Discontinuous Attractor Dimension at the Synchronization Transition of Time-Delayed Chaotic Systems
| Autor: | Valentin Flunkert, Wolfgang Kinzel, Steffen Zeeb, Thomas Dahms, Eckehard Schöll, Ido Kanter |
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| Rok vydání: | 2012 |
| Předmět: |
Correlation dimension
Mathematical analysis Minkowski–Bouligand dimension Dimension function FOS: Physical sciences Lyapunov exponent Nonlinear Sciences - Chaotic Dynamics Nonlinear Sciences::Chaotic Dynamics symbols.namesake Bernoulli's principle Dimension (vector space) Hausdorff dimension Attractor symbols Chaotic Dynamics (nlin.CD) Mathematics |
| Zdroj: | Digital.CSIC. Repositorio Institucional del CSIC instname |
| DOI: | 10.48550/arxiv.1210.2821 |
| Popis: | 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. © 2013 American Physical Society. |
| Databáze: | OpenAIRE |
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