Fractional dynamics of coupled oscillators with long-range interaction
Tarasov, Vasily E. ; Zaslavsky, George M.
arXiv, 0512013 / Harvested from arXiv
Text on arXiv
We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power-wise 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 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 fractional derivative leads also 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.
Publié le : 2005-12-06
Classification:  Nonlinear Sciences - Pattern Formation and Solitons,  Condensed Matter - Statistical Mechanics,  Mathematical Physics,  Nonlinear Sciences - Adaptation and Self-Organizing Systems,  Nonlinear Sciences - Chaotic Dynamics,  Physics - Classical Physics 
@article{0512013,
     author = {Tarasov, Vasily E. and Zaslavsky, George M.},
     title = {Fractional dynamics of coupled oscillators with long-range interaction},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0512013}
}

Tarasov, Vasily E.; Zaslavsky, George M. Fractional dynamics of coupled oscillators with long-range interaction. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0512013/