Collective patterns arising out of spatio-temporal chaos

Details Collective patterns arising out of spatio-temporal chaos Collective patterns arising out of spatio-temporal chaos

1995-04-10

arxiv.org/abs/chao-dyn/9504006v1

Nonlinear Sciences

Chaotic Dynamics

11 pages (Revtex) + 5 figures (postscript)

Scientific paper

10.1063/1.166169

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under a periodic boundary condition. Thus the spatial inhomogeneity of the statistical state arises through a spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.

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