So far, we have considered only systems which are not distributed (i.e. are described by a finite set of differential equations). However, the majority of the results obtained are also applicable to distributed active systems, provided that spatial coherence of the patterns is maintained. Because of the long-range spatial order, the dynamics of coherent patterns can be effectively described by models involving only a small number of independent variables. As we already know, this does not exclude that the temporal behavior of a pattern will be chaotic (i.e. that long-range temporal order will be absent). In the latter case, the resulting regime can be described as “early” (or few-mode) turbulence.
KeywordsFractal Dimension Lyapunov Exponent Strange Attractor Spatial Coherence Correlation Radius
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