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

被引：5

作者：

Zeeb, Steffen ^{[1
]}

Dahms, Thomas ^{[2
]}

Flunkert, Valentin ^{[2
,3
]}

Schoell, Eckehard ^{[2
]}

Kanter, Ido ^{[4
]}

Kinzel, Wolfgang ^{[1
]}

机构：

[1] Univ Wurzburg, Inst Theoret Phys, D-97074 Wurzburg, Germany

[2] Tech Univ Berlin, Inst Theoret Phys, D-10623 Berlin, Germany

[3] IFISC UIB CSIC, Inst Fis Interdisciplinar & Sistemas Complejos, E-07122 Palma de Mallorca, Spain

[4] Bar Ilan Univ, Dept Phys, IL-52900 Ramat Gan, Israel

来源：

PHYSICAL REVIEW E | 2013年 / 87卷 / 04期

关键词：

Time delay;

D O I：

10.1103/PhysRevE.87.042910

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

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. DOI: 10.1103/PhysRevE.87.042910

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页数：10

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