We consider a chain of nonlinear oscillators with long-range interaction of the type 1l1+α, where l is a distance between oscillators and 0<α<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 α that is responsible for the complexity of the medium and that strongly influences possible regimes of the dynamics, especially near α=2 and α=1. We study different spatiotemporal patterns of the dynamics depending on α and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.

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