Issue
EPL
Volume 87, Number 5, September 2009
Article Number 50002
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/87/50002
Published online 18 September 2009
EPL, 87 (2009) 50002
DOI: 10.1209/0295-5075/87/50002

Detecting generalized synchronization by the generalized angle

Zonghua Liu1, Jie Zhou1 and Toyonori Munakata2

1   Institute of Theoretical Physics and Department of Physics, East China Normal University Shanghai, 200062, China
2   Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University Kyoto 606-8501, Japan

zhliu@phy.ecnu.edu.cn

received 15 May 2009; accepted in final form 21 August 2009; published September 2009
published online 18 September 2009

Abstract
Although much progress has been made in analyzing complex systems, our analysis tools are not enough from the points of convenience and efficiency. We here introduce a novel tool, i.e., the generalized angle, to analyze complex systems and show that generalized synchronization can be measured by an order parameter depending only on the generalized angle of an arbitrary high-dimensional (n > 2) trajectory. For generalized synchronization, the order parameter will be close to unity. With the increase of coupling strength, the slope of the order parameter will have a drastic change at the transition point of generalized synchronization. Numerical simulations have confirmed the theoretical predictions.

PACS
05.45.Xt - Synchronization; coupled oscillators.
05.45.Tp - Time series analysis.

© EPLA 2009