【作者】 柴元；

【导师】 吕翎；

【作者基本信息】 辽宁师范大学 ， 理论物理， 2010， 硕士

【摘要】 复杂网络的同步研究是目前复杂网络研究最活跃的领域之一。由于复杂网络的同步能够解释自然界的许多复杂现象,并紧密联系现实社会,所以,对复杂网络的同步研究具有一定的实际意义和广泛的应用前景。本文对复杂网络的研究进展做了概括性的介绍,包括复杂网络模型的建立、网络的性质、网络同步的意义以及国内外研究现状。同时,还介绍了复杂网络同步的两个重要判定方法：主稳定函数判据和Lyapunov函数判定法以及目前已报道的几个典型的复杂网络同步实例。在此基础上,采用单变量耦合连接方式,通过backstepping方法构造Lyapunov函数,研究了同结构链式网络的时空混沌同步问题。以Gray-Scott系统为例,仿真模拟验证了该网络同步原理的可行性。此方法只需在复杂网络节点终端加入一个控制器,便可以实现整个网络的同步,因此同步代价小,便以实际应用。另外,本文还依据主稳定函数判据,研究了异结构树状网络的时空混沌同步问题。通过确定网络的最大Lyapunov指数,得到了实现网络同步的条件。采用具有时空混沌行为的Panfilov系统、Fitzhugh—Nagumo系统以及Plankton系统作为网络节点,仿真模拟验证了该方法的有效性。更多还原

【Abstract】 Synchronization study of complex network is the one of the most active areas of complex network study at present. The synchronization of complex network can explain many complex phenomena in nature, and close contact with the real world. Therefore, synchronization study of complex network has some practical significance and wide applications. The research progress of complex network is recapitulative introduced in this thesis, including established complex network models, the features of network, the significance of network synchronization and research status at home and abroad. At the same time, two criterions of the synchronization of complex network:Master stability function criterion and Lyapunov function criterion are described, as well as several typical reported examples of the complex network synchronization are introduced. On this basis, Lyapunov function is constructed by backstepping design for single variable coupling connections, and the spatiotemporal chaos synchronization in chain network with topology equipollence is investigated. Taking the Gray-Scott spatiotemporal chaos system as an example, the simulation results show that the synchronization principle is feasibility. In this method, only one controller is added at the terminal node of complex network and synchronization of the entire network can be achieved, meaning the low-cost synchronization and convenient practical applications. In addition, the spatiotemporal chaos synchronization in tree network with different structure is studied in our work based on the Master stability function criterion. The condition for complex network synchronization is obtained by determining the largest Lyapunov index of the network. The Panfilov, Fitzhugh-Nagumo and Plankton spatiotemporal chaos systems are taken as network nodes, respectively, numerical simulation results show the effectiveness of the method.更多还原