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

Citation
L. Brunnet et al., LONG-RANGE ORDER WITH LOCAL CHAOS IN LATTICES OF DIFFUSIVELY COUPLED ODES, Physica. D, 78(3-4), 1994, pp. 141-154
Citations number
43
Categorie Soggetti
Mathematical Method, Physical Science",Physics,"Physycs, Mathematical
Journal title
ISSN journal
01672789
Volume
78
Issue
3-4
Year of publication
1994
Pages
141 - 154
Database
ISI
SICI code
0167-2789(1994)78:3-4<141:LOWLCI>2.0.ZU;2-9
Abstract
The existence of non-trivial collective behavior in lattices of diffus ively coupled differential equations is investigated. For a two-dimens ional square lattice of Rossler systems, a rotating long-range order i s observed. This case is best described in terms of a complex Ginzburg -Landau (CGL) equation submitted to the local noise produced by the ch aotic Rossler units. The parameters of this CGL equation are estimated to be in the so-called ''Benjamin-Feir stable'' region. The collectiv e oscillation regime thus corresponds to the linearly-stable, spatiall y-homogeneous solution of the equivalent CGL equation. The possibility of more complex collective behavior in similar systems is discussed.