TY - JOUR
T1 - Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions
AU - Schouten-Straatman, W.M.
AU - Hupkes, Hermen Jan
PY - 2019
Y1 - 2019
N2 - We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum limit. For the verification of the spectral properties, we need to study a functional differential equation of mixed type (MFDE) with unbounded shifts. We avoid the use of exponential dichotomies and phase spaces, by building on a technique developed by Bates, Chen and Chmaj for the discrete Nagumo equation. This allows us to transfer several crucial Fredholm properties from the PDE setting to our discrete setting.
AB - We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum limit. For the verification of the spectral properties, we need to study a functional differential equation of mixed type (MFDE) with unbounded shifts. We avoid the use of exponential dichotomies and phase spaces, by building on a technique developed by Bates, Chen and Chmaj for the discrete Nagumo equation. This allows us to transfer several crucial Fredholm properties from the PDE setting to our discrete setting.
UR - http://www.scopus.com/inward/record.url?scp=85066443250&partnerID=8YFLogxK
U2 - 10.3934/dcds.2019205
DO - 10.3934/dcds.2019205
M3 - Article
SN - 1078-0947
VL - 39
SP - 5017
EP - 5083
JO - Discrete and Continuous Dynamical Systems A
JF - Discrete and Continuous Dynamical Systems A
IS - 9
ER -