Chaotic oscillations in singularly perturbed FitzHugh-Nagumo systems
Chaotic Dynamics
2013-12-10 v2
Abstract
We consider the singularly perturbed limit of periodically excited two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such systems are essentially governed by an one-dimensional map and present a numerical scheme to accurately compute it together with its Lyapunov exponent. We then investigate the occurrence of chaos by varying the parameters of the system, with especial emphasis on the simplest possible chaotic oscillations. Our results corroborate and complement some recent works on bifurcations and routes to chaos in certain particular cases corresponding to piecewise linear FitzHugh-Nagumo-like systems.
Keywords
Cite
@article{arxiv.1306.3428,
title = {Chaotic oscillations in singularly perturbed FitzHugh-Nagumo systems},
author = {Peterson T. C. Barbosa and Alberto Saa},
journal= {arXiv preprint arXiv:1306.3428},
year = {2013}
}
Comments
16 pages, 6 figures, final version to appear in Chaos, Solitons & Fractals