Fixed-time periodic stabilization of discontinuous reaction–diffusion Cohen–Grossberg neural networks

This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction-diffusion Cohen-Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction-diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction-diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.