基于Kolmogorov熵的新三维混沌系统动力学分析

Dynamical Analysis of a New Three-dimensional Chaotic Systems Based on the Kolmogorov Theory

提出了一个利用正弦纠缠函数方法构造的新三维混沌系统,基本的原理是纠缠2个或多个稳定的线性子系统,形成人为的混沌系统.对该系统耗散性、吸引子的存在性、平衡点的稳定性、Hopf分岔特性进行了研究,同时利用Kolmogorov熵的理论,通过计算机辅助软件,分析了不同参数对系统的影响,根据不同长度的参数空间,计算得到了与理论一致的正的常量Kolmogorov熵,证明了系统的混沌状态.

A new chaotic system was proposed by sine entanglement function.The basic principle is to entangle two or multiple stable linear subsystems by entanglement functions to form an artificial chaotic system such that each of them evolves in a chaotic manner.The dynamics,the existence and stability of Hopf bifurcation and the dynamic characteristics of the system was discussed.The effects of different parameter variation on dynamic behavior of the system were investigated through Kolmogorov entropy theory and numerical simulations.And we computed the Kolmogorov entropy under the different value of the phase space＇s length.The results show that the Kolmogorov entropy of the system is a positive constant and the state of the system is chaos.