Existence and Uniqueness of Limit Cycle in Discontinuous Planar Differential Systems

• Fangfang Jiang ^[1] ; Jitao Sun ^[1]
  1. [1] Tongji University

     Tongji University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 15, Nº 1, 2016, págs. 67-80
• Idioma: inglés
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• Resumen

  • In this paper, we investigate the existence and uniqueness of limit cycle for a class of discontinuous planar piecewise smooth differential systems with four regions separated by three vertical parallel lines. We first show the continuity and qualitative properties of half Poincaré mappings, and then by some analysis techniques we provide several criteria concerning the existence, uniqueness and stability of limit cycle for the discontinuous planar differential system. Finally, an example possessing a unique stable sliding limit cycle is presented to illustrate the obtained result.