On a relaxation oscillator with periodic threshold

The authors analyze a relaxation oscillator which includes a hysteresis element with periodic thresholds. The fundamental interests are in recognition and classification of various nonlinear phenomena. As the period of thresholds varies, the system exhibits various interesting periodic responses. Birfurcation diagrams are shown. The response includes hysteresis characteristics and has some universality. In some parameter region, the system exhibits quasi-periodic oscillation. A sufficient condition is derived for this oscillation. Some of the theoretical results were confirmed by laboratory measurements