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Fractional dynamics of coupled oscillators with long-range interaction.
- Source :
-
Chaos (Woodbury, N.Y.) [Chaos] 2006 Jun; Vol. 16 (2), pp. 023110. - Publication Year :
- 2006
-
Abstract
- We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha, when 0<alpha<2. We consider a few models of coupled oscillators and show how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on alpha. The presence of a fractional derivative also leads to the occurrence of localized structures. Particular solutions for fractional time-dependent complex Ginzburg-Landau (or nonlinear Schrodinger) equation are derived. These solutions are interpreted as synchronized states and localized structures of the oscillatory medium.
Details
- Language :
- English
- ISSN :
- 1054-1500
- Volume :
- 16
- Issue :
- 2
- Database :
- MEDLINE
- Journal :
- Chaos (Woodbury, N.Y.)
- Publication Type :
- Academic Journal
- Accession number :
- 16822013
- Full Text :
- https://doi.org/10.1063/1.2197167