Zero-Hopf bifurcation of a 5D hyperchaotic quadratic polynomial differential systems

A zero-Hopf equilibrium of a 5-dimensional autonomous differential system is an equilibrium point for which the Jacobian matrix of the system evaluated at that equilibrium has three zero eigenvalues and a pair of purely imaginary eigenvalues. Using the averaging theory we provide sufficient conditio...

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Detalles Bibliográficos
Autores: Diab, Zouhair, Guirao, Juan Luis Garcia|||0000-0003-2788-809X, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:318293
Acceso en línea:https://ddd.uab.cat/record/318293
https://dx.doi.org/urn:doi:10.1016/j.matcom.2025.06.021
Access Level:acceso abierto
Palabra clave:Periodic orbit
Averaging theory
Zero-Hopf bifurcation
Hyperchaotic
Polynomial differential system
Descripción
Sumario:A zero-Hopf equilibrium of a 5-dimensional autonomous differential system is an equilibrium point for which the Jacobian matrix of the system evaluated at that equilibrium has three zero eigenvalues and a pair of purely imaginary eigenvalues. Using the averaging theory we provide sufficient conditions for the existence of at least two families periodic orbits bifurcating from a zero-Hopf equilibrium point of a 5-dimensional hyperchaotic quadratic polynomial differential system studied in Diab et al. (2021). We also provide analytical expressions for the initial conditions of these two families. This zero-Hopf equilibrium point is very special because it is contained in a straight line filled with zero-Hopf equilibria.