Global bifurcations of multiple limit cycles in the FitzHugh-Nagumo system

2011/04/15 by Valery A. Gaiko, Gaiko, Valery A. · 1 citation
Mathematics · #34C05 #34C07 #34C23 #37G05 #37G10 #37G15 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:34C05 #msc:34C07 #msc:34C23 #msc:37G05 #msc:37G10 #msc:37G15

paper · pdf · doi:10.48550/arxiv.1104.3019

22 pages

arxiv created 2011/04/15 · arxiv updated 2015/03/18

Abstract

In this paper, we complete the global qualitative analysis of the well-known FitzHugh-Nagumo neuronal model. In particular, studying global limit cycle bifurcations and applying the Wintner-Perko termination principle for multiple limit cycles, we prove that the corresponding dynamical system has at most two limit cycles.

Cited by

• Global bifurcations of limit cycles in a Holling-type dynamical system

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