二维随机耦合Logistic映射的混沌特征  

Chaotic characteristics of two dimensional random coupled Logistic map

作　　者：余文慧 高仕龙[2,3] YU Wen-Hui;GAO Shi-Long(College of Science,Xihua University,Chengdu 610039,China;College of Mathematics and Information Science,Leshan Normal University,Leshan 614000,China;Research Centre of Applied Mathematics,Leshan Normal University,Leshan 614000,China)

机构地区：[1]西华大学理学院,成都610039 [2]乐山师范学院数学与信息科学学院,乐山614000 [3]乐山师范学院应用数学研究中心,乐山614000

出　　处：《四川大学学报（自然科学版）》2019年第4期581-587,共7页Journal of Sichuan University(Natural Science Edition)

基　　金：四川科技计划(2018JY0256);四川省教育厅科研项目(16TD0029)

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.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.

关 键 词：二维LOGISTIC映射 混沌 LYAPUNOV指数 两点分布 

分 类 号：O29[理学—应用数学]