【作者】 王瑞兵；

【导师】 姚洪兴；

【作者基本信息】 江苏大学 ， 应用数学， 2007， 硕士

【摘要】 近年来，复杂网络引起了国际科学界的广泛重视，已成为统计物理、随机图论、计算机网络、生态学、生物学以及社会学的研究热点，并与其它许多学科领域相互渗透，有着巨大的应用前景。本文作者的工作是围绕复杂网络的形成机制及网络中的节点同步展开的。本文主要包括以下几方面内容：1．对复杂网络的研究背景与研究现状、发展思路进行了较为全面的介绍和总结。2．介绍了复杂网络的基本理论和几种经典的复杂网络模型，讨论了小世界网络与无标度网络的一些动力学特性。3．本文分析了三个相互耦合节点构成的环状网络的同步情况。大多数对复杂网络同步的研究中，都采取线性化网络节点的办法，因此只能得到复杂网络局部同步的条件。本文并未采取这种方法，而是利用矩阵变换及Lyapunov稳定性理论对网络的节点同步进行了分析，提出了一种关于网络节点全局同步的方案，结果证明了当耦合系数满足一定的条件时，节点间的全局同步可以实现。最后用Matlab进行了数值仿真，给出了系统的同步误差图。4．研究了复杂网络中的保密通信问题，把网络中一个节点的混沌系统作为发射系统，要发送的有用信号调制在发射系统的混沌信号中，把网络中另一个节点的混沌系统作为接收系统，利用节点间的混沌同步可在接收端恢复信道中传输的有用信号，数值仿真表明了该方案的有效性。更多还原

【Abstract】 Network is a kind of widespread phenomenon between nature and human society. It is composed by many nodes with special link. Recently, complex network has been an active research of the nonlinear subject. This new technology promises to have a significant impact on many novel engineering applications. The challenging research field has become a scientific inter-discipline involving many other fields. In this paper, my dissertation mainly focuses on the chaos synchronization of complex network and secure communication. The main content is depicted as follows:1. To the synchronization of complex network in the research background and study conditions are proceeded very full-scale introduction and summaries.2. A general introduction about classical complex network models and the dynamical behavior is presented in chapter 2, it is useful for us to understand complex network.3. Considering the three bidirectional coupled nodes in the complex network, the sufficient condition for the global synchronization and asymptotical stability based on the Lyapunov stability theorem and matrix transformation. Unlike the approaches were used in most researches, the complex network is not linearized in this paper. Both theoretical analysis and simulation result show the effectiveness and feasibility of the method.4. On the foundation of the third chapter of research complex network’s synchronization, discussed the use chaos system synchronization to carry on the security communication. A node of tree nodes is regarded as the transmitter, one other node is regarded as the receiver and digital signals are masked by coupling synchronized chaos. The modulation can be detected and accurately restored by using the synchronous chaotic signal at the receiver.更多还原