Rigorous analyses of windows in a symmetric circuit

Two types of windows are found in a symmetric circuit that cannot be seen in the logistic map and are inherent in the symmetric structure of this circuit. One type of window exhibits complex bifurcation phenomena such as symmetry breaking and symmetry recovering in its own region, while the other type of window appears when one chaotic attractor bifurcates to two periodic attractors. The authors derive a one-dimensional Poincare map from the circuit by the degeneration technique and prove rigorously that the two types of windows appear alternatively and infinitely many times inside some windows by applying a certain scaling mechanism on the Poincare map