Stability in asymmetric Hopfield nets with transmission delays. (English) Zbl 0815.92001

Gopalsamy, K.; He, Xue-zhong

Physica D 76, No. 4, 344-358 (1994).

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.

MSC:

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

Keywords:

asymmetric Hopfield nets; transmission delays; sufficient conditions; delay independent stability; equilibria; Hopfield’s graded response networks; continuously distributed delays

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