Global stability analysis of fractional-order Hopfield neural networks with time delay

• The stability criterion of linear fractional-order systems with time delay is deduced.
• The existence and uniqueness of equilibrium point for fractional-order time delay neural networks are analyzed.
• Global stability conditions of fractional-order time delay neural networks are obtained by using Lyapunov method.

In this paper, the global stability analysis of fractional-order Hopfield neural networks with time delay is investigated. A stability theorem for linear fractional-order systems with time delay is presented. And, a comparison theorem for a class of fractional-order systems with time delay is shown. The existence and uniqueness of the equilibrium point for fractional-order Hopfield neural networks with time delay are proved. Furthermore, the global asymptotic stability conditions of fractional-order neural networks with time delay are obtained. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.