Discontinuous attractor dimension at the synchronization transition of time-delayed chaotic systems

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....

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Veröffentlicht in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2013-04, Vol.87 (4), p.042910-042910, Article 042910
Hauptverfasser: Zeeb, Steffen, Dahms, Thomas, Flunkert, Valentin, Schöll, Eckehard, Kanter, Ido, Kinzel, Wolfgang
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container_title Physical review. E, Statistical, nonlinear, and soft matter physics
container_volume 87
creator Zeeb, Steffen
Dahms, Thomas
Flunkert, Valentin
Schöll, Eckehard
Kanter, Ido
Kinzel, Wolfgang
description 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.
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