Abstract
Copyright © 2014 John Wiley & Sons, Ltd. 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-.
| Original language | English |
|---|---|
| Pages (from-to) | 4289-4299 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 38 |
| Issue number | 17 |
| DOIs | |
| Publication status | Published - 30 Nov 2015 |
Keywords
- averaging theory
- FitzHugh-Nagumo system
- periodic orbit
- zero-Hopf bifurcation
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Euzébio, R. D., Llibre, J., & Vidal, C. (2015). Zero-Hopf bifurcation in the FitzHugh-Nagumo system. Mathematical Methods in the Applied Sciences, 38(17), 4289-4299. https://doi.org/10.1002/mma.3365