Chaotic phenomena in a four-dimensional circuit with two ideal diodes

The authors analyze a four-dimensional autonomous circuit. The dynamics of this circuit are described by a fourth-order differential equation including two small parameters. The circuit contains two diodes. The resistances of the diodes when they are on correspond to the two small parameters. Moreover, a degeneration technique is used which means that the diodes are assumed to operate as two ideal switches. In the case where the degeneration technique is used, the solution of the equation is constrained in a piecewise manner onto a two-dimensional plane. Therefore, the one-dimensional Poincare map can be derived strictly and it can explain the chaotic phenomena very well. The justifiability of the method using this degeneration technique is verified mathematically and experimentally