The spectrum and stability of travelling pulses in a coupled FitzHugh-Nagumo equation  

作　　者：Qi Qiao Xiang Zhang 

机构地区：[1]School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China [2]Key Laboratory of Scientific and Engineering Computing(Ministry of Education),and Shanghai Frontier Science Center of Modern Analysis(CMA-Shanghai),Shanghai Jiao Tong University,Shanghai 200240,China

出　　处：《Science China Mathematics》2024年第5期975-1010,共36页中国科学（数学）（英文版）

基　　金：supported by National Key R&D Program of China(Grant No.2022YFA1005900);National Natural Science Foundation of China(Grant Nos.12071284 and 12161131001);supported by National Natural Science Foundation of China(Grant No.11871334);Innovation Program of Shanghai Municipal Education Commission(Grant No.2021-01-07-00-02-E00087)。

摘　　要：For a coupled slow-fast FitzHugh-Nagumo(FHN)equation derived from a reaction-diffusionmechanics(RDM)model,Holzer et al.(2013)studied the existence and stability of the travelling pulse,which consists of two fast orbit arcs and two slow ones,where one fast segment passes the unique fold point with algebraic decreasing and two slow ones follow normally hyperbolic critical curve segments.Shen and Zhang(2021)obtained the existence of the travelling pulse,whose two fast orbit arcs both exponentially decrease,and one of the slow orbit arcs could be normally hyperbolic or not at the origin.Here,we characterize both the nonlinear and spectral stability of this travelling pulse.

关 键 词：coupled FitzHugh-Nagumo equation singular perturbation travelling pulse SPECTRUM nonlinear stability spectral stability 

分 类 号：O175[理学—数学]