Analysis of an interrupted circuit with fast-slow bifurcation

In this paper, we discuss, with focus on the border-collision bifurcation, the relationship between the fast-scale bifurcation and the slow-scale bifurcation in an interrupted electric circuit. First, we show the circuit model and explain its dynamics. Then, we define the discrete map in the fast-scale dynamics and the slow-scale dynamics, respectively. Using the discrete map, we derive the 1-parameter bifurcation diagram in the slow-scale dynamics. Finally, we discuss how the border-collision bifurcation in the fast-scale dynamics affects the slow-scale bifurcation.