参数周期切换下logistic电路的动力学行为及其分岔分析

摘要

研究不同参数下两logistic电路之间进行周期切换时的复杂动力学行为。切换系统不仅表现为各个子系统动力特性的简单连接，而且会产生各种连接不同周期轨道的分岔，甚至导致混沌等复杂振荡行为。通过构造整体的Poincaré映射，并基于 Floquet理论，对整个切换系统进行分岔分析。研究表明，鞍结分岔和跨临界分岔将连接不动点以及各种周期1轨道，而周期轨道又可经级联倍周期分岔通往混沌。%A modified discrete-time system obtained from the standard logistic circuit with periodic parameter-switc-hing scheme is presented to explore the oscillation and bifurcation mechanism of the switching discrete-time map. Poincarémap of the whole system is defined by suitable sections and local maps.Under certain parameter condi-tions,different types of period 1 traj ectories and chaos may be observed.Meanwhile,based on the Floquet theory, it is found that turning point bifurcations and saddle-node bifurcations determined the transitions between the differ-ent types of the period 1 traj ectory,while cascading of period-doubling bifurcation may lead the system to chaotic movement.