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 Space-Time Chaos
Volker Ahlers and Arkady Pikovsky
Department of Physics, University of Potsdam, Postfach 601553, D-14415 Potsdam, Germany
(Received 24 October 2001; published 7 June 2002)
We study two coupled spatially extended dynamical systems which exhibit space-time 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 one-dimensional systems is found to be
generically in the universality class of the Kardar-Parisi-Zhang equation with a growth-limiting 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 .
It has been observed in lasers, electronic circuits, and
chemical reactions . In recent years, the synchroniza-
tion of spatially extended chaotic systems has attracted
particular interest . Experimentally, the most promis-
ing systems to observe this phenomenon are optical ones.
Indeed, broad-area semiconductor lasers  demonstrate