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

Instituto de Investigaciones en Ingeniería Eléctrica "Alfredo Desages", Departamento de Ingeniería Eléctrica y de Computadoras, Universidad Nacional de Sur, Av. Alem 1253, (B8000CPB) Bahía Blanca, Argentina

CONICET, Argentina

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DIEGO M. ALONSO

CONICET, Argentina

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, and

JORGE L. MOIOLA

CONICET, Argentina

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https://doi.org/10.1142/S0218127408020409Cited by:9 (Source: Crossref)

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.

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