Györi, István; Hartung, Ferenc Stability results for cellular neural networks with delays. (English) Zbl 1072.34077 Electron. J. Qual. Theory Differ. Equ. 2003, Suppl., Paper No. 13, 14 p. (2003). Summary: We give a sufficient condition to imply global asymptotic stability of a delayed cellular neural network of the form \[ \dot x_i(t) = -d_i x_i(t)+ \sum_{j=1}^na_{ij} f(x_j(t)) +\sum_{j=1}^nb_{ij}f(x_j(t-\tau_{ij}))+u_i,\qquad t\geq0,\quad i=1,\dots,n, \] with \(f(t)=\frac 12(|t+1|-|t-1|)\). In order to prove this stability result, we need a sufficient condition which guarantees that the trivial solution of the linear delay system \[ \dot z_i(t) = \sum_{j=1}^na_{ij} z_j(t) +\sum_{j=1}^nb_{ij}z_j(t-\tau_{ij}),\qquad t\geq0,\quad i=1,\dots,n, \] is asymptotically stable independently of the delays \(\tau_{ij}\). MSC: 34K20 Stability theory of functional-differential equations PDFBibTeX XMLCite \textit{I. Györi} and \textit{F. Hartung}, Electron. J. Qual. Theory Differ. Equ. 2003, Paper No. 13, 14 p. (2003; Zbl 1072.34077) Full Text: EuDML EMIS