Global dynamics of the Selkov systems
Cao, Chen (Shanghai Jiao Tong University. CMA-Shanghai. School of Mathematical Sciences)
Chen, Hebai (Central South University. Hunan Research Center of the Basic Discipline for Analytical Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tang, Yilei (Shanghai Jiao Tong University. CMA-Shanghai. School of Mathematical Sciences)

Date:	2025
Abstract:	The aim of this paper is to investigate the problem of limit cycles and global dynamics for the general case of the Selkov system. By applying limit cycle theory for Liénard systems, we first transform the Selkov systems into Liénard systems. Then the theory and techniques related to limit cycles for Liénard systems can be utilized and further developed. We obtain a new criterion for the uniqueness of limit cycles in general Liénard systems. Consequently, we address the majority of parameter cases for the conjecture regarding the uniqueness of limit cycles proposed in the literature. Finally, we present the global bifurcations and dynamical structures of the system in the Poincaré disc.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Generalitat de Catalunya 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycle ; Degenerate Hopf bifurcation ; Generalized heteroclinic loop ; Selkov system ; Liénard system
Published in:	Physica D: Nonlinear Phenomena, Vol. 482 (November 2025) , art. 134894, ISSN 0167-2789

DOI: 10.1016/j.physd.2025.134894

Available from: 2027-11-30 Postprint 32 p, 1.5 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles