A gallery of oscillations in a resonant electric circuit: Hopf-Hopf and fold-flip interactions

G. REVEL; D. M. ALONSO; J. L. MOIOLA

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

World Scientific Publishing

Año: 2008 vol. 18 p. 481 - 494

0218-1274

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. It is shown the existence of quasi-periodic solutions with two (2D torus) and three (3D torus) frequency components. These last, 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, continuation of several limit cycle bifurcations and indication of resonance points.