Dynamical behaviors of Cohen–Grossberg neural networks with mixed time delays and discontinuous activations

In this paper, we investigate the dynamical behaviors of a novel class of Cohen–Grossberg neural networks with not only mixed time delays, i.e., time varying delays and distributed delays, but also discontinuous activations, which may be unbounded or nonmonotonic. Some sufficient conditions are derived to ensure the existence, uniqueness of the equilibrium, global exponential asymptotic stability of the solution and the associated output of the solution converging to the output equilibrium point in measure by using the Leray–Schauder alternative theorem in multivalued analysis, matrix theory and generalized Lyapunov-like approach. Some recent results in the literature are generalized and significantly improved. One example is provided to demonstrate the effectiveness of the theoretical results.