Turing Patterns in CNN’s-Part I: Once Over Lightly

Abstruct-The aim of this three part tutorial is to focus the reader’s attention to a new exciting behavior of a particular class of cellular neural networks (CNNs): Turing pattern formation in two-grid coupled CNNs. We first analyze the reduced Chua’s circuit as the basic cell for the two-grid coupled CNNs capable of producing Turing patterns. We use a nonstandard normalization to derive a dimensionless state equation of the individual cell. Then, we present an intuitive explanation of Turing pattern formation mechanism for a 1-D two-grid coupled array in relation to the original mechanism proposed by Turing. Finally, we derive the first two conditions for Turing pattern formation, discuss the boundary conditions, and illustrate via an example on how the number of the equilibrium points of a CNN increases rapidly even though each isolated cell has only one equilibrium point. This study is continued in the next two parts of this tutorial where analytical derivations and various computer simulation results are presented as well. I