Flip and Hopf Bifurcations of Discrete-Time Fitzhugh-Nagumo Model
OMS-Vol. 2 (2018), Issue 1, pp. 209–220 Open Access Full-Text PDF
Qamar Din, Sadaf Khaliq
Abstract:In this paper, dynamics of a two-dimensional Fitzhugh-Nagumo model is discussed. The discrete-time model is obtained with the implementation of forward Euler’s scheme. We present the parametric conditions for local asymptotic stability of steady-states. It is shown that the two-dimensional discrete-time model undergoes period-doubling bifurcation and Neimark-Sacker bifurcation at its positive steady-state. Furthermore, in order to illustrate theoretical discussion some interesting numerical examples are presented.