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Delay-dependent global stability condition for delayed Hopfield neural networks. (English) Zbl 1138.34036
Consider the differential-delay system $${dx\over dt}=- Cx(t)+ AS(x(t-\tau))+ b\tag{$*$}$$ with $x\in\bbfR^n$, $S(x(t-\tau))= [s_1(x_1(t- \tau_1),\dots, s_n(x_n(t-\tau_n))]^T$, $C= \text{diag}(c_1,\dots, c_n)$, $c_i> 0$, $\tau_n\ge 0$. The activator functions $s_i$ are assumed to be bounded and globally Lipschitzian. Let $x^*$ be an equilibrium point of $(*)$. The authors derive a sufficient (matrix) condition for $x^*$ to be globally asymptotically stable. The proof is based on a Lyapunov functional.

MSC:
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
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References:
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