On stability of disturbed Hopfield neural networks with time delays

In real application, the dynamics of Hopfield neural network is often affected by disturbing signals and time delays, so it is worthwhile to study dynamical properties of this type of neural network. Firstly, the ideal solution is defined as the solution of the network without disturbing signals. In order to ensure uniqueness, L2-gain stability, global stability or global exponential stability of the ideal solution, corresponding sufficient conditions are presented, respectively, using homotopic method, inequality techniques, M-matrix properties or one time-delay inequality. All the obtained results are illustrated by several simulations.