周期脉冲作用下Logistic映射的复杂动力学行为及其分岔分析  

Bifurcation analysis of complex behavior in the Logistic map via periodic impulsive force

作　　者：姜海波[1] 李涛[1] 曾小亮[1] 张丽萍[1] 

机构地区：[1]盐城师范学院数学科学学院,盐城224002

出　　处：《物理学报》2013年第12期89-97,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11202180;61273106;11171290);江苏省自然科学基金(批准号:BK2010292;BK2010293);江苏省高校自然科学基金(批准号:10KJB510026);国家级大学生创新创业训练计划(批准号:201210324009);江苏省大学生实践创新训练计划(批准号:2012JSSPITP2378)~~

摘　　要：研究了两种周期脉冲作用下Logistic映射的复杂动力学行为.随着参数的变化,该系统产生平衡解、周期解、混沌等现象,且该系统可经级联倍周期分岔到达混沌.通过构造Poincar映射,对周期脉冲作用下Logistic映射进行了分岔分析.最后基于Floquet理论揭示了该系统周期解的分岔机理.The complex dynamics of the Logistic map via two types of periodic impulsive forces is investigated in this paper. With the parameter varying, the system produces the phenomenon such as equilibrium solutions, periodic solutions, and chaotic solutions. Furthermore the system can evolve into chaos by a cascading of period-doubling bifurcations. The Poincar6 map of the Logistic map via periodic impulsive force is constructed and its bifurcation is analyzed. Finally, the Floquet theory is used to explore the bifurcation mechanism for the periodic solutions.

关 键 词：LOGISTIC映射 脉冲 周期解 分岔机理 

分 类 号：O415.5[理学—理论物理] O175.7[理学—物理]