Wavelet phase synchronization and chaoticity.
It has been shown that the so-called "wavelet phase" (or "time-scale") synchronization of chaotic signals is actually synchronization of smoothed functions with reduced chaotic fluctuations. This fact is based on the representation of the wavelet transform with the Morlet wavelet as a solution of the Cauchy problem for a simple diffusion equation with initial condition in a form of harmonic function modulated by a given signal. The topological background of the resulting effect is discussed. It is argued that the wavelet phase synchronization provides information about the synchronization of an averaged motion described by bounding tori instead of the fine-level classical chaotic phase synchronization.
Postnikov
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Department of Theoretical Physics, Kursk State University, 305000 Kursk, Russia. postnicov@gmail.com
D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D015233:Models, Statistical; D009038:Motion; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods; D012815:Signal Processing, Computer-Assisted; D013499:Surface Properties