Hopf Bifurcation in an Oscillatory-Excitable Reaction-Diffusion Model with Spatial Heterogeneity

被引：6
作者：
Ambrosio, Benjamin [1 ]
机构：
[1] Normandie Univ, UNIHAVRE, LMAH, FR CNRS 3335,ISCN, F-76600 Le Havre, France
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2017年 / 27卷 / 05期
关键词：
FitzHugh-Nagumo; reaction-diffusion; Hopf bifurcation; center-manifold theorem; SYSTEMS;
D O I：
10.1142/S0218127417500651
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We focus on the qualitative analysis of a reaction-diffusion model with spatial heterogeneity. The system is a generalization of the well-known FitzHugh-Nagumo system, in which the excitability parameter is space dependent. This heterogeneity allows to exhibit concomitant stationary and oscillatory phenomena. We prove the existence of a Hopf bifurcation and determine an equation of the center-manifold in which the solution asymptotically evolves. Numerical simulations illustrate the phenomenon.
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页数：13
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