Analysis of phase synchronization of coupled chaotic oscillators with empirical mode decomposition

Symplectic geometry spectrum analysis of nonlinear time series

Various time-series decomposition techniques, including wavelet transform, singular spectrum analysis, empirical mode decomposition and independent component analysis, have been developed for non-linear dynamic system analysis. In this paper, we describe a symplectic geometry spectrum analysis (SGSA) method to decompose a time series into a set of independent additive components. SGSA is performed in four steps: embedding, symplectic QR decomposition, grouping and diagonal averaging. The obtained components can be used for de-noising, prediction, control and synchronization. We demonstrate the effectiveness of SGSA in reconstructing and predicting two noisy benchmark nonlinear dynamic systems: the Lorenz and Mackey-Glass attractors. Examples of prediction of a decadal average sunspot number time series and a mechanomyographic signal recorded from human skeletal muscle further demonstrate the applicability of the SGSA method in real-life applications.

Order parameter for the transition from strong to weak generalized synchrony from empirical mode decomposition analysis

We examine driven nonlinear dynamical systems that are known to be in a state of generalized synchronization with an external drive. The chaotic time series of the response system are subject to empirical mode decomposition analysis. The instantaneous intrinsic mode frequencies (and their variance) present in these signals provide suitable order parameters for detecting the transition between the regimes of strong and weak generalized synchrony. Application is made to a variety of chaotically driven flows as well as maps.

Data analysis using a combination of independent component analysis and empirical mode decomposition

A combination of independent component analysis and empirical mode decomposition (ICA-EMD) is proposed in this paper to analyze low signal-to-noise ratio data. The advantages of ICA-EMD combination are these: ICA needs few sensory clues to separate the original source from unwanted noise and EMD can effectively separate the data into its constituting parts. The case studies reported here involve original sources contaminated by white Gaussian noise. The simulation results show that the ICA-EMD combination is an effective data analysis tool.