Three nonlinear analysis techniques, including cross-recurrence plot, line of synchronization, and cross-wavelet transform, are proposed to estimate the coherent phase vibrations of nonlinear and non-stationary time series. The case study utilizes the monthly averages of sunspot areas during the time interval from May 1874 to August 2014. The following prominent results are found: (1) the phase-leading hemisphere of long-term sunspot areas has changed twice in the past 140 years, indicating that the hemispheric imbalances and apparent phase differences on both hemispheres are a prevalent behavior and are not anomalous; (2) the alternating regularity of hemispheric asynchronism exhibits a cyclical pattern of 4.5+3.5 cycles, and the magnetic flux excess in a certain hemisphere during the ascending branch of a cycle can be taken as an indication of the phase-leading hemisphere in this cycle. We firmly believe that powerful nonlinear approaches are more advanced than classical linear methods when they are combined to determine the dynamic complexity of nonlinear physical systems.
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Citation
Linhua Deng
"
Nonlinear estimation of coherent phase vibrations for statistical signals through multivariable analyses
", Proc. SPIE 9631, Seventh International Conference on Digital Image Processing (ICDIP 2015), 96312C (July 6, 2015); doi:10.1117/12.2196994; http://dx.doi.org/10.1117/12.2196994
