一类 Filippov 型 Faraday 模型的分岔与混沌动力学分析

数学物理学报 ›› 2025, Vol. 45 ›› Issue (5): 1616-1631.

一类 Filippov 型 Faraday 模型的分岔与混沌动力学分析

席雨杉,段霁程,陈荣三^*(),肖海军

中国地质大学 (武汉) 数学与物理学院武汉 430074

收稿日期:2024-11-20 修回日期:2025-03-20 出版日期:2025-10-26 发布日期:2025-10-14
通讯作者: * 陈荣三,E-mail:rchen@cug.edu.cn.
基金资助:
国家自然科学基金(12172340)

Sliding Bifurcation and Complex Dynamics Analysis of a Class of Filippov-Type Faraday Model

Yushan Xi,Jicheng Duan,Rongsan Chen^*(),Haijun Xiao

School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan 430074

Received:2024-11-20 Revised:2025-03-20 Online:2025-10-26 Published:2025-10-14
Supported by:
NSFC(12172340)

摘要/Abstract

摘要：

针对阈值控制策略下 Faraday 模型的稳定性及其分岔与混沌现象进行了深入分析, 建立了一类三维 Filippov 型 Faraday 模型. 运用非光滑动力系统的定性技术, 探讨了两个子系统平衡点的存在性和稳定性. 此外还研究了滑动向量场中平衡点的稳定性及分岔集, 揭示了丰富的动力学行为, 包括倍周期分岔、滑动分岔和穿越分岔等. 该研究能够广泛应用于各类发电设备和能源管理系统中, 为实现更加高效和智能的能源管理提供理论支持.

关键词: Filippov 型系统, Faraday 模型, 阈值控制策略, 滑动分岔, 混沌

Abstract:

The stability of the Faraday model and its bifurcation and chaos phenomena under the threshold control strategy are deeply analyzed, and a class of three-dimensional Filippov-type Faraday models is established. The existence and stability of the equilibrium points of the two subsystems are investigated by using the qualitative technique of nonsmooth dynamical systems. The stability of the equilibrium point and the set of bifurcations in the sliding vector field are also investigated, revealing rich dynamical behaviors including multiplicative bifurcations, sliding bifurcations, and crossing bifurcations. This study can be widely applied to various kinds of power generation equipment and energy management systems, providing theoretical support for realizing more efficient and intelligent energy management.

Key words: Filippov-type system, Faraday model, threshold control strategy, sliding bifurcation, chaos

中图分类号:

O175.14

席雨杉, 段霁程, 陈荣三, 肖海军. 一类 Filippov 型 Faraday 模型的分岔与混沌动力学分析[J]. 数学物理学报, 2025, 45(5): 1616-1631.

Yushan Xi, Jicheng Duan, Rongsan Chen, Haijun Xiao. Sliding Bifurcation and Complex Dynamics Analysis of a Class of Filippov-Type Faraday Model[J]. Acta mathematica scientia,Series A, 2025, 45(5): 1616-1631.

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