Interaction between discontinuity and non-invertibility in a relaxation oscillator

Abstract

A sinusoidally driven relaxation oscillator is studied by investigating the underlying one dimensional phase dynamics. The map turns out to be a combination of conventional and “inverse” circle maps showing different types of supercritical behaviour. The critical lines in the parameter space that correspond to the parameter values where the map becomes non-invertible or discontinuous are obtained analytically. Between these critical lines the system shows either chaos (if the map is non-invertible) or complete phase locking (if the map is discontinuous). Above these two lines the mapping function is discontinuous as well as non-invertible. We report different mechanisms of the interaction between these two competing characteristics and the induced dynamical phenomena. The general idea of these descriptions should be common for a large group of relaxation oscillators and their corresponding combined circle maps. © 1994, Elsevier Science B.V. All rights reserved. All rights reserved.