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Title: Phase coherence and attractor geometry of chaotic electrochemical oscillators
Authors: Zou, Y
Donner, RV
Wickramasinghe, M
Kiss, IZ
Small, M
Kurths, J
Issue Date: Sep-2012
Source: Chaos, Sept. 2012, v. 22, 033130, p. 1-13
Abstract: Chaotic attractors are known to often exhibit not only complex dynamics but also a complex geometry in phase space. In this work, we provide a detailed characterization of chaotic electrochemical oscillations obtained experimentally as well as numerically from a corresponding mathematical model. Power spectral density and recurrence time distributions reveal a considerable increase of dynamic complexity with increasing temperature of the system, resulting in a larger relative spread of the attractor in phase space. By allowing for feasible coordinate transformations, we demonstrate that the system, however, remains phase-coherent over the whole considered parameter range. This finding motivates a critical review of existing definitions of phase coherence that are exclusively based on dynamical characteristics and are thus potentially sensitive to projection effects in phase space. In contrast, referring to the attractor geometry, the gradual changes in some fundamental properties of the system commonly related to its phase coherence can be alternatively studied from a purely structural point of view. As a prospective example for a corresponding framework, recurrence network analysis widely avoids undesired projection effects that otherwise can lead to ambiguous results of some existing approaches to studying phase coherence. Our corresponding results demonstrate that since temperature increase induces more complex chaotic chemical reactions, the recurrence network properties describing attractor geometry also change gradually: the bimodality of the distribution of local clustering coefficients due to the attractor’s band structure disappears, and the corresponding asymmetry of the distribution as well as the average path length increase.
Keywords: Chaos
Complex networks
Numerical analysis
Publisher: American Institute of Physics
Journal: Chaos 
ISSN: 1054-1500
EISSN: 1089-7682
DOI: 10.1063/1.4747707
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 Y. Zou et al., Chaos: an interdisciplinary journal of nonlinear science 22, 033130 (2012) and may be found at
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