Multistability of HNNs with almost periodic stimuli and continuously distributed delays

In this article, we investigate multistability of Hopfield neural networks (HNNs) with almost periodic stimuli and continuously distributed delays. By employing the theory of exponential dichotomy and Schauder's fixed point theorem, sufficient conditions are gained for the existence of 2N almost periodic solutions which lie in invariant regions. Meanwhile, we derive some new criteria for the networks to converge toward these 2N almost periodic solutions and the domain of attraction is also given. The obtained results are new, general and improve corresponding results existing in previous literature.