QUALITATIVE ANALYSIS OF CERTAIN REACTION-DIFFUSION SYSTEMS OF THE FITZHUGH-NAGUMO TYPE

被引：3

作者：

Ambrisio, B. ^{[1
,2
]}

机构：

[1] Normandie Univ, UNIHAVRE, LMAH, FR CNRS 3335,ISCN, F-76600 Le Havre, France

[2] Hudson Sch Math, New York, NY 10001 USA

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2023年 / 12卷 / 06期

关键词：

  Hopf bifurcation; reaction-diffusion; FizHugh-Nagumo; Liouville equa-tion; LaSalle's principle; NERVE AXON EQUATIONS; OSCILLATORY TAILS; HOMOCLINIC ORBITS; TRAVELING-WAVES; STABILITY; EXISTENCE; PROPAGATION; PULSES;

D O I：

10.3934/eect.2023023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. This article aims to provide insights into the qualitative analysis of some nonlinear Reaction-Diffusion (RD) systems arising in Neuroscience. We first introduce a non-homogeneous FitzHugh-Nagumo (nhFHN) featuring excitability and oscillatory properties. Then, we discuss the qualitative analysis of a toy model related to nhFHN. In particular, we focus on the convergence of solutions of the toy model toward different solutions (fixed point, periodic) and show the existence of a cascade of Hopf bifurcations. Finally, we connect this analysis to the nhFHN system.

引用

页码：1507 / 1526

页数：20

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