Bifurcations of Periodic Solutions in a Coupled Oscillator with Voltage Ports

In this paper, we study bifurcations of equilibrium points and periodic solutions observed in a resistively coupled oscillator with voltage ports. We classify equilibrium points and periodic solutions into four and eight di erent types, respectively, according to their symmetrical properties. By calculating D-type of branching sets (symmetry-breaking bifurcations) of equilibrium points and periodic solutions, we show that all types of equilibrium points and periodic solutions are systematically found. Possible oscillations in two coupled oscillators are presented by calculating Hopf bifurcation sets of equilibrium points. A parameter region in which chaotic oscillations exist is also shown by obtaining a cascade of period-doubling bifurcation sets. key words: bifurcation, symmetry, coupled system, nonlinear circuit