Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos
Chaotic Dynamics
2009-11-13 v1 Pattern Formation and Solitons
Abstract
We consider a chain of nonlinear oscillators with long-range interaction of the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha <2. In the continues limit the system's dynamics is described by the Ginzburg-Landau equation with complex coefficients. Such a system has a new parameter alpha that is responsible for the complexity of the medium and that strongly influences possible regimes of the dynamics. We study different spatial-temporal patterns of the dynamics depending on alpha and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.
Keywords
Cite
@article{arxiv.0707.3941,
title = {Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos},
author = {G. M Zaslavsky and M. Edelman and V. E. Tarasov},
journal= {arXiv preprint arXiv:0707.3941},
year = {2009}
}
Comments
22 pages, 10 figures