Accession Number : ADA331584

Title :   Nonlinear Circuits and Neural Networks (AASERT FY94).

Descriptive Note : Final rept. 1 Aug 94-31 Jul 97,

Corporate Author : CALIFORNIA UNIV BERKELEY

Personal Author(s) : Chua, Leon O.

PDF Url : ADA331584

Report Date : 31 OCT 1997

Pagination or Media Count : 6

Abstract : Cellular Nonlinear Networks (CNNs) are large arrays of nonlinear circuits coupled to their immediate neighbors. During this funding period we have made many advances in understanding the pattern-forming dynamics of such circuits and their relationship to problems in physics and biology, we have explicated the image processing capabilities of such CNNs, including spatial filtering and multiscale analysis, and finally we have obtained rigorous mathematical results concerning the dynamic behavior of simple CNN arrays. Large arrays of compete cells have elsewhere been shown to demonstrate interesting pattern forming behaviors such as the reaction-diffusion systems of Turing, the propagation of autowaves, and the Ising spin system. We have shown that the simple first-order CNN is capable of exhibiting the essential features found in these systems. And, due to the continuous-time nonlinear dynamics and general neighborhood weights the patterns formed by the CNN proved to he a study in their own right. The linear spatial convolution operation is essential in all manner of nonlinear and linear image processing algorithms. Under this funding, we demonstrated an approach by which any arbitrary FIR filter could be implemented in a robust and straightforward manner via a CNN Universal Machine (CNNUM) algorithm - by using only a standard 3 x 3 B-template. In addition, a general canonical form was proposed for such CNN linear convolutions, which also takes into account the use of an A-template and previous approaches to convolution. Finally, we initiated an investigation into a rigorous analysis of the CNN dynamics as a function of the template parameters. The first theorems have been obtained for the two-cell CNN case. We expect generalizations of such results to verify the proper behavior of many CNN image processing templates.

Descriptors :   *INTEGRATED CIRCUITS, *NONLINEAR ANALYSIS, *SOLID STATE ELECTRONICS, *CIRCUIT ANALYSIS, LINEAR SYSTEMS, SPATIAL DISTRIBUTION, NEURAL NETS, DYNAMIC RESPONSE, FINITE DIFFERENCE THEORY, NONLINEAR SYSTEMS, PHYSICS, TEMPLATES, DOPING, SPATIAL FILTERING, ELECTRICAL NETWORKS, EQUIVALENT CIRCUITS, THEOREMS, REACTOR LATTICE PARAMETERS.

Subject Categories : Electrical and Electronic Equipment

Distribution Statement : APPROVED FOR PUBLIC RELEASE