A GALLERY OF OSCILLATIONS IN A RESONANT ELECTRIC CIRCUIT: HOPF-HOPF AND FOLD-FLIP INTERACTIONS

Abstract

In this work, the dynamics of a coupled electric circuit is studied. Several bifurcation diagrams associated with the truncated normal form of the Hopf-Hopf bifurcation are presented. The bifurcation curves are obtained by numerical continuation methods. The existence of quasi-periodic solutions with two (2D torus) and three (3D torus) frequency components is shown. These, in certain way, are close (or have a tendency to end up) to chaotic motion. Furthermore, two fold-flip bifurcations are detected in the vicinity of the Hopf-Hopf bifurcation, and are classified correspondingly. The analysis is completed with time simulations, the continuation of several limit cycle bifurcations and the indication of resonance points.