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Global attractivity in delayed Hopfield neural network models. (English) Zbl 0917.34036
The authors study the global attractivity of delayed Hopfield neural network models in two different ways. They obtain sufficient conditions for the global asymptotic stability independent of delays by constructing Lyapunov functionals but without assuming monotonicity and differentiability of the activation functions. The theory of monotone dynamical systems is applied to obtain criteria for the global attractivity of the delayed model in case the activation functions are monotone and smooth. Many examples are given to clarify the ideas.

MSC:
37-XX Dynamical systems and ergodic theory
92B20 Neural networks for/in biological studies, artificial life and related topics
34D20 Stability of solutions to ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
34K20 Stability theory of functional-differential equations
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