On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center
Llibre, Jaume ![Identificador ORCID](/img/uab/orcid.ico)
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Salhi, Tayeb ![Identificador ORCID](/img/uab/orcid.ico)
(University Mohamed El Bachir El Ibrahimi. Department of Mathematics (Algeria))
Data: |
2022 |
Resum: |
While the limit cycles of the discontinuous piecewise differential systems formed by two linear differential systems separated by one straight line have been studied intensively, and up to now there are examples of these systems with at most 3 limit cycles. There are almost no works studying the limit cycles of the discontinuous piecewise differential systems formed by one linear differential system and a quadratic polynomial differential system separated by one straight line. In this paper using the averaging theory up to seven order we prove that the discontinuous piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center separated by one straight line can have 8 limit cycles. More precisely, at every order of the averaging theory from order one to order seven we provide the maximum number of limit cycles that can be obtained using the averaging theory. |
Ajuts: |
Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911
|
Drets: |
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Llengua: |
Anglès |
Document: |
Article ; recerca ; Versió acceptada per publicar |
Matèria: |
Linear focus ;
Linear center ;
Quadratic weak focus ;
Quadratic center ;
Limit cycle ;
Discontinuous piecewise differential system |
Publicat a: |
Chaos, solitons and fractals, Vol. 160 (July 2022) , art. 112256, ISSN 0960-0779 |
DOI: 10.1016/j.chaos.2022.112256
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Registre creat el 2022-11-02, darrera modificació el 2024-08-01