基于复杂网络拓扑结构的耦合映象格子的动力学研究

【作者】 陈伟；

【导师】 康戈文；

【作者基本信息】 电子科技大学 ， 控制理论与控制工程， 2006， 硕士

【摘要】 最近几十年来,复杂动力系统的同步和控制受到了各方面的关注,耦合映象格子由于其简单方便,一直是研究时空混沌动力学行为的一个典型的模型。在过去,大部分的工作把研究重点放在了耦合配置为完全随机或者完全规则的耦合映象格子系统中。但是完全随机和完全规则的网络是不现实的,实际生活中的网络连接既非随机也非完全规则,而处于两者之间。复杂网络近年来受到来自各个领域的越来越多的关注,其中无标度网络是复杂网络研究中最重要的模型之一,它遵从幂律分布,如我们的WWW网络。网络中的节点除了表现出随机的模式外,还有一些象实际网络中集线器那样具有大量连接关系的节点。这样的特性显著地影响了网络的运行方式。本论文正是对具有无标度拓扑结构的耦合映象格子的动力学行为进行了研究,主要内容和创新点如下:1.利用Lyapunov指数对具有规则网络结构的耦合映象格子系统的动力学行为进行研究;2.对具有无标度网络结构的耦合映象格子系统的动力学行为进行了详细研究;为了使系统达到同步,我们的策略是应用三种反馈方法(常数反馈和两种时延反馈)对系统的部分节点进行控制以达到我们期望的状态。对于时延反馈控制,临界反馈控制值线性地随着耦合映象格子的耦合强度的线性增长而增大;当控制强度大于临界反馈控制值时,具有无标度拓扑结构的耦合映象格子系统会失去同步状态进而出现间歇振荡现象。更多还原

【Abstract】 Over the past decades, dynamical synchronization and control in complex dynamical systems has attracted much attention. A typical case is the coupled map lattices (CML) which are often used as a convenient model to study characteristics of some spatiotemporal systems. In the past, however, most of these works have been concentrated on the CML in which assumes that the coupling configuration is completely regular or random. It is well known that, regular networks and random networks are both useful idealizations, but interactions in real world are neither completely regular nor completely random, and lie in somewhere between the extremes of order and randomness. Recently, complex networks attract more and more attentions from various fields of science and engineering. Scale-free network is one of the most important complex network models, where the degree distribution obeys a power law form,like the Internet and the WWW. Besides the nodes of these networks with a random pattern of connections, some nodes act as“very connected”hubs, a fact that dramatically influences the way of how the network operates.In this dissertation, dynamical synchronization and control in coupled map lattices(CML) with scale-free (SF)topology have been analyzed. The main results are as follows:1.Dynamical behavior in coupled map lattices with regular topology are investigated by using Lyapunov componet.2.Dynamical behavior in coupled map lattice with scale-free topology are investigated in detail. Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength is increased linearly as the coupled strength is increased linearly. The CML with SF loses synchronization and intermittency occurs if control strength is greater than the critical feedback strength.更多还原