Complete Stability in Multistable Delayed Neural Networks

Abstract

We investigate the complete stability for multistable delayed neural networks. A new formulation modified from the previous studies on multistable networks is developed to derive componentwise dynamical property. An iteration argument is then constructed to conclude that every solution of the network converges to a single equilibrium as time tends to infinity. The existence of 3(n) equilibria and 2(n) positively invariant sets for the n-neuron system remains valid under the new formulation. The theory is demonstrated by a numerical illustration.