Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation

Abstract

This tutorial paper proposes a subclass of cellular neural
networks (CNN) having no inputs (i.e., autonomous) as a universal active
substrate or medium for modeling and generating many pattern formation
and nonlinear wave phenomena from numerous disciplines, including
biology, chemistry, ecology, engineering, and physics. Each CNN is
defined mathematically by its cell dynamics (e.g., state equations) and
synaptic law, which specifies each cell's interaction with its
neighbors. We focus on reaction-diffusion CNNs having a linear synaptic
law that approximates a spatial Laplacian operator. Such a synaptic law
can be realized by one or more layers of linear resistor couplings. An
autonomous CNN made of third-order universal cells and coupled to each
other by only one layer of linear resistors provides a unified active
medium for generating trigger (autowave) waves, target (concentric)
waves, spiral waves, and scroll waves. When a second layer of linear
resistors is added to couple a second capacitor voltage in each cell to
its neighboring cells, the resulting CNN can be used to generate various
turing patterns