一个非线性系统的混沌现象分析及数值仿真
Chaos Analysis and Numerical Simulation of a Nonlinear System
摘要: 本文讨论了一个根据Liu系统变化而来的非线性系统，分析其混沌现象并进行数值仿真。讨论了系统的对称性、耗散性、奇点及其局部稳定性，说明了系统的全局稳定性和吸引子的存在性。结合不同参数变化下的分岔图与最大李雅普诺夫指数分析了系统发生混沌的区间，根据不同参数下的吸引子、庞加莱截面、时间序列和返回映射等指标，描述系统的混沌特性。通过仿真的结果说明此非线性系统混沌行为的普适性。
Abstract:
In this paper, a nonlinear system based on the change of Liu system is discussed, and its chaos is analyzed and simulated. The symmetries, dissipations, singularities and local stability of the system are discussed. The global stability and the existence of attractors are explained. According to the different parameters of the attractor, Poincare section, time series and return map, the chaotic characteristics of the system are described. The simulation results show that the chaotic behavior of the nonlinear system is universal.
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