2 research outputs found
New way to achieve chaotic synchronization in spatially extended systems
We study the spatio-temporal behavior of simple coupled map lattices with
periodic boundary conditions. The local dynamics is governed by two maps,
namely, the sine circle map and the logistic map respectively. It is found that
even though the spatial behavior is irregular for the regularly coupled
(nearest neighbor coupling) system, the spatially synchronized (chaotic
synchronization) as well as periodic solution may be obtained by the
introduction of three long range couplings at the cost of three nearest
neighbor couplings.Comment: 5 pages (revtex), 7 figures (eps, included
Synchronisation in Coupled Sine Circle Maps
We study the spatially synchronized and temporally periodic solutions of a
1-d lattice of coupled sine circle maps. We carry out an analytic stability
analysis of this spatially synchronized and temporally periodic case and obtain
the stability matrix in a neat block diagonal form. We find spatially
synchronized behaviour over a substantial range of parameter space. We have
also extended the analysis to higher spatial periods with similar results.
Numerical simulations for various temporal periods of the synchronized
solution, reveal that the entire structure of the Arnold tongues and the
devil's staircase seen in the case of the single circle map can also be
observed for the synchronized coupled sine circle map lattice. Our formalism
should be useful in the study of spatially periodic behaviour in other coupled
map lattices.Comment: uuencoded, 1 rextex file 14 pages, 3 postscript figure