On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
Han, Maoan (Shanghai Normal University. Department of Mathematics (China))
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Tian, Yun (Shanghai Normal University. Department of Mathematics (China))

Date:	2020
Abstract:	Here we study the Lotka-Volterra systems in R3, i. e. the differential systems of the form dxi/dt = xi(ri - Σ3j=1 aijxj), i = 1, 2, 3. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least six periodic orbits bifurcating from one of their equilibrium points. The tool for proving this result is the averaging theory of third order.
Grants:	Ministerio de Ciencia e Innovación MDM-2014-0445 Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Lotka-Volterra polynomial differential systems ; Periodic orbit ; Hopf bifurcation ; Averaging theory
Published in:	Mathematics, Vol. 8, Issue 7 (July 2020) , art. 1137, ISSN 2227-7390

DOI: 10.3390/math8071137

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