Mean-square exponentially input-to-state stability of stochastic Cohen–Grossberg neural networks with time-varying delays

•First, we extend the Halanay inequality established in [33] to the stochastic Halanay delay differential inequality with variable coefficients such that it is effective for stochastic functional systems.•Second, we remove the rather restrictive condition that τ̇(t)<1, which is required in [5], [13], [14], [30], [31] and [32]. So our result is less conservative.•Finally, compared with the results in [13], [14] and [16], our model is more general and more practical since we considered the stochastic effect and variable coefficients.

In this paper, a class of stochastic Cohen–Grossberg neural networks with time-varying delays is considered. By utilizing Razumikhin technique and constructing new Halanay differential inequalities, some sufficient conditions ensuring the mean-square exponential input-to-state stability of the networks are obtained. Two numerical examples are given to illustrate the efficiency of the derived results.