An experimental study on long transient oscillations in cooperative CNN rings

The paper considers a class of one-dimensional circular standard cellular neural network (CNN) arrays with a typical three-segment piecewise linear activation and two-sided cooperative (positive) interactions (a cooperative CNN ring). Numerical simulations show that in a wide range of interconnection parameters, and for a wide set of initial conditions, the solutions of a cooperative CNN ring display unexpectedly long oscillations, lasting even hundreds of cycles, before they eventually converge toward an equilibrium point. The goal of this paper is to confirm the presence of such long-transient oscillations through laboratory experiments on a simple discrete-component prototype of a cooperative CNN ring with 16 cells and to analyze some of their salient features. Analytical results are also provided to support the numerical and experimental findings.

I. Introduction

In this paper we investigate some fundamental dynamical properties of a class of one-dimensional circular standard cellular neural network (CNN) arrays with a typical three-segment piecewise linear (PL) activation and two-sided interactions (a CNN ring).