PMID: 11308569Apr 20, 2001Paper

Instability versus nonlinearity in certain nonautonomous oscillators: A critical dynamical transition driven by the initial energy

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
C Degli Esposti Boschi, L Ferrari

Abstract

The equation of motion q+Omega(2)(t)q+alpha/q/(gamma-2)q=0 (gamma>2) for the real coordinate q(t) is studied, as an example of the interplay between nonlinearity and instability. Two contrasting mechanisms determine the behavior of q(t), when the time-varying frequency Omega(t) does produce exponential instability in the linear equation q (lin)+Omega(2)(t)q(lin)=0. At low energy, the exponential instability is the dominant effect, while at high energy the bounding effect of the autonomous nonlinear term prevails. Starting from low initial energies, the result of this competition is a time-varying energy characterized by quasiperiodic peaks, with an average recurrence time T(peak). A closed critical curve S(omega) exists in the initial phase space, whose crossing corresponds to a divergence of the recurrence time T(peak). The divergence of T(peak) has a universal character, expressed by a critical exponent a=1. The critical curve S(omega) is the initial locus of the solutions that vanish asymptotically. A close relationship exists between this dynamical transition and the transition from mobile to self-trapped polarons in one spatial dimension. The application to a number of physical problems is addressed, with special attention...Continue Reading

References

Feb 1, 1985·Physical Review A: General Physics·R LiviA Vulpiani
Apr 1, 1985·Physical Review A: General Physics·R LiviA Vulpiani
Jun 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Y WangP L Zhang
Dec 12, 1988·Physical Review Letters·A ChaoM Syphers
Mar 23, 1992·Physical Review Letters·T SatogataG Tsironis
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·L Ferrari, Degli Esposti Boschi C

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Citations

Nov 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kirone Mallick, Philippe Marcq
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E Papp, C Micu

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