On Metastability of Cellular Neural Networks with Random Perturbations

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 trial metastability analysis of cellular neural networks with multi-stable equilibria analytically and numerically. Via the large deviation theory, we can define the MOST stable equilibrium according to the minimum action 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 equilibrium as defined, even if the trajectory is initiated right at the other stable equilibria or its attracting basins. We provide a sufficient condition to find the most stable equilibrium by estimating and comparing the minimal value of the action functional in the random perturbation theory. In addition, we give a simulation of 2-dimensional CNN system to illustrate the theoretical result.