Periodicity Manifestations in the Turbulent Regime of Globally Coupled Map Lattice

Details Periodicity Manifestations in the Turbulent Regime of Globally Coupled Map Lattice Periodicity Manifestations in the Turbulent Regime of Globally Coupled Map Lattice

2000-06-23

arxiv.org/abs/nlin/0006038v1

Nonlinear Sciences

Chaotic Dynamics

34 pages, 8 Postscript figures, all in GCML-MSCA.Zip

Scientific paper

10.1103/PhysRevE.62.3489

We revisit the globally coupled map lattice (GCML). We show that in the so called turbulent regime various periodic cluster attractor states are formed even though the coupling between the maps are very small relative to the non-linearity in the element maps. Most outstanding is a maximally symmetric three cluster attractor in period three motion (MSCA) due to the foliation of the period three window of the element logistic maps. An analytic approach is proposed which explains successfully the systematics of various periodicity manifestations in the turbulent regime. The linear stability of the period three cluster attractors is investigated.

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