Analysis of Synchronization Phenomena in Broadband Signals with Nonlinear Excitable Media
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Research Article Analysis of Synchronization Phenomena in Broadband Signals with Nonlinear Excitable Media Anton Chernihovskyi,1, 2 Christian E. Elger,1 and Klaus Lehnertz1, 2, 3 1 Department
of Epileptology, University of Bonn, Sigmund-Freud Street 25, 53105 Bonn, Germany for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany 3 Interdisciplinary Center for Complex Systems, University of Bonn, R¨ omerstr. 164, 53117 Bonn, Germany 2 Helmholtz-Institute
Correspondence should be addressed to Anton Chernihovskyi, [email protected] Received 23 September 2008; Revised 28 February 2009; Accepted 18 August 2009 Recommended by Ronald Tetzlaff We apply the method of frequency-selective excitation waves in excitable media to characterize synchronization phenomena in interacting complex dynamical systems by measuring coincidence rates of induced excitations. We relax the frequency-selectivity of excitable media and demonstrate two applications of the method to signals with broadband spectra. Findings obtained from analyzing time series of coupled chaotic oscillators as well as electroencephalographic (EEG) recordings from an epilepsy patient indicate that this method can provide an alternative and complementary way to estimate the degree of phase synchronization in noisy signals. Copyright © 2009 Anton Chernihovskyi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. Introduction Excitable media (EM) are spatially distributed excitable systems that can rapidly propagate excitations (suprathreshold impulses) over long distances without damping. Such traveling waves have been observed in many scientific contexts and—as it is now widely accepted—play an important role in information processing in many biological systems. EM are usually modeled as a collection of locally coupled units with excitable or threshold dynamics [1]. Neighboring units of the medium interact with each other via diffusion-like transport processes which, in many cases, results in a spatially homogeneous steady state. Recent studies extended the notion of excitability of EM to spatially distributed systems, whose unperturbed steady state resembles spatiotemporal chaos. This results in a steady state that actively destroys long-range spatiotemporal correlations and thus prevents the propagation of a single excitation. To generate and then to facilitate a wave-propagation phenomenon, the EM have to be driven with perturbations of appropriate amplitudes and
certain (resonant) frequencies. Thus, the phenomenon of frequency-selective excitation waves in EM [2–5] provides a possible way to extend the conventional amplitude-selective notion of excitability in dynamical systems. Applying an unknown signal as a local perturbation to the first unit of EM and measuring the number of excitations in the last unit provide a possibility to detect the presence of rhythmi
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