Complex dynamics and stability of Hopfield neural networks with delays

Abstract

In this paper, by utilising the Lyapunov functional method, we analyse the global asymptotic stability of Hopfield neural networks with delays. We obtain some new sufficient conditions to ensure the global asymptotic stability of the model being independent of delays. By using the Lyapunov second method for special cases, we also get that the equilibrium of the system is locally asymptotically stable when the delay is under a critical value; and when the delay is equal to this value, Hopf bifurcation will occur and the equilibrium is unstable; and when the delay is above the critical value, the system will demonstrate complex dynamics. Finally, numerical simulations are presented to verify the analytical results.