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Zero-Hopf bifurcation in the FitzHugh-Nagumo system
Fecha
2015-11-30Registro en:
Mathematical Methods in the Applied Sciences, v. 38, n. 17, p. 4289-4299, 2015.
1099-1476
0170-4214
10.1002/mma.3365
2-s2.0-84959321263
Autor
Universidade Estadual Paulista (Unesp)
Universitat Autònoma de Barcelona
Universidad Del Bío-Bío
Institución
Resumen
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-.