Smooth dynamical systems which realize arithmetical and logical operations

Abstract

Although many biological and man-made systems combine aspects of digital and analog processing, until recently there has been very little theoretical work on models this type and many basic questions remain unresolved. In this paper we describe input-output systems governed by ordinary differential equations i) whose behavior is robust in the sense that certain well-defined qualitative aspects of the output depend only on certain well-defined qualitative aspects of the input and ii) are capable of generating behavior of the type one usually associates with digital systems. It is show that rather simple differential equation models can robustly execute arithmetical and logical operations; in particular, we show that continuous-time dynamical systems can simulate arbitrary finite automata.

This work was supported in part by the U.S. Department of the Air Force under grant AFOSR-96-00197, in part by the U.S. Army Research Office under grant DAAL03-86-K-0171, and in part by the National Science Foundation under grant CDR-85-00108.