基于符号动力学的DC/DC开关变换器“周期3即混沌”证明

Proof of “Period Three Implies Chaos” in DC/DC Switching Converter Based on Symbolic Dynamics

开关变换器与其符号序列拓扑共轭,可将符号动力学用于开关变换器系统的特性研究。对DC/DC开关变换器中的切分岔跟阵发混沌现象进行研究,用符号序列的幂次代表阵发混沌发生的周期间隔,用广义合成律从符号动力学的角度证明"周期3意味着混沌"。从一种崭新的角度出发,基于符号动力学的方法分析DC/DC开关变换器的非线性混沌特征,最后用仿真实验验证切分岔和阵发混沌的产生。

A switching converter is topologically conjugated with its symbolic sequence, which can be used to study the characteristics of a switching converter system. In this paper, the existence of tangent bifurcations and intermittent chaos in a DC/DC switching converter are studied, and the power of symbolic sequence is used to represent the periodic intervals occurring in the intermittent chaos. According to symbolic dynamics, “Period three implies chaos” is proved using the generalized composition rule. From a new point of view, the nonlinear chaos characteristics of the DC/DC switching converter are analyzed based on symbolic dynamics. Finally, simulation experiments verified the occurrence of tangent bifurcations and intermittent chaos.