Globally exponential stability and dissipativity for nonautonomous neural networks with mixed time-varying delays

• We establish a extented Halanay-type inequalty.
• We obtain the less conservative conditions for guaranteeing the dissipativity and stability of non-autonomous neural networks.
• It׳s noting that the states in this paper is not needed to be positive on the domain and the exponent of convergence also can be estimated.

In this paper, the problems of globally exponential stability, dissipativity and solutions’ existence are investigated for nonautonomous neural networks with mixed time-varying delays as well as general activation functions. The mixed time-varying delays consist of both discrete and distributed delays. First, we give a Halanay inequality and combine matrix measure function inequality, sufficient conditions are established to ensure the dissipativity and globally exponential stability of the solutions of the considered neural networks in the end, then a criterion are obtained to guarantee the existence of the solutions of system. Finally, numerical examples are given to show the effectiveness of our theoretical results.