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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.

92B20General theory of neural networks (mathematical biology)
34D99Stability theory of ODE
Full Text: DOI
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