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Delay-dependent exponential stability of cellular neural networks with time-varying delays. (English) Zbl 1094.34055
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 \(x\in \mathbb{R}^n\), \(A, B, C\) are constant matrices; \(f\) is Lipschitzian and \(\tau(t) > 0\).
Sufficient conditions for global exponential stability are given.

MSC:
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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