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A new algorithm is described for detecting hidden changes in the topological structure of the dynamics of a nonlinear system due to the perturbations in the driving signals. The proposed method is based on the use of a double sliding window and wavelet decomposition and calculates the Jensen–Shannon divergence between the probability distributions of the normalised wavelet coefficients of the first half of the sliding window and those of the second half of the sliding window. Applying the proposed approach to the Duffing and Hénon–Heiles systems, real-life signals showed their effectiveness at detecting small discontinuities in the dynamic behaviour of the system even when the system is chaotic. [ABSTRACT FROM AUTHOR]

In this study, we present a new method for assessing the functional connectivity between the drive and the noisy response chaotic oscillators with significant frequency mismatch. This method is based on the footprint of the drive oscillator on the response oscillator. Specifically, we calculate the magnitude squared coherence between the intrinsic frequency of the drive oscillator and the oscillation frequency of the dynamics of the spectral energy of the response oscillator. The spectral energy of the response oscillator is estimated using a modified S-transform algorithm with a short sliding window. We apply the proposed approach to master–slave Rössler systems and coupled Van der Pol oscillators with a frequency ratio of ∼ 1:4 and show that when the slave signal is contaminated with white Gaussian noise at different signal-to-noise ratios (SNR), the new algorithm is well suited to assess the presence of coupling with a priori known direction in noisy, unidirectionally coupled chaotic oscillators, especially in the case of weak and moderate coupling. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel algorithm for the detection changes in the spatio-spectral dynamics of a multivariate time series based on a sliced cross-bispectrum. The singular value decomposition is performed on the matrix of the sliced cross-bispectrum at every frequency of the bandwidth, and a 2D spectrum of the eigenvalues is obtained. The changes in the dynamics are translated into differences between the reference and current values of the 2D eigenvalue spectrum. Hellinger divergence as the measure of the distance between eigenvalue spectrum matrices is used. The performance of the proposed approach is tested on model data and applied to multi-channel electroencephalogram recordings from epilepsy patients to detect ictal states. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that the block circulant matrix decomposition technique makes the multivariate singular spectrum analysis (M-SSA) a well suited tool for detecting of changes of the correlation structure in non-stationary multivariate time series in the presence of high observational noise levels. The major drawback of M-SSA, that it operates on a large covariance matrix and becomes computationally expensive, can be avoided by reordering the Toeplitz-block covariance matrix into a block Toeplitz matrix, embedding this into a block circulant matrix and efficiently block-diagonalizing this by the means of the Fast Fourier Transform (FFT) using the well known algorithm. The overall degree of synchronization among multiple-channel signals is defined by the synchronization index (the S-estimator) of the rearranged and truncated eigenvalue spectrum. Throughout the experiment, the high capability of the proposed algorithm to detect the lag-synchronized state under the influence of strong noise is validated with simulated data-a network of time series generated by autoregressive models (AR) and a network of coupled chaotic Roessler oscillators. [ABSTRACT FROM AUTHOR]