自治分段线性振荡系统的离散映射数值建模与稳定性分析

为研究自治分段线性振荡系统中出现的分叉及混沌动力学行为，系统建模及稳定性分析是一种必不可少的分析手段. 本文通过构造周期内离散映射解析模型，并结合边界条件的动态数值求解，提出了一种动态离散映射数值建模方法，进而推导了用以判定系统周期闭轨稳定性的Jacobian 矩阵求解模型. 最后，本文以电力电子系统中一种常用的5 维软开关逆变自治振荡电路作为实例，通过模型仿真观察到频率的分叉现象，并根据Jacobian 矩阵的特征乘数对系统的稳定性进行了研究. 基于该模型的仿真分析结果与实验系统中所观察到的现象一致，从而验证了该方法的有效性.

Study on Discrete Time Mapping Modeling and Stability Analysis for Piecewise Autonomous Oscillation Systems

System modeling and local stability analysis of equilibrium points are indispensable for analysis of bifurcation and chaos behaviors observed in piecewise autonomous oscillation system. This paper presents a novel dynamic discrete mapping modeling method and local stability criterion of equilibrium points. This modeling method sets up discrete mapping model and boundary equations in analytic form respectively. With the aid of Newton-Raphson algorithm, the boundary equations can be solved dynamically. Combining the mapping model with boundary dynamic solutions, this mapping model can fulfill the requirements of fast-scale bifurcation analysis. To verify this modeling method, an autonomous oscillation circuit used in power electronics soft switched converter is constructed. A frequency bifurcation phenomenon is captured in both simulation results and experiment system. The analysis results of this bifurcation phenomena show consistency between model simulation and experiment system.