On the limit cycles of a quartic model for Evolutionary Stable Strategies
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gouveia, Luiz Fernando (Universidade Estadual de Campinas)
Santana, Paulo Henrique Reis (Universidade Estadual Paulista "Júlio de Mesquita Filho")

Date:	2025
Abstract:	This paper studies the number of centers and limit cycles of the family of planar quartic polynomial vector fields that has the invariant algebraic curve (4x2 - 1)(4y2 - 1) = 0. The main interest for this type of vector fields comes from their appearance in some mathematical models in Game Theory composed by two players. In particular, we find examples with five nested limit cycles surrounding the same singularity, as well as examples with four limit cycles formed by two disjoint nests, each one of them with two limit cycles. We also prove a Berlinski˘ ı's type result for this family of vector fields.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
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 cycles ; Evolutionary Stable Strategies ; Center-focus ; Cyclicity ; Berlinski˘ı's Theorem
Published in:	Nonlinear Analysis: Real World Applications, Vol. 84 (August 2025) , art. 104313, ISSN 1468-1218

DOI: 10.1016/j.nonrwa.2024.104313

Available from: 2027-08-31 Postprint

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles