title: Discontinuous attractor dimension at the synchronization transition of time-delayed chaotic systems.
abstract: The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents for iterated maps and for two coupled semiconductor lasers. We argue that the Kaplan-Yorke dimension must be discontinuous at the transition and compare it to the correlation dimension. For a system of Bernoulli maps, we indeed find a jump in the correlation dimension. The magnitude of the discontinuity in the Kaplan-Yorke dimension is calculated for networks of Bernoulli units as a function of the network size. Furthermore, the scaling of the Kaplan-Yorke dimension as well as of the Kolmogorov entropy with system size and time delay is investigated.
authors.affiliation: Institute of Theoretical Physics, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany. steffen.zeeb@physik.uni-wuerzburg.de
authors.forename: Steffen
authors.initials: S
authors.lastname: Zeeb
authors.forename: Thomas
authors.initials: T
authors.lastname: Dahms
authors.forename: Valentin
authors.initials: V
authors.lastname: Flunkert
authors.forename: Eckehard
authors.initials: E
authors.lastname: Schöll
authors.forename: Ido
authors.initials: I
authors.lastname: Kanter
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Kinzel