Discontinuous Attractor Dimension at the Synchronization Transition of   Time-Delayed Chaotic Systems
  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. 
Steffen Zeeb, Thomas Dahms, Valentin Flunkert, Eckehard Sch\"oll, Ido   Kanter, Wolfgang Kinzel
nlin.CD