一类三维保守系统中的同宿轨异宿环和混沌
Homoclinic Orbits, Heteroclinic Cycle and Chaos in a Three-Dimensional Conservative System
DOI: 10.12677/aam.2025.144219, PDF,    国家自然科学基金支持
作者: 杨 廷, 蔡 玥*：江西财经大学信息管理与数学学院，江西 南昌；路 凯：长江大学信息与数学学院，湖北 荆州
关键词: 同宿轨；异宿环；混沌；共存轨道；Homoclinic Orbit； Heteroclinic Cycle； Chaos； Coexisting Orbit
摘要: 本文研究了一个三维保守系统的同宿轨、异宿环和混沌。当系统有一条平衡点曲线时，我们得到连接原点的两条同宿轨并且给出了解析表达式。在另一条件下，我们发现系统存在一个异宿环，并且给出了解析表达式。当系统有无穷多孤立平衡点时，我们分析了这些平衡点的稳定性，发现系统具有暂态混沌现象。此外，系统展示了一些共存的轨道，包括混沌和周期轨共存，拟周期轨和周期轨共存，混沌和拟周期轨共存。
Abstract: This paper investigates the homoclinic orbits, heteroclinic cycle and chaos in a three-dimensional conservative system. First, if the system has a curve of equilibria, we get two homoclinic orbits associating with the origin and give the analytical expression. Under another condition, the system has a heteroclinic cycle and the analytical expression is also given. Second, if the system has infinitely many isolated equilibria, we analyse the stabilities of the equilibria. In this case, we find that the system could show transient chaos phenomenon. Moreover, several coexisting orbits are found in the system, including coexisting chaotic orbit and periodic orbits, coexisting quasi-periodic orbits and periodic orbits, coexisting chaotic orbit and quasi-periodic orbits.
文章引用：杨廷, 蔡玥, 路凯. 一类三维保守系统中的同宿轨异宿环和混沌[J]. 应用数学进展, 2025, 14(4): 954-967. https://doi.org/10.12677/aam.2025.144219

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