The FitzHugh-Nagumo Model Described by Fractional Difference Equations: Stability and Numerical Simulation

被引：9

作者：

Hamadneh, Tareq ^{[1
]}

Hioual, Amel ^{[2
]}

Alsayyed, Omar ^{[3
]}

Al-Khassawneh, Yazan Alaya ^{[4
]}

Al-Husban, Abdallah ^{[5
]}

Ouannas, Adel ^{[6
]}

机构：

[1] Al Zaytoonah Univ Jordan, Fac Sci, Dept Math, Amman 11733, Jordan

[2] Univ Oum EL Bouaghi, Lab Dynam Syst & Control, Oum El Bouaghi 04000, Algeria

[3] Hashemite Univ, Fac Sci, Dept Math, POB 330127, Zarqa 13133, Jordan

[4] Zarqa Univ, Data Sci & Artificial Intelligence Dept, Zarqa 13110, Jordan

[5] Irbid Natl Univ, Fac Sci & Technol, Dept Math, Irbid 21110, Jordan

[6] Univ Oum EL Bouaghi, Dept Math & Comp Sci, Oum El Bouaghi 04000, Algeria

来源：

AXIOMS | 2023年 / 12卷 / 09期

关键词：

fractional discrete reaction-diffusion equations; FitzHugh-Nagumo model; global asymptotic stability; Lyapunov functional; NOISE; CALCULUS;

D O I：

10.3390/axioms12090806

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this work is to describe the dynamics of a discrete fractional-order reaction-diffusion FitzHugh-Nagumo model. We established acceptable requirements for the local asymptotic stability of the system's unique equilibrium. Moreover, we employed a Lyapunov functional to show that the constant equilibrium solution is globally asymptotically stable. Furthermore, numerical simulations are shown to clarify and exemplify the theoretical results.

引用

页数：20

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