Flip and Hopf Bifurcations of Discrete-Time Fitzhugh-Nagumo Model

Qamar Din, Sadaf Khaliq
2018 Open Journal of Mathematical Sciences  
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
more » ... sting numerical examples are presented. Mathematics Subject Classification: 39A30, 40A05, 92D25, 92C50.
doi:10.30538/oms2018.0029 fatcat:xfyjqtqbh5eihajy7eobex2rdi