Bifurcation Analysis in an Interrupted Dynamical System with State Dependent Input

This paper addresses the first step to investigate the bifurcation phenomena observed in the current-controlled DC-DC converter with thermoelectric module, and therefore we propose a simple interrupted dynamical system which simulates dynamic behavior of the DC-DC converter with thermoelectric module in nature. The dynamic behavior of the proposed system can be described by one dimensional topology, and therefore, we can define the return map. By using the return map, the rigorous bifurcation analysis can be possible. Because the proposed system simulates dynamic behavior of the converter, the clarified circuit fundamental characteristics are applicable to the converters in nature. First, we show an interrupted electric circuit with state dependent input that simulates the switching operation of a current-controlled DC-DC converter with a thermoelectric power generation module as a power supply. Next, we define the return map for analyzing bifurcation phenomena observed in the circuit. Finally, the bifurcation phenomena occurring in the circuit are observed using the return map, and the qualitative properties of this circuit are clarified.