Global synchronisation in translation invariant coupled map lattices

Bastien Fernandez (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

A sufficient condition for global synchronisation in coupled map lattices (CML) with translation invariant coupling and arbitrary individual map is proved. As in [Jost \& Joy, 2001] where CML with reflection invariant couplings are considered, the condition only involves the linearised dynamics in the diagonal, namely for all points in the diagonal, the derivative must be contractive in all transverse directions. In addition to this result, a (weaker) condition that ensures the CML attractor to be composed of either 2-periodic or constant configurations, is also obtained.

Domaines: Dynamique Chaotique [nlin.CD]

Bastien Fernandez. Global synchronisation in translation invariant coupled map lattices. International journal of bifurcation and chaos in applied sciences and engineering , 2008, 18, pp.3455-3459. ⟨hal-00261306⟩