Zero-Hopf bifurcation in the Chua's circuit
Ginoux, Jean-Marc ![ORCID Identifier](/img/uab/orcid.ico)
(Université de Toulon. Laboratoire LSIS)
Llibre, Jaume ![ORCID Identifier](/img/uab/orcid.ico)
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Date: |
2023 |
Abstract: |
An equilibrium point of a differential system in R 3 such that the eigenvalues of the Jacobian matrix of the system at the equilibrium are 0 and ±ωi with ω > 0 is called a zero-Hopf equilibrium point. First, we prove that the Chua's circuit can have three zero-Hopf equilibria varying its three parameters. Later, we show that from the zero-Hopf equilibrium point localized at the origin of coordinates can bifurcate one periodic orbit. Moreover, we provide an analytic estimation of the expression of this periodic orbit and we have determined the kind of the stability of the periodic orbit in function of the parameters of the perturbation. The tool used for proving these results is the averaging theory of second order. |
Grants: |
European Commission 777911 Agencia Estatal de Investigación PID2019-104658GB-I00
|
Note: |
Altres ajuts: acords transformatius de la UAB |
Rights: |
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Language: |
Anglès |
Document: |
Article ; recerca ; Versió publicada |
Published in: |
Journal of Mathematical Physics, Vol. 64, Issue 7 (July 2023) , art. 72701, ISSN 1089-7658 |
DOI: 10.1063/5.0137020
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Record created 2023-11-21, last modified 2024-02-27