The limit cycles of the Higgins-Selkov systems
Chen, Hebai (Central South University. School of Mathematics and Statistics (People's Republic of China))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tang, Yilei (Shanghai Jiao Tong University. School of Mathematical Sciences (People's Republic of China))

Date:	2021
Abstract:	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.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Higgins-Selkov system ; Liénard system of arbitrary degree ; Uniqueness of limit cycles ; Nonexistence of Limit cycles
Published in:	Journal of Nonlinear Science, Vol. 31, Issue 5 (October 2021) , art. 85, ISSN 1432-1467

DOI: 10.1007/s00332-021-09742-0

Postprint 20 p, 565.6 KB

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