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Zbl 1094.34055
Zhang, Qiang; Wei, Xiaopeng; Xu, Jin
Delay-dependent exponential stability of cellular neural networks with time-varying delays.
(English)
[J] Chaos Solitons Fractals 23, No. 4, 1363-1369 (2005). ISSN 0960-0779

The authors analyze certain nonlinear delay differential equations (with time-varying delays) that model cellular neural networks. These equations are of the form $$x'(t)=-Cx(t) + Af(x(t)) + Bf(x(t -\tau(t))) + u,$$ where $x\in \bbfR^n$, $A, B, C$ are constant matrices; $f$ is Lipschitzian and $\tau(t) > 0$.\par Sufficient conditions for global exponential stability are given.
[Stig-Olof Londen (Helsinki)]
MSC 2000:
*34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K60 Applications of functional-differential equations
92B20 General theory of neural networks

Keywords: differential-delay equations; exponential stability; cellular neural networks

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