Three nested limit cycles in discontinuous piecewise linear differential systems with two zones

In this paper we study a planar piecewise linear differential system formed by two regions separated by a straight line so that one system has a real unstable focus and the other a virtual stable focus which coincides with the real one. This system was introduced by S.-M. Huan and X.-S. Yang in [8]...

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Detalhes bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Ponce, Enrique|||0000-0003-0467-5032
Tipo de documento: artigo
Data de publicação:2012
País:España
Recursos:Universitat Autònoma de Barcelona
Repositório:Dipòsit Digital de Documents de la UAB
Idioma:inglês
OAI Identifier:oai:ddd.uab.cat:150531
Acesso em linha:https://ddd.uab.cat/record/150531
Access Level:Acceso aberto
Palavra-chave:Non-smooth differential system
Limit cycle
Piecewise linear differential system
Descrição
Resumo:In this paper we study a planar piecewise linear differential system formed by two regions separated by a straight line so that one system has a real unstable focus and the other a virtual stable focus which coincides with the real one. This system was introduced by S.-M. Huan and X.-S. Yang in [8] who numerically showed that it can exhibit 3 limit cycles surrounding the real focus. This is the first example that a non-smooth piecewise linear differential system with two zones can have 3 limit cycles surrounding a unique equilibrium. We provide a rigorous proof of this numerical result.