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

Qamar Din | Zendy; Sadaf Khaliq | Zendy

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

Author(s) -

Qamar Din,

Sadaf Khaliq

Publication year - 2018

Publication title -

open journal of mathematical sciences

Language(s) - English

Resource type - Journals

eISSN - 2616-4906

pISSN - 2523-0212

DOI - 10.30538/oms2018.0029

Subject(s) - discrete time and continuous time , hopf bifurcation , bifurcation , parametric statistics , mathematics , stability (learning theory) , euler's formula , period doubling bifurcation , steady state (chemistry) , euler method , statistical physics , control theory (sociology) , mathematical analysis , physics , computer science , nonlinear system , statistics , quantum mechanics , chemistry , control (management) , machine learning , artificial intelligence

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. Mathematics Subject Classification: 39A30, 40A05, 92D25, 92C50.

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