Existence and stability of square-mean almost periodic solutions to a spatially extended neural network with impulsive noise

Our work is concerned with a neural network with n nodes, where the activity of the k-th cell depends on external, stochastic inputs as well as the coupling generated by the activity of the adjacent cells, transmitted through a diffusion process in the network. This paper aims to throw some light on time-varying, stochastically perturbed, neuronal networks. We show thatwhen the coefficients oscillate around a reference value, with oscillations that are almost periodic and suitably small in percentage, then there exists a unique solution for the system, that is almost periodic and uniformly bounded in the square-mean norm for all times.