对零碎非线性动态系统进行切换诱导的分支分析:一种半分析方法
Kai Jiang1, Jianzhe Huang1, Xilin Fu2
1School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China.
Chaos (Woodbury, N.Y.)
|July 23, 2025
概括
这项研究引入了一种新的半分析框架,以完全分析零碎的非线性动态系统. 它可以发现隐藏的分叉路线和复杂的动态,在系统中切换行为.
科学领域:
- 非线性动力学和控制系统
- 混沌理论和分叉分析
- 电路理论和电子系统
背景情况:
- 零碎的非线性动态系统由于在不连续边界的矢量场变化而表现出独特的行为.
- 在稳定状态反应中,暂时的动态持续存在,使分析复杂化,并阻碍了隐藏的分叉路线的识别.
- 现有的分析方法难以捕捉这些系统中的全部动态,包括短暂的组件.
研究的目的:
- 开发一个全面的框架来分析零碎的非线性动态系统.
- 系统地描述流量切换动态,发现隐藏的分支路径.
- 为了能够完全分析由流量切换引起的非常规分叉.
主要方法:
- 一个半分析框架,整合了一般化映射结构和局部奇点理论.
- 在切换点开发一种通用的映射形式主义,在切换点上具有封闭形式的约束条件.
- 有更高阶奇点的周期运动的参数化.
主要成果:
- 拟议的框架有效地描述了不连续边界的流转动态.
- 可以获得部分非线性动态系统的完整分支树.
- 对一块非线性memristor电路的分析揭示了复杂的分叉和混乱的行为.
结论:
- 开发的半分析框架提供了一种系统的方法来分析碎片式非线性系统中的复杂动态.
- 这种方法有助于发现以前无法访问的不稳定隐藏的分叉路口.
- 该方法具有多功能性,适用于广泛的零件式非线性系统,包括memristor电路.
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