八模类Lorenz系统的全局动力学特性及数值模拟

Global dynamics characteristics and numerical simulation of eight-mode-like Lorenz system

运用Matlab中的Simulink组件,通过理论和数值模拟分析一个八模类Lorenz混沌系统的非线性特性,从对称性、耗散性、空间相图、功率谱、Poincare映射、分岔图等几个方面展示了该系统具有丰富的动力学行为。通过构造广义李雅普诺夫函数给出新的全局指数吸引集及其指数估计速率,该类系统解的界估计为其控制和同步提供理论依据,通过计算机模拟证明,数值模拟与理论计算的结果相吻合。

The nonlinear characteristic properties of eight-mode Lorenz-like chaotic system are analyzed by theoretical and numerical simulation based on Simulink in Matlab software. The rich dynamic behavior of the novel chaotic system is demonstrat-ed in the aspects of symmetry,dissipation,space phase diagram,power spectrum,Poincare mapping and bifurcation diagram. The globally exponential attractive set and its exponential estimation rate are given via constructing the generalized Lyapunov function. The boundedness obtained in this paper provides the theoretic foundation for chaotic control and chaotic synchroniza-tion of the system. Numerical simulation results show the effectiveness of the proposed scheme,and is consistent with the results of theoretical calculation.