding simulation examples demonstrate the effectiveness of the proposed scheme. 相似文献
16.
研究两个对称非线性耦合混沌系统的同步问题.通过对系统线性项与非线性项的适当分离, 构造一个特殊的非线性耦合项,发现在耦合强度α=05附近的某一区域里存在稳定的 混沌同步现象.提供判断同步误差稳定性的方程,利用线性系统的稳定性分析准则和条件Lya punov指数来检验同步状态的稳定性.新方法适用于连续时间系统的混沌同步,也适用于具有 两个(或多于两个)正Lyapunov指数的超混沌系统.以Lorenz系统,超混沌Rssler 系统作 为算例,数值模拟结果证实所提新方法的有效性.
关键词:
混沌
同步
非线性耦合
稳定性准则
超混沌 相似文献
17.
Zheng Zhi-gang Feng Xiao-qin Ao Bin Michael C. Cross 《Frontiers of Physics in China》2006,1(4):458-467
In this paper, partial synchronization (PaS) in networks of coupled chaotic oscillator systems and synchronization in sparsely
coupled spatiotemporal systems are explored. For the PaS, we reveal that the existence of PaS patterns depends on the symmetry
property of the network topology, while the emergence of the PaS pattern depends crucially on the stability of the corresponding
solution. An analytical criterion in judging the stability of PaS state on a given network are proposed in terms of a comparison
between the Lyapunov exponent spectrum of the PaS manifold and that of the transversal manifold. The competition and selections
of the PaS patterns induced by the presence of multiple topological symmetries of the network are studied in terms of the
criterion. The phase diagram in distinguishing the synchronous and the asynchronous states is given. The criterion in judging
PaS is further applied to the study of synchronization of two sparsely coupled spatiotemporal chaotic systems. Different synchronization
regimes are distinguished. The present study reveals the intrinsic collective bifurcation of coupled dynamical systems prior
to the emergence of global synchronization. 相似文献
18.
Zhou CT 《Chaos (Woodbury, N.Y.)》2006,16(1):013124
A cross-correlation coefficient of complex fields has been investigated for diagnosing spatiotemporal synchronization behavior of coupled complex fields. We have also generalized the subsystem synchronization way established in low-dimensional systems to one- and two-dimensional Ginzburg-Landau equations. By applying the indicator to examine the synchronization behavior of coupled Ginzburg-Landau equations, it is shown that our subsystem approach may be of better synchronization performance than the linear feedback method. For the linear feedback Ginzburg-Landau equation, the nonidentical system exhibits generalized synchronization characteristics in both amplitude and phase. However, the nonidentical subsystem may exhibit complete-like synchronization properties. The difference between complex fields for driven and response systems gives a linear scaling with the change of their parameter difference. 相似文献
19.
Huang Liang Lai Ying-Cheng Kwangho Park Wang Xingang Lai Choy Heng Robert A. Gatenby 《Frontiers of Physics in China》2007,2(4):446-459
Synchronization in complex networks has been an active area of research in recent years. While much effort has been devoted
to networks with the small-world and scale-free topology, structurally they are often assumed to have a single, densely connected
component. Recently it has also become apparent that many networks in social, biological, and technological systems are clustered,
as characterized by a number (or a hierarchy) of sparsely linked clusters, each with dense and complex internal connections.
Synchronization is fundamental to the dynamics and functions of complex clustered networks, but this problem has just begun
to be addressed. This paper reviews some progress in this direction by focusing on the interplay between the clustered topology
and network synchronizability. In particular, there are two parameters characterizing a clustered network: the intra-cluster
and the inter-cluster link density. Our goal is to clarify the roles of these parameters in shaping network synchronizability.
By using theoretical analysis and direct numerical simulations of oscillator networks, it is demonstrated that clustered networks
with random inter-cluster links are more synchronizable, and synchronization can be optimized when inter-cluster and intra-cluster
links match. The latter result has one counterintuitive implication: more links, if placed improperly, can actually lead to
destruction of synchronization, even though such links tend to decrease the average network distance. It is hoped that this
review will help attract attention to the fundamental problem of clustered structures/synchronization in network science.
相似文献
20.
We investigate the problem of detecting clusters exhibiting higher-than-average internal connectivity in networks of interacting systems. We show how the average association objective formulated in the context of spectral graph clustering leads naturally to a clustering strategy where each system is assigned to at most one cluster. A residual set is formed of the systems that are not members of any cluster. Maximization of the average association objective leads to a discrete optimization problem, which is difficult to solve, but a relaxed version can be solved using an eigendecomposition of the connectivity matrix. A simple approach to extracting clusters from a relaxed solution is described and developed by applying a variance maximizing solution to the relaxed solution, which leads to a method with increased accuracy and sensitivity. Numerical studies of theoretical connectivity models and of synchronization clusters in a lattice of coupled Lorenz oscillators are conducted to show the efficiency of the proposed approach. The method is applied to an experimentally obtained human resting state functional magnetic resonance imaging dataset and the results are discussed. 相似文献