Stability results for cellular neural networks with delays
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-...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2004-08-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=173 |
| Summary: | 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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| ISSN: | 1417-3875 1417-3875 |