Pattern Formation Properties of Cellular Neural Networks

摘要

Cellular Nonlinear Networks (CNNs) are large arrays of nonlinear circuits coupledto their immediate neighbors. In the past year we have made many advances in understanding the pattern forming dynamics of such circuits and their relationship to problems in physics and biology. Large arrays of complex cells have been shown to demonstrate many interesting pattern forming behaviors. Celebrated examples include the reaction diffusion systems of Turing used to explain aMmal markings, the propagation of autowaves and the 'synergy' effect, and the Ising spin system and discrete bistable systems used to describe magnetic media and metal alloys. In the past year, we have shown that the simple first order CNN is capable of exhibiting features found in these systems. However, due to the continuous time nonlinear dynamics and general neighborhood weights the patterns formed by the CNN are a study in their own right. In fact, the piecewise linear sigmoid allows many theorems to be derived, which are not otherwise possible, about stable patterns supported by the CNN medium.