Degenerate Fold-Hopf Bifurcations in a Rössler-Type System
We study the Hopf and the fold--Hopf bifurcations of the R\"ossler--type differential system * =-y-z, =x ay, =-cz byz, * with b 0. We show that the classical Hopf bifurcation cannot be applied to this system for detecting the fold--Hopf bifurcation, which here is studied using the averaging the...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:182532 |
| Acceso en línea: | https://ddd.uab.cat/record/182532 https://dx.doi.org/urn:doi:10.1142/S0218127417500687 |
| Access Level: | acceso abierto |
| Palabra clave: | Averaging theory Fold-Hopf bifurcation Periodic orbit Rössler system Zero-Hopf bifurcation |
| Sumario: | We study the Hopf and the fold--Hopf bifurcations of the R\"ossler--type differential system * =-y-z, =x ay, =-cz byz, * with b 0. We show that the classical Hopf bifurcation cannot be applied to this system for detecting the fold--Hopf bifurcation, which here is studied using the averaging theory. Our results show that a Hopf bifurcation takes place at the equilibrium (-ac/b,c/b,-c/b) when c=a<0. This Hopf bifurcation becomes a fold--Hopf bifurcation when c=a=0. |
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