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

AutorZeeb, Steffen; Dahms, Thomas; Flunkert, Valentín ; Schöll, Eckehard; Kanter, Ido; Kinzel, Wolfgang
Fecha de publicación10-abr-2013
EditorAmerican Physical Society
CitaciónPhysical Review - Section E - Statistical Nonlinear and Soft Matter Physics 87(4): 042910 (2013)
ResumenThe 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.
Versión del editorhttp://dx.doi.org/10.1103/PhysRevE.87.042910
URIhttp://hdl.handle.net/10261/116774
DOI10.1103/PhysRevE.87.042910
Identificadoresdoi: 10.1103/PhysRevE.87.042910
issn: 1539-3755
e-issn: 1550-2376
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