Windows in a non-autonomous circuit with symmetry

A symmetric structure exists in many chaos-generating circuits. In those circuits, interesting bifurcation phenomena based on the symmetry of circuits, such as symmetry recovery, symmetry breaking, etc., are observed. In this study, two types of interesting windows are observed in a circuit with symmetry which we propose. This circuit has a pair of diodes. We consider the case in which the pair of diodes operates as a pair of ideal switches. In this case, the Poincare´ map can be derived rigorously as a one-dimensional map. We prove that a countably infinite number of two types of windows are generated alternately by applying the theorem written in a previous paper (Nishio et al, IEEE Trans. Circuits Syst., vol. 37, no. 4, pp. 473-487, 1990) to the one-dimensional map