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Stability in asymmetric Hopfield nets with transmission delays. (English) Zbl 0815.92001
Summary: Sufficient conditions are derived for the delay independent stability of the equilibria in Hopfield’s graded response networks of the type $$dx\sb i (t)/dt = - b\sb i x\sb i(t) + \sum\sp n\sb{j=1} a\sb{ij}f\sb j \bigl( \mu\sb j x\sb j(t - \tau\sb{ij}) \bigr) + F\sb i(t) \quad (i = 1,2, \dots,n)$$ when the external inputs $F\sb i$ are held temporally uniform. A generalization to continuously distributed delays is briefly indicated. Several illustrative examples are numerically simulated and the results of simulations are graphically displayed.

MSC:
92B20General theory of neural networks (mathematical biology)
34D99Stability theory of ODE
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References:
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