| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain
[2] UNESP, IBILCE, Dept Matemat, BR-1505400 Sao Jose De Rio Preto, SP - Brazil
[3] Univ Bio Bio, Dept Matemat, Concepcion - Chile
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | MATHEMATICAL METHODS IN THE APPLIED SCIENCES; v. 38, n. 17, p. 4289-4299, NOV 30 2015. |
| Web of Science Citations: | 3 |
| Abstract | |
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-. Copyright (C) 2014 JohnWiley \& Sons, Ltd. (AU) | |
| FAPESP's process: | 10/18015-6 - A study for minimal sets in non-smooth systems in dimensions two and three |
| Grantee: | Rodrigo Donizete Euzébio |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 12/05635-1 - Study of families of periodic orbits and their bifurcations in differential equations of finite dimension |
| Grantee: | Rodrigo Donizete Euzébio |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |