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arXiv · 1210.2821

Discontinuous Attractor Dimension at the Synchronization Transition of Time-Delayed Chaotic Systems

Steffen Zeeb·Thomas Dahms·Valentin Flunkert·Eckehard Schöll·Ido Kanter·Wolfgang Kinzel
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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.

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Steffen Zeeb, Thomas Dahms, Valentin Flunkert, Eckehard Schöll, Ido Kanter, Wolfgang Kinzel. 2012-10-10. Discontinuous Attractor Dimension at the Synchronization Transition of Time-Delayed Chaotic Systems. https://doi.org/10.1103/physreve.87.042910

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