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

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

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-...

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Bibliographic Details
Main Authors: Qamar Din, Sadaf Khaliq
Format: Article
Language:English
Published: Ptolemy Scientific Research Press 2018-08-01
Series:Open Journal of Mathematical Sciences
Subjects:
Fitzhugh-Nagumo model; Flip bifurcation; Hopf bifurcation.
Online Access:https://openmathscience.com/flip-and-hopf-bifurcations-of-discrete-time-fitzhugh-nagumo-model-2/
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spelling doaj-186b001f076043968299377a649da60c2020-11-25T02:15:10ZengPtolemy Scientific Research PressOpen Journal of Mathematical Sciences2616-49062523-02122018-08-012120922010.30538/oms2018.0029Flip and Hopf Bifurcations of Discrete-Time Fitzhugh-Nagumo ModelQamar Din0Sadaf Khaliq1Department of Mathematics, The University of Poonch Rawalakot, Pakistan.Department of Mathematics, The University of Poonch Rawalakot, Pakistan.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.https://openmathscience.com/flip-and-hopf-bifurcations-of-discrete-time-fitzhugh-nagumo-model-2/Fitzhugh-Nagumo model; Flip bifurcation; Hopf bifurcation.
collection DOAJ
language English
format Article
sources DOAJ
author Qamar Din
Sadaf Khaliq
spellingShingle Qamar Din
Sadaf Khaliq
Flip and Hopf Bifurcations of Discrete-Time Fitzhugh-Nagumo Model
Open Journal of Mathematical Sciences
Fitzhugh-Nagumo model; Flip bifurcation; Hopf bifurcation.
author_facet Qamar Din
Sadaf Khaliq
author_sort Qamar Din
title Flip and Hopf Bifurcations of Discrete-Time Fitzhugh-Nagumo Model
title_short Flip and Hopf Bifurcations of Discrete-Time Fitzhugh-Nagumo Model
title_full Flip and Hopf Bifurcations of Discrete-Time Fitzhugh-Nagumo Model
title_fullStr Flip and Hopf Bifurcations of Discrete-Time Fitzhugh-Nagumo Model
title_full_unstemmed Flip and Hopf Bifurcations of Discrete-Time Fitzhugh-Nagumo Model
title_sort flip and hopf bifurcations of discrete-time fitzhugh-nagumo model
publisher Ptolemy Scientific Research Press
series Open Journal of Mathematical Sciences
issn 2616-4906
2523-0212
publishDate 2018-08-01
description 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.
topic Fitzhugh-Nagumo model; Flip bifurcation; Hopf bifurcation.
url https://openmathscience.com/flip-and-hopf-bifurcations-of-discrete-time-fitzhugh-nagumo-model-2/
work_keys_str_mv AT qamardin flipandhopfbifurcationsofdiscretetimefitzhughnagumomodel
AT sadafkhaliq flipandhopfbifurcationsofdiscretetimefitzhughnagumomodel
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