二维随机耦合Logistic映射的混沌特征

Chaotic characteristics of two dimensional random coupled logistic map

摘要:

本文研究二维随机耦合Logistic映射的混沌特征.当系统的耦合系数满足两点分布时，本文从相图、Lyapunov指数的角度研究得出：当耦合系数按一定的概率在混沌和非混沌区间跳跃时，系统可按周期分岔和Hopf分岔走向混沌．特别地，系统轨道的概率密度函数揭示了系统状态的演化规律．

Abstract:

The chaotic characteristics of two dimensional random coupled logistic map are studied in this paper. The coupling coefficients of the system are considered to obey two points distribution，and the phase diagram and Lyapunov exponents are exploited to judge the system state. Numerical results show that, the system can lead to chaos based on periodic bifurcation and Hopf bifurcation when the coupling coefficients jump between the chaotic and non-chaotic regions according to certain probability. In particular, the probability density functions of the system orbits reveal the evolution of the system.