Duffing-WS型小世界网络的混沌行为

Chaotic behaviors of the Duffing-WS small world network

摘要:

近年来，复杂网络逐渐成为非线性动力系统研究的一个热点. 对复杂网络混沌行为的产生机制及其对系统参数的依赖性进行研究，可以为复杂网络的混沌控制提供理论基础. 本文研究了一种新的Duffing-WS型小世界网络的混沌行为. 本文首先利用变分法推导了系统的最大李雅普诺夫指数，并将其作为混沌判据讨论了系统的混沌行为对其参数的依赖. 结果显示，该网络具有比单个Duffing方程复杂得多的混沌行为.

Abstract:

Recently, chaotic behavior of complex network becomes a hot topic of nonlinear dynamical system. The emergence and parameter dependence of the chaotic behaviors are theoretical basis of the chaotic control of complex network. In this paper, we consider a new type of Duffing-WS type small world network. Firstly, we derive an expression for the maximum Lyapunov index by using the variational method. Then we investigate the emergence of chaos by using the Lyapunov index as criterion. Finally, the dependence of the chaotic behaviors on the system parameters is discussed. It is shown that this network processes much more complicated chaotic behaviors than the classic Duffing equation.