Turbulence in Globally Coupled Maps

Details Turbulence in Globally Coupled Maps Turbulence in Globally Coupled Maps

1996-03-05

arxiv.org/abs/chao-dyn/9603004v1

Nonlinear Sciences

Chaotic Dynamics

6 pages LaTeX; 6 figures available upon request from authors. To appear in Phys. Rev. E (1996)

Scientific paper

10.1103/PhysRevE.53.6032

The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map lattices. New features arise in the globally coupled system; for instance, the transition to turbulence takes place discontinuously at some critical values of the parameters of the system. The critical boundaries between different regimes (laminar, turbulent and fully turbulent) of the system are calculated on the parameter space. Windows of turbulence are present on some ranges of the coupling parameter. The system also exhibits nontrivial collective behavior. A map for the instantaneous fraction of turbulent elements is proposed. This map describes many of the observed properties of the system.

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