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
Rn
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.