Journal of Guangxi Normal University(Natural Science Edition) ›› 2025, Vol. 43 ›› Issue (3): 98-105.doi: 10.16088/j.issn.1001-6600.2024061401

• Mathematics and Statistics • Previous Articles     Next Articles

Singular Cycles Bifurcation Leading to Limit Cycles in 2-Dimensional Piecewise Affine Systems

ZHANG Xiaoqian, WANG Lei*   

  1. Department of Mathematics and Statistics, Hefei University, Hefei Anhui 230601, China
  • Received:2024-06-14 Revised:2024-08-19 Online:2025-05-05 Published:2025-05-14

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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.

Key words: singular cycles, bifurcation, Poincaré map, stability, piecewise affine system

CLC Number:  O175.1
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