On conditions leading to chaos in feedback systems

Abstract

The purpose of this paper is to describe a simple mechanism which yields (numerically) chaos in non-linear feedback systems. We also give an effective, but partially heuristic, analysis based on singular perturbation methods coupled with a study of a first return map. An interesting feature of the class of systems studied here is that the first return map cannot be defined as a continuous map of a connected set into itself. In this respect the situation appears to be closely related to the flows postulated in [5] and [6].