Periodic orbits in the zero-Hopf bifurcation of the Rössler system
A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi ̸= 0 and 0. For a such equilibrium there is no a general theory for knowing when from this equilibrium bifurcates a small-amplitude periodic orbit moving the parameters of the system. We provide here an algorithm for...
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| Format: | article |
| Publication Date: | 2014 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:150679 |
| Online Access: | https://ddd.uab.cat/record/150679 |
| Access Level: | Open access |
| Keyword: | Averaging theory Periodic orbit Rössler system Zero-Hopf bifurcation |
| Summary: | A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi ̸= 0 and 0. For a such equilibrium there is no a general theory for knowing when from this equilibrium bifurcates a small-amplitude periodic orbit moving the parameters of the system. We provide here an algorithm for solving this problem. In particular, first we characterize the values of the parameters for which a zero-Hopf equilibrium point takes place in the Rössler systems, and we find two one-parameter families exhibiting such equilibria. After for one of these families we prove the existence of one periodic orbit bifurcating from the zero-Hopf equilibrium. The algorithm developed for studying the zero-Hopf bifurcation of the Rössler systems can be applied to other differential system in Rn. |
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