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Causal decomposition depicts a cause-effect relationship that is not based on the concept of prediction, but based on the phase dependence of time series. It has been validated in both stochastic and deterministic systems and is now anticipated for its application in the complex dynamic process. Here, we present an extension of causal decomposition in the mutual complex dynamic process: cause and effect of time series are inherited in the decomposition of intrinsic components in a similar time scale. Furthermore, we illustrate comparative studies with predominate methods used in neuroscience, and show the applicability of the method particularly to physiological time series in brain-muscle interactions, implying the potential to the causality analysis in the complex physiological process.
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled through mea
We employ the framework of the Koopman operator and dynamic mode decomposition to devise a computationally cheap and easily implementable method to detect transient dynamics and regime changes in time series. We argue that typically transient dynamic
In this paper, we explore how network centrality and network entropy can be used to identify a bifurcation network event. A bifurcation often occurs when a network undergoes a qualitative change in its structure as a response to internal changes or e
This paper presents a new array response control scheme named complex-coefficient weight vector orthogonal decomposition ($ textrm{C}^2textrm{-WORD} $) and its application to pattern synthesis. The proposed $ textrm{C}^2textrm{-WORD} $ algorithm is a
We investigate the predictability problem in dynamical systems with many degrees of freedom and a wide spectrum of temporal scales. In particular, we study the case of $3D$ turbulence at high Reynolds numbers by introducing a finite-size Lyapunov exp