Spatiotemporal dynamic of a coupled neutral-type neural network with time delay and diffusion

Abstract

In this paper, a delayed neutral-type neural network with diffusion is considered. Three spatiotemporal dynamic problems of such network, i.e., stability, Turing instability and oscillation, are addressed in detail. It is found that the diffusion may lead to Turing instability, and the time delay may result in oscillation. Then, a novel computing method is proposed to investigate the oscillation properties. Finally, numerical results not only verify the obtained results but also show the diffusion coefficients have a great effect on the appearance of pattern. There are six spatiotemporal patterns when diffusion varying.