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 < 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. (c) 2007 American Institute of Physics.
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