The Stability Of Cellular Neural Networks Under Random Disturbance

Since cellular neural networks (CNNs) were introduced by L. O. Chua and L. Yang in1988, its stability has been investigated in many papers due to its important application in signal processing, pattern recognition and many other fields. Metastability is known as the phenomenon that a multi-stable system may have transitions between different stable states under random perturbations of proper intensity. In this paper, we make a metastability analysis of cellular neural networks with multi-stable equilibria analyt-ically and numerically. Via the large deviation theory, we can define the MOST stable equilibrium according to the minimum action functional of the transition paths between these equilibria. Under a proper intensity of white noise, the trajectories from any initial position will go and stay near the most stable equilibria or their attracting basins. We provide a sufficient condition to find the most stable equilibrium by estimating and com-paring the minimal value of the action functional in the random perturbation theory. In addition, we give a simulation of2-dimensional CNN system to illustrate the theoretical result.