Quasiperiodic and chaotic discrete breathers in a parametrically driven system without linear dispersion

P. Maniadis, T. Bountis

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We study a one-dimensional lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DB's) can be explicitly constructed by an exact separation of their time and space dependence. Introducing parametric periodic driving, we first show how a variety of such DB's can be obtained by selecting spatial profiles from the homoclinic orbits of an invertible map and combining them with initial conditions chosen from the Poincaré surface of section of a simple Duffing's equation. Placing then our initial conditions at the center of the islands of a major resonance, we demonstrate how the corresponding DB can be stabilized by varying the amplitude of the driving. We thus discover around elliptic points a large region of quasiperiodic breathers, which are stable for very long times. Starting with initial conditions close to the elliptic point at the origin, we find that as we approach the main chaotic layer, a quasiperiodic breather either destabilizes by delocalization or turns into a chaotic breather, with an evidently broadbanded Fourier spectrum before it collapses. For some breather profiles stable quasiperiodic breathers exist all the way to the separatrix of the Duffing equation, indicating the presence of large regions of tori around the DB solution in the multidimensional phase space. We argue that these strong localization phenomena are due to the absence of phonon resonances, as there are no linear dispersion terms in our lattices. We also show, however, that these phenomena persist in more realistic physical models, in which weak linear dispersion is included in the equations of motion, with a sufficiently small coefficient.

Original languageEnglish
Article number046211
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume73
Issue number4
DOIs
Publication statusPublished - 2006
Externally publishedYes

Fingerprint

Discrete Breathers
Breathers
linear systems
Duffing Equation
Initial conditions
profiles
time dependence
equations of motion
Fourier Spectrum
Separatrix
oscillators
Anharmonic Oscillator
Homoclinic Orbit
orbits
Phonon
Quartic
Physical Model
Invertible
coefficients
Phase Space

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Quasiperiodic and chaotic discrete breathers in a parametrically driven system without linear dispersion. / Maniadis, P.; Bountis, T.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 73, No. 4, 046211, 2006.

Research output: Contribution to journalArticle

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