GEOMETRICAL RESONANCE ANALYSIS OF CHAOS SUPPRESSION IN THE BICHROMATICALLY DRIVEN VAN-DER-POL OSCILLATOR

Authors
CHACON R SANCHEZ M MARTINEZ JA
Citation
R. Chacon et al., GEOMETRICAL RESONANCE ANALYSIS OF CHAOS SUPPRESSION IN THE BICHROMATICALLY DRIVEN VAN-DER-POL OSCILLATOR, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(2), 1997, pp. 1541-1549
Citations number
38
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
Journal title
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics → ACNP
ISSN journal
1063651X
Volume
56
Issue
2
Year of publication
1997
Pages
1541 - 1549
Database
ISI
SICI code
1063-651X(1997)56:2<1541:GRAOCS>2.0.ZU;2-S
Abstract
Elimination of chaotic behavior in the harmonically driven van der Pol oscillator by means of a comparatively weak additional forcing was st udied through geometrical resonance analysis. We considered commensura te and incommensurate cases together with the effect of the phase diff erence between the forcings. The analysis provided parameter-space reg ions for regularization that were corroborated by numerical experiment s, including instances with clearly large chaos-inducing forcing. A re interpretation of a classical result, due to Cartwright and Littlewood [J. London Math. Sec. 20, 180 (I945)], was also derived by means of g eometrical resonance analysis.