广西师范大学学报（自然科学版）2025，Vol.43Issue(3)：98-105,8.DOI:10.16088/j.issn.1001-6600.2024061401
二维分段仿射系统奇异环分岔诱导的极限环
Singular Cycles Bifurcation Leading to Limit Cycles in 2-Dimensional Piecewise Affine Systems
摘要
Abstract
For a class of two-dimensional piecewise affine system with parameters,the existence of singular cycles is obtained by adjusting the structure of the invariant manifolds of subsystems.Then,after selecting a suitable transversal in a small neighborhood of the singular cycles,the composite Poincaré map is constructed to obtain the one-side stability of the singular cycles by the flow map generated by the subsystems,and the existence and stability of the limit cycles induced by the bifurcation of the singular cycles.Finally,two examples are given to illustrate the applications of the main results.关键词
奇异环/分岔/Poincaré映射/稳定性/分段仿射系统Key words
singular cycles/bifurcation/Poincaré map/stability/piecewise affine system分类
数理科学引用本文复制引用
张晓倩,王磊..二维分段仿射系统奇异环分岔诱导的极限环[J].广西师范大学学报（自然科学版）,2025,43(3):98-105,8.基金项目
国家自然科学基金青年项目(12302034) （12302034）
安徽省高校自然科学研究重点项目(KJ2021A0996) （KJ2021A0996）
合肥大学数学重点学科建设项目(2023xk06) （2023xk06）
