Dynamics of the chain of forced oscillators with long-range interaction: from synchronization to chaos.
We consider a chain of nonlinear oscillators with long-range interaction of the type 1l(1+alpha), where l is a distance between oscillators and 0<alpha<2. In the continuous limit, the system's dynamics is described by a fractional generalization of 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, especially near alpha=2 and alpha=1. We study different spatiotemporal patterns of the dynamics depending on alpha and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.
Zaslavsky
G M
GM
Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012, USA.
Edelman
M
M
Tarasov
V E
VE
D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D010825:Physics / Q000379:methods; D013816:Thermodynamics