Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 1053-1065.

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Study on Periodic Solutions of a Class of Continuous and Discontinuous Piece-Wise Linear Systems

Jing Yang1,Changcheng Ke1,Zhouchao Wei1,2,*()   

  1. 1 School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan 430074
    2 Zhejiang Research Institute, China University of Geosciences(Wuhan), Hangzhou 311305
  • Received:2019-09-14 Online:2021-08-26 Published:2021-08-09
  • Contact: Zhouchao Wei
  • Supported by:
    the NSFC(11772306);the NSF of Zhejiang Province(LY20A020001)


In recent years, the study of non-smooth systems has become a hot spot, and the qualitative analysis of piece-wise linear systems has become an indispensable research problem. In this paper, a transformed Michelson differential system is studied, and the existence of periodic solutions for continuous and discontinuous piece-wise linear systems is proved by means of average theory.

Key words: Continuous piece-wise linear differential system, Discontinuous piece-wise linear differential system, Periodic solution, Average theory

CLC Number: 

  • O175