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 \[ dx_ i (t)/dt = - b_ i x_ i(t) + \sum^ n_{j=1} a_{ij}f_ j \bigl( \mu_ j x_ j(t - \tau_{ij}) \bigr) + F_ i(t) \quad (i = 1,2, \dots,n) \] when the external inputs \(F_ i\) 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.


92B20 Neural networks for/in biological studies, artificial life and related topics
34D99 Stability theory for ordinary differential equations
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