2N almost periodic attractors for CNNs with variable and distributed delays

In this paper, we investigate dynamics of 2N almost periodic attractors for cellular neural networks (CNNs) with variable and distributed delays. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of CNNs into 2N compact convex subsets. Then the existence of 2N almost periodic solutions lying in compact convex subsets is attained due to employment of the theory of exponential dichotomy and Schauder's fixed point theorem. Meanwhile, we derive some new criteria for the networks to converge toward these 2N almost periodic solutions and exponential attracting domains are also given correspondingly. The obtained results are new and can be applied to a large class of neural networks.