A directed weighted complex network for characterizing chaotic dynamics from time series

Gao, Zhong-Ke; Jin, Ningde

doi:10.1016/j.nonrwa.2011.08.029

Cited by 137 publications

(61 citation statements)

References 47 publications

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“…Paper [1] proposed a directed weighted complex network from time series. Multivariate weighted complex network analysis was proposed in paper [2] for characterizing nonlinear dynamic behavior in two-phase flow.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Model Equipped with the Minimum Cycle Decomposition Concept for Short-Term Forecasting of Electrical Load Time Series

Shen³

et al. 2017

Neural Process Lett

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Electricity load forecasting is an essential, however complicated work. Due to the influence of a large number of uncertain factors, it shows complicated nonlinear combination features. Therefore, it is difficult to improve the prediction accuracy and the tremendous breadth of applicability especially for using a single method. In order to improve the performance including accuracy and applicability of electricity load forecasting, in this paper, a concept named minimum cycle decomposition (MCD) that the raw data are grouped according to the minimum cycle was proposed for the first time. In addition, a hybrid prediction model (HMM) based on one-order difference, ensemble empirical model decomposition (EEMD), mind evolutionary computation (MEC) and wavelet neural network (WNN) was also proposed in this study. The HMM model consists of two parts. Part one, pre-processing, known as one order difference to remove the trend of subsequence and EEMD to reduce the noise, was performed by HMM model on each subset. Part two, the WNN optimized by MEC (WNN + MEC) was applied on resultant subseries. Finally, a number of different models were used as the comparative experiment to validate the effectiveness of the presented method, such as back propagation neural network (BP-1), BPNN combined MCD (BP-2), WNN combined MCD (WNNM), a HMM (DEEPLSSVM) based on one-order difference, EEMD, particle swarm optimization and least squares support vector machine and a hybrid model (DEESGRNN) based on one-order difference, EEMD, simulate anneal and generalized regression neural network. Certain evaluation measurements are taken into account to assess the performance. Experiments were carried out on QLD (Queensland) and NSW (New South Wales) electricity markets historical data, and the experimental results show that the MCD has the advantages of improving model accuracy and of generalization ability. In addition, the simulation results also suggested that the proposed hybrid model has better performance. B Zhaoshuang He

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Section: Introductionmentioning

confidence: 99%

A Hybrid Model Equipped with the Minimum Cycle Decomposition Concept for Short-Term Forecasting of Electrical Load Time Series

Shen³

et al. 2017

Neural Process Lett

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“…It is a particularly useful tool among the large set of concepts and methods dealing with multi-scale analysis of mono-and multi-variate time series, which include temporal multifractal analysis [19][20][21][22], directed weighted network representations of time series using the delayed coordinate embedding method combined with a distance that provides an adjacency matrix [23][24][25][26], and a variety of techniques at the intersection of nonlinear dynamical system theory, statistical time series analysis, fractals, cellular automata, machine learning methods, wavelet transform methods, fuzzy logic and more [27,28].…”

Section: Introductionmentioning

confidence: 99%

Early Warning Signals of Financial Crises with Multi-Scale Quantile Regressions of Log-Periodic Power Law Singularities

Zhang

Sornette

2015

SSRN Journal

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We augment the existing literature using the Log-Periodic Power Law Singular (LPPLS) structures in the log-price dynamics to diagnose financial bubbles by providing three main innovations. First, we introduce the quantile regression to the LPPLS detection problem. This allows us to disentangle (at least partially) the genuine LPPLS signal and the a priori unknown complicated residuals. Second, we propose to combine the many quantile regressions with a multi-scale analysis, which aggregates and consolidates the obtained ensembles of scenarios. Third, we define and implement the so-called DS LPPLS Confidence™ and Trust™ indicators that enrich considerably the diagnostic of bubbles. Using a detailed study of the "S&P 500 1987" bubble and presenting analyses of 16 historical bubbles, we show that the quantile regression of LPPLS signals contributes useful early warning signals. The comparison between the constructed signals and the price development in these 16 historical bubbles demonstrates their significant predictive ability around the real critical time when the burst/rally occurs.

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“…Various other methods have been developed to distinguish between deterministic chaos and noise [25][26][27][28][29] and applied to EEG data to detect seizure [25]. These positive and promising results, however, have not lead to any real application so far.…”

Section: Introductionmentioning

confidence: 99%

Reliability of unstable periodic orbit based control strategies in biological systems

Mishra

Hasse

Biswal

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems are now routinely used as evidence for low dimensional chaos . Extracting accurate dynamical information from the detected UPO trajectories are vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics. Unstable periodic orbits (UPOs) analysis has now become an established tool for detecting determinism in biological systems. If the system is truly deterministic, accurate UPO characteristics can be further used for application of control or anti control strategies with potential medical application. However, accurate biological time series analysis for UPOs critically depend on the length of data set, strength of noise, type of geometry, nonstationarity etc. In this work we show that it is possible to establish determinism through UPO analysis in presence of all these factors. However, the inaccuracy in the measured UPO parameters and non-stationarity nature of biological systems mean only adaptive control strategies are useful for successful chaos control in such systems. At the same time, comparable success of adaptive control strategies on a stochastic neural network model of epileptic slices demand more stringent criteria for linking adaptive control success with determinism.

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A directed weighted complex network for characterizing chaotic dynamics from time series

Cited by 137 publications

References 47 publications

A Hybrid Model Equipped with the Minimum Cycle Decomposition Concept for Short-Term Forecasting of Electrical Load Time Series

A Hybrid Model Equipped with the Minimum Cycle Decomposition Concept for Short-Term Forecasting of Electrical Load Time Series

Early Warning Signals of Financial Crises with Multi-Scale Quantile Regressions of Log-Periodic Power Law Singularities

Reliability of unstable periodic orbit based control strategies in biological systems

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