一类3D分片非线性系统的异宿环
Heterocilinic Cycle of a Class of 3D Piecewise Nonlinear Systems
DOI: 10.12677/PM.2021.111010, PDF,    国家自然科学基金支持
作者: 吴宝龙, 杨启贵：华南理工大学数学学院，广东 广州
关键词: 分片非线性系统；不变流形；异宿环；Piecewise Nonlinear System； Invariant Manifold； Heterocilinic Cycle
摘要: 本文研究了一类具有两个鞍–焦点和一个不连续边界的3D分片非线性系统。通过恰当的变换确定了子系统的稳定流形和不稳定流形。基于稳定流形和不稳定流形建立了系统存在横截穿过切换面两次的异宿环的充分条件，并运用了一个数值实例验证结果的正确性。
Abstract: In this paper, one studies a class of 3D piecewise nonlinear systems with two saddle foci and one discontinuous boundary. The stable manifold and unstable manifold of the subsystem are deter-mined by coordinate transformation. Based on stable manifolds and unstable manifolds, the suffi-cient conditions for the existence of heteroclinic loops which cross the switching surface twice are given. Finally, a numerical example is given to verify the correctness of the theorem.
文章引用：吴宝龙, 杨启贵. 一类3D分片非线性系统的异宿环[J]. 理论数学, 2021, 11(1): 62-73. https://doi.org/10.12677/PM.2021.111010

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