Article info.

ABSTRACT

Received 21 Feb 2017
Revised 21 Jun 2017

Accepted 30 Mar 2018

In this article, a class of FitzHugh-Nagumo model is studied. First, all necessary conditions for the parameters of system are found in order to have one stable fixed point which presents the resting state for this famous model. After that, using the Hopf’s theorem proofs analytically the existence of a Hopf bifurcation, that is a critical point where a system’s stability switches and a periodic solution arises. More precisely, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues cross the complex plane imaginary axis. Moreover, with the suitable assumptions for the dynamical system, a small-amplitude limit cycle branches from the fixed point.

Keywords

FitzHugh-Nagumo model, fixed point, Hopf bifurcation, limit cycle

Cited as: Em, P.V.L., 2018. A study of fixed points and Hopf bifurcation of Fitzhugh-Nagumo model. Can Tho University Journal of Science. 54(2): 112-121.