从退化的双同宿环附近分支出周期解

数学物理学报 ›› 2025, Vol. 45 ›› Issue (5): 1729-1744.

• • 上一篇

从退化的双同宿环附近分支出周期解

龙斌^*(),刘莹

陕西科技大学数学与数据科学学院西安 10021

收稿日期:2024-11-05 修回日期:2025-04-15 出版日期:2025-10-26 发布日期:2025-10-14
通讯作者: * 龙斌,E-mail:longbin210@126.com

Periodic Solutions Bifurcated from a Degenerate Double Homoclinic Loop

Bin Long^*(),Ying Liu

School of Mathematics and Data Science, Shaanxi University of Science and Technology, xi'an 710021

Received:2024-11-05 Revised:2025-04-15 Online:2025-10-26 Published:2025-10-14

摘要/Abstract

摘要：

该文考虑了高维系统中具有双同宿环的自治微分方程在周期扰动下的分支问题. 该双同宿环由同宿于同一双曲平衡点的两条退化的同宿轨构成. 通过应用 Lin 方法推导出了相应的分支函数. 在一定条件下, 证明了该分支函数存在零点, 进而得出扰动方程在未扰动的双同宿环附近存在周期解.

关键词: Lin 方法, 指数二分性, 周期解, 分支

Abstract:

This paper investigates the bifurcation problem of autonomous differential equations with double homoclinic loops in high-dimensional systems under periodic perturbations. The double homoclinic loop consist of two degenerate homoclinic orbits connecting to the same hyperbolic equilibrium. Applying Lin's method to the double homoclinic loops, we derived the bifurcation function. Under certain conditions, the existence of zeros for these bifurcation functions is proven. Consequently, the perturbed system possesses periodic solutions near the unperturbed double homoclinic loop.

Key words: Lin's method, exponential dichotomy, periodic solutions, bifurcation

中图分类号:

O175.1

龙斌, 刘莹. 从退化的双同宿环附近分支出周期解[J]. 数学物理学报, 2025, 45(5): 1729-1744.

Bin Long, Ying Liu. Periodic Solutions Bifurcated from a Degenerate Double Homoclinic Loop[J]. Acta mathematica scientia,Series A, 2025, 45(5): 1729-1744.

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从退化的双同宿环附近分支出周期解

Periodic Solutions Bifurcated from a Degenerate Double Homoclinic Loop

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