Multistability and New Attraction Basins of Almost-Periodic Solutions of Delayed Neural Networks

In this paper, we investigate multistability of almost-periodic solutions of recurrently connected neural networks with delays (simply called delayed neural networks). We will reveal that under some conditions, the space R(n) can be divided into 2(n) subsets, and in each subset, the delayed n-neuron neural network has a locally stable almost-periodic solution. Furthermore, we also investigate the attraction basins of these almost-periodic solutions. We reveal that the attraction basin of almost-periodic trajectory is larger than the subset, where the corresponding almost-periodic trajectory is located. In addition, several numerical simulations are presented to corroborate the theoretical results.