**Stability results for cellular neural networks with delays**

**I. Győri**, Department of Mathematics and Computing, University of Veszprém, Veszprém, Hungary**F. Hartung**, Department of Mathematics and Computing, University of Veszprém, Veszprém, Hungary

E. J. Qualitative Theory of Diff. Equ., Proc. 7'th Coll. Qualitative Theory of Diff. Equ., No. 13. (2004), pp. 1-14.

Communicated by P. Eloe.
| Received on 2003-09-29 Appeared on 2004-08-31 |

**Abstract: **In this paper 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,\ldots,n,

$$

where $f(t)=\frac 12(|t+1|-|t-1|)$. 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,\ldots,n

$$

is asymptotically stable independently of the delays $\tau_{ij}$.

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