一类四维非光滑系统的同宿环和异宿环定性分析
Qualitative Analysis of Homoclinic and Heteroclinic Orbits in a Class of Non-Smooth Four-Dimensional Systems
DOI: 10.12677/aam.2025.141025, PDF,    科研立项经费支持
作者: 王艺颖, 刘佳玮*, 李峥嵘, 郑依平, 任昊宇：河北经贸大学统计与数学学院，河北 石家庄
关键词: 同宿环；异宿环；混沌；非光滑动力系统；Homoclinic Cycle； Heteroclinic Cycle； Chaos； Non-Smooth Dynamical System
摘要: 由于高维非光滑系统的复杂性，准确预测其同宿环和异宿环极其困难。本文针对一类四维非光滑动力系统，分别提出了能够精确检测同宿环和异宿环的判据，并利用数学分析和定性理论对其进行了严格证明。此外，本文还建立了此类特殊环诱导系统混沌的存在条件。最后，通过数值算例验证了结果的有效性。
Abstract: Due to the complexity of high-dimensional non-smooth systems, accurately predicting homoclinic cycles or heteroclinic cycles is extremely difficult. This paper proposes some criterion for precisely detecting homoclinic cycles and heteroclinic cycles in a kind of four-dimensional non-smooth dynamical systems, respectively. By combining mathematical analysis with qualitative theory, this work presents a rigourous proof of that. Further, it establishes existence conditions of chaos induced by such special cycles in the considered system. Finally, the numerical simulation for two designed examples is offered to test the validity of obtained results.
文章引用：王艺颖, 刘佳玮, 李峥嵘, 郑依平, 任昊宇. 一类四维非光滑系统的同宿环和异宿环定性分析[J]. 应用数学进展, 2025, 14(1): 217-232. https://doi.org/10.12677/aam.2025.141025

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