An approach to information propagation in 1-D cellular neural networks-Part I: Local diffusion

This is the first of two companion papers devoted to a deep analysis of the dynamics of information propagation in the simplest nontrivial Cellular Neural Network (CNN), which is one-dimensional and has connections between nearest neighbors only. We will show that two behaviors are possible: local diffusion of information between neighboring cells and global propagation through the entire array. This paper deals with local diffusion, of which we will first give an accurate definition, before computing the template parameters for which the CNN has this behavior. Next we will compute the number of stable equilibria, before examining the convergence of any trajectory toward them, for three different kinds of boundary conditions: fixed Dirichlet, reflective, and periodic