Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/5374
Title: Geometric and dynamic perspectives on phase-coherent and noncoherent chaos
Authors: Zou, Y
Donner, RV
Kurths, J
Issue Date: Mar-2012
Source: Chaos, Apr. 2012, v. 22, no. 1, 013115, p. 1-12
Abstract: Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.
Keywords: Chao
Geometry
Nonlinear dynamical systems
Numerical analysis
Time series
Publisher: American Institute of Physics
Journal: Chaos 
ISSN: 1054-1500
EISSN: 1089-7682
DOI: 10.1063/1.3677367
Rights: © 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Yong Zou, Reik V. Donner and Jürgen Kurths, Chaos: an interdisciplinary journal of nonlinear science 22, 013115 (2012) and may be found at http://link.aip.org/link/?cha/22/013115
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