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-...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Ptolemy Scientific Research Press
2018-08-01
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| Series: | Open Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://openmathscience.com/flip-and-hopf-bifurcations-of-discrete-time-fitzhugh-nagumo-model-2/ |
| Summary: | 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. |
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| ISSN: | 2616-4906 2523-0212 |