Spatial correlations of synchronization errors in extended chaotic systemsI. G. Szendro1, M. A. Rodríguez2 and J. M. López2
1 Max-Planck-Institut für Physik Komplexer Systeme - Nöthnitzer Straße 38, D-01187 Dresden, Germany, EU
2 Instituto de Física de Cantabria (IFCA), CSIC-UC - E-39005 Santander, Spain, EU
received 9 December 2008; accepted in final form 1 April 2009; published April 2009
published online 6 May 2009
We discuss the temporal evolution of correlations of synchronization errors in spatially extended chaotic systems near (and below) the synchronization transition. We exploit the fact that, by construction, synchronization errors are finite perturbations of the coupled system in order to analyze the dynamics of the error and how their properties are determined by the nearby phase transition. We introduce a novel diagram plot that allows us to identify the transition universality class in a very intuitive and computationally inexpensive way.
05.45.Jn - High-dimensional chaos.
05.45.Xt - Synchronization; coupled oscillators.
68.35.Ct - Interface structure and roughness.
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