Stability and synchronization of a ring of identical cells with delayed coupling
type: Item
instance of: scholarly article
title: Stability and synchronization of a ring of identical cells with delayed coupling
zbMATH Open document ID: 1071.34079
author: Yuan Yuan
author: Sue Ann Campbell
published in: Journal of Dynamics and Differential Equations
publication date: 2005-03-15T00:00:00Z
review text: The subject of the paper is a ring of coupled identical systems with time delayed, nearest neighbor coupling \[ x_i' = -x_i(t) + \alpha f(x_i(t-\tau_s)) + \beta [g(x_{i-1}(t-\tau))+ g (x_{i+1}(t-\tau))], \quad (i \mod n), \tag{1} \] where \(f,g\in C^3\) are bounded functions. In addition, it assumed that \(f(0)=g(0)=0\), \(f'(0)=g'(0)=1\); \(f'(x)>0\), \(g'(x)>0\) for all \(x\in \mathbb{R}\); \(xf''(x)<0\) and \(xg''(x)<0\) for all \(x\neq 0\); and \(f'''(0)<0\), \(g'''(0)<0\). The authors study the local stability of the trivial solution \(x_i=0\) as well as the existence and stability of the synchronized solutions of (1). Lyapunov functionals are used to establish global stability of the synchronized solutions.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K19
Mathematics Subject Classification ID: 34K25
zbMATH DE Number: 2145908
zbMATH Keywords: delay differential equations
zbMATH Keywords: neural networks
zbMATH Keywords: stability
zbMATH Keywords: symmetry
zbMATH Keywords: synchronization
reviewed by: S. Yanchuk
describes a project that uses: XPPAUT
MaRDI profile type: Publication
full work available at URL: s10884-004-6114-y
OpenAlex ID: W2064534817
DOI: 10.1007/S10884-004-6114-Y
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description: scientific article; zbMATH DE number 2145908