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.