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...
| Autores: | , , |
|---|---|
| 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 |
| 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. |
|---|