Chaos in some 1-D discontinuous maps that appear in the analysis of electrical circuits

Abstract

Several representative examples of nonlinear electronic circuits modeled by discontinuous 1-dimensional maps, including the 1-D maps derived from Chua's circuit, are reviewed. Although very little general results are presently available for studying the chaotic dynamics of such 1-D maps, an important subclass C where useful properties are known is identified and reviewed. This subclass is characterized by monotonic expansive maps within each continuous subinterval, and where the map assumes at each discontinuity point a left and a right limit equal in value to the boundary (end points) of the defining interval I. The main property characterizing discontinuous maps belonging to class C is that they possess a good invariant measure, which can be translated roughly by saying the associated chaotic attractor can be proved rigorously to be ergodic. >