Zero-Hopf bifurcation in the FitzHugh-Nagumo system
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Data
2015-11-30
Autores
Euzébio, Rodrigo D. [UNESP]
Llibre, Jaume
Vidal, Claudio
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Resumo
We characterize the values of the parameters for which a zero-Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+, and P- in the FitzHugh-Nagumo system. We find two two-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at the origin is a zero-Hopf equilibrium. For these two families, we prove the existence of a periodic orbit bifurcating from the zero-Hopf equilibrium point O. We prove that there exist three two-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at P+ and at P- is a zero-Hopf equilibrium point. For one of these families, we prove the existence of one, two, or three periodic orbits starting at P+ and P-.
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averaging theory, FitzHugh-Nagumo system, periodic orbit, zero-Hopf bifurcation
Como citar
Mathematical Methods in the Applied Sciences, v. 38, n. 17, p. 4289-4299, 2015.