# American Institute of Mathematical Sciences

May  2004, 4(2): 435-456. doi: 10.3934/dcdsb.2004.4.435

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

 1 Centre de Physique Theorique CNRS Luminy, Case 907 13288 Marseille CEDEX 09 2 Centre de Physique Theorique (FRUMAM), CNRS Luminy, Case 907, 13288 Marseille CEDEX 09, France

Received  October 2002 Revised  January 2003 Published  February 2004

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, upper and lower bounds of the corresponding symbolic systems are obtained. As a consequence, 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.
Citation: B. Fernandez, P. Guiraud. Route to chaotic synchronisation in coupled map lattices: Rigorous results. Discrete & Continuous Dynamical Systems - B, 2004, 4 (2) : 435-456. doi: 10.3934/dcdsb.2004.4.435
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