On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3

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...

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Detalles Bibliográficos
Autores: Han, Maoan, Llibre, Jaume|||0000-0002-9511-5999, Tian, Yun
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:232162
Acceso en línea:https://ddd.uab.cat/record/232162
https://dx.doi.org/urn:doi:10.3390/math8071137
Access Level:acceso abierto
Palabra clave:Lotka-Volterra polynomial differential systems
Periodic orbit
Hopf bifurcation
Averaging theory
Descripción
Sumario: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.