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

AuthorsZeeb, Steffen; Dahms, Thomas; Flunkert, Valentín ; Schöll, Eckehard; Kanter, Ido; Kinzel, Wolfgang
Issue Date10-Apr-2013
PublisherAmerican Physical Society
CitationPhysical Review - Section E - Statistical Nonlinear and Soft Matter Physics 87(4): 042910 (2013)
AbstractThe 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. © 2013 American Physical Society.
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevE.87.042910
Identifiersdoi: 10.1103/PhysRevE.87.042910
issn: 1539-3755
e-issn: 1550-2376
Appears in Collections:(IFISC) Artículos
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