LONG-RANGE ORDER WITH LOCAL CHAOS IN LATTICES OF DIFFUSIVELY COUPLED ODES

The existence of non-trivial collective behavior in lattices of diffusively coupled differential equations is investigated. For a two-dimensional square lattice of Rossler systems, a rotating long-range order is observed. This case is best described in terms of a complex Ginzburg-Landau (CGL) equation submitted to the local noise produced by the chaotic Rossler units. The parameters of this CGL equation are estimated to be in the so-called ''Benjamin-Feir stable'' region. The collective oscillation regime thus corresponds to the linearly-stable, spatially-homogeneous solution of the equivalent CGL equation. The possibility of more complex collective behavior in similar systems is discussed.