Analysis of a ferroresonant circuit using bifurcation theory and continuation techniques

In this contribution, the analysis of the dynamics of a ferroresonant circuit are presented using continuation techniques and bifurcation theory. Despite its great simplicity, this circuit can assume a diverse range of steady-state regimes including fundamental and subharmonic ferroresonance, quasiperiodic oscillations, and chaos. The system dynamics are explored through the continuation of periodic solutions of the associated circuit equations. A detailed picture is drawn of various transitions between the individual periodic steady-state regimes of the circuit. Bifurcation points are computed, revealing a clearly defined succession of periodic steady-state regimes, including the Feigenbaum route to chaos through a cascade of period doublings. The analysis presented is performed using the freely available software package XPPAUT. The contribution of this paper is to provide a detailed description of how to define the circuit equations in XPPAUT and how to conduct the interactive bifurcation analysis. The proposed approach is shown to be both computationally efficient and robust, as it eliminates the need for numerically critical and long lasting transient simulations.