AASERT Supplement to Nonlinear Circuits and Neural Networks.

Abstract : Cellular Nonlinear Networks (CNNs) are large arrays of nonlinear circuits coupled to their immediate neighbors. During the past three years, while partially funded by this grant, graduate student Kenneth R. Crounse, working with the principle investigator and their associates, have made many advances in understanding the dynamics of such arrays, especially their spatial pattern forming properties and the generation of spatial disorder. Pattern formation in CNNs was found to be amenable to analysis by the Turing instability and synergetics paradigms. Both of these methods are widely used to explain phenomena in physics and biology, some of which have been demonstrated on the CNN (e.g., angelfish stripes). In addition, interpreting the CNN behavior in terms of the synergetics paradigm was shown to be useful for the design of some CNN image processing templates (e.g., fingerprint enhancement). We have also developed a general method for the implementation of general Cellular Automata on the CNN Universal Machine. Cellular automata can be used as models for many complex physical systems. In particular, we have investigated methods for producing disorder through reversible gas-like automata. Some applications being explored are random number generation and cryptography