Type I vs. type II excitable systems with delayed coupling
type: Item
instance of: scholarly article
title: Type I vs. type II excitable systems with delayed coupling
zbMATH Open document ID: 1100.34060
author: Ines Grozdanović
author: Nebojša Vasović
author: N. Burić
published in: Chaos, Solitons and Fractals
publication date: 2005-05-12T00:00:00Z
review text: The authors analyze the oscillatory dynamics of coupled type I and type II excitable systems. The system of equations has the following form \[ \dot x_i = X(x_i,y_i)+C(x_i,x_{i+1}(t-\tau),x_{i-1}(t-\tau) ), \] \[ \dot y_i = Y(x_i,y_i), \quad i=1,2,\dots,N, \;\tau>0, \] with periodic boundary conditions on \(0\) and \(N\)th unit. Two representative examples are considered: FitzHugh-Nagumo and Terman-Wang models, for which \(X=-x^3+(a+1)x^2-ax-y+I\), \(Y=bx-\gamma y\), and \(X=-x^3+3x-y+2+I\), \(Y=\varepsilon[\alpha (1+\tanh(x/\beta))-y]\), respectively. Two types of coupling are considered: diffusive coupling with \(C(x_i,x_{i+1}(t-\tau),x_{i-1}(t-\tau))=c(-2x_i+x_{i-1}(t-\tau) +x_{i+1}(t-\tau))\) and sigmoid coupling with \(C(x_i,x_{i+1}(t-\tau),x_{i-1}(t-\tau))=c \tan^{-1} (x_{i-1}(t-\tau)-x_0)+c\tan^{-1} (x_{i+1}(t-\tau)-x_0)\), where \((x_0,y_0)\) is a stationary solution. For the above mentioned models, the stability of a synchronized state is studied. One of the authors' main conclusions is that that within the same class, characterized by the excitability type and the coupling, the dynamics qualitatively depends only on whether the number of units is even or odd.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K23
Mathematics Subject Classification ID: 92C20
zbMATH DE Number: 2167635
zbMATH Keywords: type I and type II excitable systems
zbMATH Keywords: delay
zbMATH Keywords: coupling
zbMATH Keywords: synchronization
MaRDI profile type: Publication
full work available at URL: j.chaos.2004.06.033
OpenAlex ID: W2029715198
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DOI: 10.1016/J.CHAOS.2004.06.033
description: scientific article; zbMATH DE number 2167635