Detection of synchronization for non-phase-coherent and non-stationary dataM. C. Romano1, M. Thiel1, J. Kurths1, I. Z. Kiss2 and J. L. Hudson2
1 Institute of Physics, University of Potsdam Am Neuen Palais 10, 14469 Potsdam, Germany
2 Department of Chemical Engineering, University of Virginia 102 Engineers Way, Charlottesville, VA 22904-479, USA
received 17 March 2005; accepted in final form 6 June 2005
published online 6 July 2005
We present a new method to detect phase as well as generalized synchronization in a wide class of complex systems. It is based on the recurrences of the system's trajectory to the neighborhood of a former state in phase space. We illustrate the applicability of the algorithm for the paradigmatic chaotic Rössler system in the funnel regime and for noisy data, where other methods to detect phase synchronization fail. Furthermore, we demonstrate for electrochemical experiments that the method can easily detect phase and generalized synchronization in non-phase-coherent and even non-stationary time series.
82.40.Bj - Oscillations, chaos, and bifurcations.
83.85.Ns - Data analysis (interconversion of data computation of relaxation and retardation spectra; time-temperature superposition, etc.).
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