Global exponential stability of anti-periodic solutions for discontinuous Cohen–Grossberg neural networks with time-varying delays

Abstract

ABSTRACT This paper presents a class of Cohen–Grossberg neural networks (CGNNs) with discontinuous activations and time-varying delays. Firstly, under the framework of Filippov solution, we derive some general sufficient conditions to guarantee the global existence of the solutions to the proposed CGNNs with discontinuous activations and time-varying delays. Then, by constructing the new Lyapunov–Krasovskii functional, some new sufficient criteria are given to ascertain the globally exponential stability of the anti-periodic solution for the considered CGNNs with discontinuous activations and time-varying delays. To the authors’ knowledge, the results established in the paper are the only available results on the anti-periodic for the discontinuous CGNNs; some previously known results are extended and complemented. Finally, simulation results of two typical numerical examples are also delineated to demonstrate the effectiveness of our theoretical results.