The limit cycles of the Higgins-Selkov systems

In this paper, we investigate the problem of limit cycles for general Higgins-Selkov systems with degree n+ 1. In particular, we first prove the uniqueness of limit cycles for a general Liénard system, which allows for discontinuity. Then, by changing the Higgins-Selkov systems into Liénard systems,...

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Detalles Bibliográficos
Autores: Chen, Hebai, Llibre, Jaume|||0000-0002-9511-5999, Tang, Yilei
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:259915
Acceso en línea:https://ddd.uab.cat/record/259915
https://dx.doi.org/urn:doi:10.1007/s00332-021-09742-0
Access Level:acceso abierto
Palabra clave:Higgins-Selkov system
Liénard system of arbitrary degree
Uniqueness of limit cycles
Nonexistence of Limit cycles
Descripción
Sumario:In this paper, we investigate the problem of limit cycles for general Higgins-Selkov systems with degree n+ 1. In particular, we first prove the uniqueness of limit cycles for a general Liénard system, which allows for discontinuity. Then, by changing the Higgins-Selkov systems into Liénard systems, theorems and some techniques for Liénard systems can be applied. After, we prove the nonexistence of limit cycles if the bifurcation parameter is outside an open interval. Finally, we complete the analysis of limit cycles for the Higgins-Selkov systems showing its uniqueness.