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.
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页码：1507 / 1526
页数：20
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