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Multistability of competitive neural networks with time-varying and distributed delays. (English) Zbl 1167.34383

Summary: For two classes of general activation functions, we investigate the multistability of competitive neural networks with time-varying and distributed delays. By formulating parameter conditions and using inequality technique, several novel delay-independent sufficient conditions ensuring the existence of \(3^N\) equilibria and exponential stability of \(2^N\) equilibria are derived. In addition, estimations of positively invariant sets and basins of attraction for these stable equilibria are obtained. Two examples are given to show the effectiveness of our theory.

MSC:

34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
37N25 Dynamical systems in biology
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