Logistic电路在参数周期切换下的动力学行为分析

Oscillations and Bifurcation Mechanisms of Logistic Circuit with Periodic Switching Scheme

根据周期切换律建立了logistic参数切换模型。指出了离散切换系统会呈现出具有各个子系统动力特性组合振荡模式,同时整个系统还会产生各种分岔,并通过不同的分岔模式连接各种周期轨道甚至使得整个系统进入混沌振荡模式。分析表明,鞍结分岔和跨临界分岔将使得不动点以及不同类型的周期1振荡之间转迁,而周期1振荡可经级联倍周期分岔通往混沌振荡,同时混沌振荡又可经由鞍结分岔直接演化为周期1振荡。

Based on the periodic parameter- switching scheme,a switched logistic circuit is established,pointing out that the discrete switched systems will exhibit dynamic characteristics of each subsystem with a combination of oscillation modes. The combined movement and the trajectory of which can be divided into parts which were determined by the subsystems. Study shows that the turning point and saddle- node bifurcations determined the transitions between the fixed point and the different types of the period 1 oscillations,while cascading of period- doubling bifurcation may lead the system to chaotic movement and the saddle- node bifurcation may cause the chaos to period 1 oscillation.