Anti-periodic solutions for high-order Hopfield neural networks with impulses

•We study high-order Hopfield neural networks (HHNNs) with time-varying delays and impulses.•Sufficient conditions for the existence and exponential stability of anti-periodic solutions are established.•An example is given to show that impulses may influence the exponentially stable behavior of anti-periodic solution.

In this paper, we consider anti-periodic solutions of high-order Hopfield neural networks (HHNNs) with time-varying delays and impulses. Sufficient conditions for the existence and exponential stability of anti-periodic solutions are established by using Krasnoselski׳s fixed point theorem and Lyapunov functions with inequality techniques. In the end, example and numerical simulations are given to illustrate our main results.