Almost periodicity for a class of delayed Cohen–Grossberg neural networks with discontinuous activations

The objective of this paper is to investigate the dynamics of a class of delayed Cohen–Grossberg neural networks with discontinuous neuron activations. By means of retarded differential inclusions, we obtain a result on the local existence of solutions, which improves the previous related results for delayed neural networks. It is shown that an M-matrix condition satisfied by the neuron interconnections, can guarantee not only the existence and uniqueness of an almost periodic solution, but also its global exponential stability. It is also shown that the M-matrix condition ensures that all solutions of the system display a common asymptotic behavior. In this paper, we prove that the existence interval of the almost periodic solution is (−∞, +∞), whereas the existence interval is only proved to be [0, +∞) in most of the literature. As special cases, we derive the results of existence, uniqueness and global exponential stability of a periodic solution for delayed neural networks with periodic coefficients, as well as the similar results of an equilibrium for the systems with constant coefficients. To the author’s knowledge, the results in this paper are the only available results on almost periodicity for Cohen–Grossberg neural networks with discontinuous activations and delays.

► We give an improved result on the local existence of solutions for delayed neural networks.
► We examine the existence of almost periodic solutions for delayed discontinuous Cohen–Grossberg neural networks.
► The existence interval of the almost periodic solution is proved to be on the whole real axis.
► We investigate the exponential stability for the almost periodic solution.