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中国物理学会期刊

基于符号序列描述的一类分段光滑系统中分岔现象与混沌分析

CSTR: 32037.14.aps.54.1084

Analysis of bifurcation and chaos in a class of piecewise smooth systems based on symbolic sequence

CSTR: 32037.14.aps.54.1084
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  • 从拓扑序列出发,提出了描述DC/DC变换器一类分段光滑系统中的分岔现象和混沌行为的符号序列方法,根据最大子序列的性态判别分岔的类型,以及检测边界碰撞分岔的发生.例如,当发生倍周期分岔时,最大子序列保持不变;当发生边界碰撞分岔时,最大子序列发生变化;混沌态则没有最大子序列.研究表明,占空比是表征DC/DC变换器一类分段光滑系统动力学行为的一个最本质的量,“饱和非线性”是引起边界碰撞分岔产生的根本原因.

     

    Based on the sequence of circuit topologies, a symbolic sequence method is proposed for analyzing the bifurcations and chaos in a class of piecewise smooth systems like DC/DC converters. The largest subsequence(LS) is used to distinguish the type of bifurcation and detect border collision bifurcation e. g., when a perioddoubling bifurcation occurs, the LS is unchanged; when border collision bifurcation occurs, the LS is changed; and when chaos occurs,the LS does not exist.It is shown that the duty ratio is an essential variable for describing the nonlinear dynamics of a class of piecewise smooth systems like DC/DC converters, and saturating nonlinearity is the root cause of border collision bifurcation.

     

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