 
Summary: VOLUME 88, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 24 JUNE 2002
Critical Properties of the Synchronization Transition in SpaceTime Chaos
Volker Ahlers and Arkady Pikovsky
Department of Physics, University of Potsdam, Postfach 601553, D14415 Potsdam, Germany
(Received 24 October 2001; published 7 June 2002)
We study two coupled spatially extended dynamical systems which exhibit spacetime chaos. The
transition to the synchronized state is treated as a nonequilibrium phase transition, where the average
synchronization error is the order parameter. The transition in onedimensional systems is found to be
generically in the universality class of the KardarParisiZhang equation with a growthlimiting term
("bounded KPZ"). For systems with very strong nonlinearities in the local dynamics, however, the
transition is found to be in the universality class of directed percolation.
DOI: 10.1103/PhysRevLett.88.254101 PACS numbers: 05.45.a, 05.40.Ca
The synchronization of chaotic systems has been a very
active field in nonlinear dynamics since its discovery [1].
It has been observed in lasers, electronic circuits, and
chemical reactions [2]. In recent years, the synchroniza
tion of spatially extended chaotic systems has attracted
particular interest [3]. Experimentally, the most promis
ing systems to observe this phenomenon are optical ones.
Indeed, broadarea semiconductor lasers [4] demonstrate
