Hopf Bifurcation Analysis of a Chaotic System
This paper is devoted to studying the stability of the unique equilibrium point and the occurrence of the Hopf bifurcation as well as limit cycles of a three-dimensional chaotic system. We characterize the parameters for which a Hopf equilibrium point takes place at the equilibrium point. In additio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Salahaddin University-Erbil
2022-12-01
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| Series: | Zanco Journal of Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://zancojournal.su.edu.krd/index.php/JPAS/article/view/1255 |
| Summary: | This paper is devoted to studying the stability of the unique equilibrium point and the occurrence of the Hopf bifurcation as well as limit cycles of a three-dimensional chaotic system. We characterize the parameters for which a Hopf equilibrium point takes place at the equilibrium point. In addition, the system has only one equilibrium point which is . It was proved that is asymptotically stable and unstable when and , respectively. Moreover, for studying the cyclicity of the system, two techniques are used which are dynamics on the center manifold and Liapunov quantities. It was shown that at most two limit cycles can be bifurcated from the origin. All the results presented in this paper have been verified by a program via Maple software. |
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| ISSN: | 2218-0230 2412-3986 |