Zero-Hopf bifurcations in three-dimensional chaotic systems with one stable equilibrium
In (Molaie et al., Int J Bifurcat Chaos 23 (2013) 1350188) the authors provided the expressions of twenty three quadratic differential systems in R3 with the unusual feature of having chaotic dynamics coexisting with one stable equilibrium point. In this paper we consider twenty three classes of qua...
| Autores: | , , |
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| 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:236665 |
| Acceso en línea: | https://ddd.uab.cat/record/236665 https://dx.doi.org/urn:doi:10.1142/S0218127420501898 |
| Access Level: | acceso abierto |
| Palabra clave: | Zero-Hopf bifurcation Periodic orbits Period-doubling route to chaos Hidden chaotic attractors |
| Sumario: | In (Molaie et al., Int J Bifurcat Chaos 23 (2013) 1350188) the authors provided the expressions of twenty three quadratic differential systems in R3 with the unusual feature of having chaotic dynamics coexisting with one stable equilibrium point. In this paper we consider twenty three classes of quadratic differential systems in R3 depending on a real parameter a which, for a = 1, coincide with the differential systems given by Molaie et al. We study the dynamics and bifurcations of these classes of differential systems by varying the parameter value a. We prove that, for a = 0 all the twenty three considered systems have a zero-Hopf equilibrium point located at the origin. For a > 0 small enough, three periodic orbits bifurcate from the origin: one of them unstable and the other two forming a pair of saddle type periodic orbits. Furthermore, we show numerically that the hidden chaotic attractors which exist for these systems when a = 1 (already described by Molaie et al.) are obtained by period-doubling route to chaos. |
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