INTERACTION BETWEEN DISCONTINUITY AND NON-INVERTIBILITY IN A RELAXATION-OSCILLATOR

A sinusoidally driven relaxation oscillator is studied by investigatin g the underlying one dimensional phase dynamics. The map turns out to be a combination of conventional and ''inverse'' circle maps showing d ifferent types of supercritical behaviour. The critical lines in the p arameter space that correspond to the parameter values where the map b ecomes non-invertible or discontinuous are obtained analytically. Betw een 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 combi ned circle maps.