二维调制耦合系统的动力学分析

Dynamical Analysis of Two Dimensional Modulated Coupled System

为进一步研究混沌系统特性,使用指数Logistic映射对传统Logistic映射进行调制,得到一个具有良好混沌性能的二维调制耦合系统。通过Lyapunov指数、分岔图分析了系统受参数影响的动力学特性,仿真结果表明,该系统可按照倍周期分岔和Hopf分岔进入混沌。通过相图、频数检验、平衡度和分岔图分析发现,与其他调制混沌系统相比,系统具有良好的遍历性和随机性,产生的混沌区域更大。

In order to further study the characteristics of chaotic system,this paper uses exponential Logistic map to modulate the traditional Logistic map,and obtains a two-dimensional modulation coupled system with good chaotic performance.The influence of parameters on the dynamic characteristics of the system is introduced by Lyapunov exponent,bifurcation diagram.The simulation results reveal the chaotic patterns of the system will emerge out of double-periodic bifurcation and Hopf bifurcation respectively.Through the phase diagram,frequency test,balance degree and bifurcation diagram analysis,the proposed system has better ergodicity,better randomness and larger chaotic region than those of other modulation chaotic systems.