Global bifurcations of multiple limit cycles in the FitzHugh-Nagumo system
Valery A. Gaiko
TL;DR
This paper provides a comprehensive global analysis of the FitzHugh-Nagumo model, establishing that it can have at most two limit cycles through bifurcation analysis and the Wintner-Perko principle.
Contribution
It is the first to complete the global bifurcation analysis of the FitzHugh-Nagumo system, proving an upper limit of two limit cycles.
Findings
Maximum of two limit cycles in the system
Application of Wintner-Perko termination principle
Complete global qualitative analysis achieved
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.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Nonlinear Dynamics and Pattern Formation · stochastic dynamics and bifurcation