Complex behaviour of a simple partial-discharge model

We examine the most simple and deterministic model of partial-discharge phenomena, or the three-capacitance equivalent circuit model with fixed parameter values. Although it is an old model proposed more than fifty years ago, here we show that its behaviour should be described with contemporary concepts of nonlinear dynamics such as devil's staircases and fractals. The model can be reduced to a class of piecewise isometries, termed double rotations. Because of the self-similar structure in the parameter space of double rotations, the average discharge rate of the three-capacitance model as a function of the applied voltage is very complex, resembling a devil's staircase, in spite of the simple appearance of the model. Our result provides comprehension of the dynamical complexity inherent in real partial-discharge phenomena.