Synchronization time in a hyperbolic dynamical system with long-range interactions
arXiv:1004.3160 · doi:10.1016/j.physa.2010.06.051
Abstract
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. We examine carefully the sychronization time and show that a inadequate observation of the system evolution leads to wrong results. We present both careful numerical experiments and a rigorous mathematical explanation confirming this fact, allowing for a generalization involving hyperbolic coupled map lattices.
22 pages (preprint format), 4 figures - accepted for publication in Physica A (June 28, 2010)