Synchronization time in a hyperbolic dynamical system with long-range interactions

Details Synchronization time in a hyperbolic dynamical system with long-range interactions Synchronization time in a hyperbolic dynamical system with long-range interactions

2010-04-19

arxiv.org/abs/1004.3160v2

Physica A, 389:5279(8) (2010)

Nonlinear Sciences

Chaotic Dynamics

22 pages (preprint format), 4 figures - accepted for publication in Physica A (June 28, 2010)

Scientific paper

10.1016/j.physa.2010.06.051

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.

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