Small Amplitude Periodic Orbits in Three-Dimensional Quadratic Vector Fields with a Zero-Hopf Singularity
We consider some families of three-dimensional quadratic vector fields having a fixed zeroHopf equilibrium.We are interested in the bifurcation of periodic ν-orbits from the singularity, that is, those small amplitude orbits that make a fixed arbitrary number ν of revolutions about a rotation axis a...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/84117 |
| Acceso en línea: | https://doi.org/10.1007/s10884-022-10208-4 http://hdl.handle.net/10459.1/84117 |
| Access Level: | acceso abierto |
| Palabra clave: | Zero-Hopf singularity Periodic orbits Poincaré map ν-cyclicity |
| Sumario: | We consider some families of three-dimensional quadratic vector fields having a fixed zeroHopf equilibrium.We are interested in the bifurcation of periodic ν-orbits from the singularity, that is, those small amplitude orbits that make a fixed arbitrary number ν of revolutions about a rotation axis and then returns to the initial point closing the orbit. When the parameters of the family are restricted to certain explicitly computable open semi-algebraic sets , we characterize those parameters that give rise to the appearance of local two-dimensional periodic invariant manifolds through the singularity. Also we use a Bautin-type analysis to study the maximum number of small-amplitude ν-limit cycles that can be made to bifurcate from the equilibrium when the parameters of the family are restricted to . We obtain global upper bounds on the number of bifurcated ν-limit cycles. |
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