Route to chaotic synchronisation in coupled map lattices: Rigorous results

Details Route to chaotic synchronisation in coupled map lattices: Rigorous results Route to chaotic synchronisation in coupled map lattices: Rigorous results

2002-10-09

arxiv.org/abs/nlin/0210019v1

Nonlinear Sciences

Chaotic Dynamics

20 pages, 4 figures

Scientific paper

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an admissibility condition, approximations of the corresponding symbolic systems are obtained. These approximations imply that the topological entropy is located between two decreasing step functions of the coupling parameter. The analysis firstly applies to mappings with piecewise affine local maps which allow explicit expressions and, in a second step, is extended by continuity to mappings with piecewise smooth local maps.

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