PMID: 11909218Mar 23, 2002Paper

Inhibition of chaotic escape from a potential well by incommensurate escape-suppressing excitations

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
R Chacón, J A Martínez

Abstract

Theoretical results are presented concerning the reduction of chaotic escape from a potential well by means of a harmonic parametric excitation that satisfies an ultrasubharmonic resonance condition with the escape-inducing excitation. The possibility of incommensurate escape-suppressing excitations is demonstrated by studying rational approximations to the irrational escape-suppressing frequency. The analytical predictions for the suitable amplitudes and initial phases of the escape-suppressing excitation are tested against numerical simulations based on a high-resolution grid of initial conditions. These numerical results indicate that the reduction of escape is reliably achieved for small amplitudes and at, and only at, the predicted initial phases. For the case of irrational escape-suppressing frequencies, the effective escape-reducing initial phases are found to lie close to the accumulation points of the set of suitable initial phases that are associated with the complete series of convergents up to the convergent giving the chosen rational approximation.

References

Jan 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Y S KivsharH Benner
May 20, 1991·Physical Review Letters·Y Braiman, I Goldhirsch
Mar 1, 1995·Chaos·Arkady S. Pikovsky, Ulrike Feudel

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Citations

Aug 9, 2006·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Ricardo Chacón
Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Chacón, J A Martínez
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R ChacónJ J Miralles
May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D ZuecoF Falo

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