【作者】 吴杰；

【导师】 孙永征；

【作者基本信息】 中国矿业大学 ， 数学， 2015， 硕士

【摘要】 近些年来,对混沌系统和复杂动态网络的同步问题的研究得到了飞速的发展,并迅速成为非线性动力学领域的研究热点.本论文主要研究了混沌及复杂动态网络的有限时间同步问题,主要包括以下几个方面的内容：第一章介绍了混沌系统同步和复杂网络同步的研究背景和相关进展.给出了本文所要用到的一些预备知识,包括常微分方程稳定性理论、随机微分方程稳定性理论和图论的相关基础理论,并给出了本文的基本架构.第二章研究了混沌系统的有限时间随机同步问题.通过设计合适的自适应控制器,利用随机微分方程稳定性理论,给出了带有噪声干扰的两个混沌系统有限时间同步的充分条件.数值模拟验证了理论结果的有效性和可行性,并讨论了噪声强度对同步速度的影响.第三章研究了复杂动态网络的有限时间同步问题.通过设计有限时间自适应控制器,利用Lyapunov稳定性理论,给出了两个复杂动态网络同步的充分条件.数值模拟验证了理论结果的有效性,并考虑了两个小世界网络的同步问题,分析了度对同步速度的影响.第四章研究了复杂网络有限时间随机同步问题.考虑了噪声对网络同步的影响,研究表明同步速度与噪声强度成反比.第五章是对本文的一个简要总结以及对未来研究工作的展望.更多还原

【Abstract】 In recent years, synchronization of chaotic systems and complex dynamical net-works has got a rapid development, and it has become a hot topic research in the field of nonlinear dynamics. In this paper, we investigate the finite-time synchronization of chaotic systems and complex dynamical networks which includes the following con-tents:In chapter 1, we introduce some background knowledge and relative develop-ment of the synchronization of chaotic systems and complex networks, and we give some preliminaries including the basic stability theory of ordinary differential equa-tions and stochastic differential equations and graph theory, which will be used in this article. And we describe a brief structure of research progress at the end of this chapter. In chapter 2, we study the finite-time stochastic synchronization of chaotic systems. We propose new adaptive controllers, with which two chaotic systems can be synchronized in finite time, and sufficient conditions for the finite-time stochastic synchronization are derived based on the stability theory of stochastic differential equations. The effective-ness and feasibility of the theoretical results are verified through numerical simulations, and at the same time the influence of noise intensity on the synchronization time is also explored. In chapter 3, we investigate finite-time synchronization between two complex dynamical networks. We propose new finite-time adaptive controllers, with which we can synchronize two complex networks in finite time, and sufficient conditions for the finite-time synchronization are derived based on the Lyapunov stability theory. Finally, numerical simulations are examined to demonstrate the effectiveness and feasibility of the theoretical results, and at the same time we explore the performance of synchro-nization of two small-world networks and analyse the effect of degree on the synchro-nization speed. In chapter 4, we investigate the finite-time stochastic synchronization between two complex dynamical networks. The influence of noise on the synchro-nization of complex networks is explored, showing that the speed of synchronization is inversely proportional to noise intensity. In chapter 5, we make a brief summary on this thesis and prospect for further research on synchronization of chaotic systems and complex dynamical networks.更多还原