Recurrence plots for the analysis of complex systems
TL;DR: The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research, and detail the analysis of data and indicate possible difficulties and pitfalls.
About: This article is published in Physics Reports.The article was published on 2007-01-01. It has received 2993 citations till now. The article focuses on the topics: Recurrence quantification analysis & Recurrence plot.
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1,620 citations
01 Mar 1995
TL;DR: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series and results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages.
Abstract: : This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)
1,545 citations
1,188 citations
University of Bremen1, Potsdam Institute for Climate Impact Research2, University of Potsdam3, University College London4, University of Padua5, Leibniz Institute of Marine Sciences6, University of St Andrews7, University of Exeter8, National Oceanography Centre, Southampton9, National Institute of Geophysics and Volcanology10, University of Cambridge11, University of Kiel12, University of Edinburgh13, University of Bristol14, Utrecht University15, Oregon State University16, Tongji University17, University of Hawaii18, University of California, Santa Cruz19
TL;DR: A new, highly resolved, astronomically dated, continuous composite of benthic foraminifer isotope records developed in the authors' laboratories reveals the key role that polar ice volume plays in the predictability of Cenozoic climate dynamics.
Abstract: Much of our understanding of Earth's past climate comes from the measurement of oxygen and carbon isotope variations in deep-sea benthic foraminifera. Yet, long intervals in existing records lack the temporal resolution and age control needed to thoroughly categorize climate states of the Cenozoic era and to study their dynamics. Here, we present a new, highly resolved, astronomically dated, continuous composite of benthic foraminifer isotope records developed in our laboratories. Four climate states-Hothouse, Warmhouse, Coolhouse, Icehouse-are identified on the basis of their distinctive response to astronomical forcing depending on greenhouse gas concentrations and polar ice sheet volume. Statistical analysis of the nonlinear behavior encoded in our record reveals the key role that polar ice volume plays in the predictability of Cenozoic climate dynamics.
655 citations
TL;DR: In this article, a new approach for analyzing the structural properties of time series from complex systems is presented, which can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases.
Abstract: This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis.
548 citations
References
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TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
16,554 citations
"Recurrence plots for the analysis o..." refers methods in this paper
...5) • The Lorenz system [78] ẋ = − (x − y), ẏ = − xz + rx − y, ż = xy − bz....
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...03 [78]: (A) RP by using the L∞-norm, (B) RP by using the L1-norm, (C) RP by using the L2-norm, (D) RP by using a fixed amount of nearest neighbours (FAN), (E) RP by using a threshold corridor [εin, εout], (F) perpendicular RP (L2-norm), (G) order patterns RP (m = 3, 1, 2, 3 = 9), (H) distance plot (unthresholded RP, L2-norm), (I) ordinal RP (m = 1, = 5), (J) RP where the y-axis represents the relative time distances to the next recurrence points but not their absolute time (“close returns plot”, L2-norm)....
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01 Jan 1981
9,756 citations
"Recurrence plots for the analysis o..." refers background in this paper
...phase space has to be reconstructed [43,44]....
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...If m 2D2 +1, where D2 is the correlation dimension of the attractor, Takens’ theorem and several extensions of it, guarantee the existence of a diffeomorphism between the original and the reconstructed attractor [44,45]....
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TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
Abstract: Certain subsystems of nonlinear, chaotic systems can be made to synchronize by linking them with common signals. The criterion for this is the sign of the sub-Lyapunov exponents. We apply these ideas to a real set of synchronizing chaotic circuits.
9,201 citations
Book•
01 Jan 1993
TL;DR: This book presents a meta-modelling framework for speech recognition that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of manually modeling speech.
Abstract: 1. Fundamentals of Speech Recognition. 2. The Speech Signal: Production, Perception, and Acoustic-Phonetic Characterization. 3. Signal Processing and Analysis Methods for Speech Recognition. 4. Pattern Comparison Techniques. 5. Speech Recognition System Design and Implementation Issues. 6. Theory and Implementation of Hidden Markov Models. 7. Speech Recognition Based on Connected Word Models. 8. Large Vocabulary Continuous Speech Recognition. 9. Task-Oriented Applications of Automatic Speech Recognition.
8,442 citations
"Recurrence plots for the analysis o..." refers background in this paper
...The purpose was to match or align two sequences [83,84]....
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Book•
01 Jan 2001TL;DR: This work discusseschronization of complex dynamics by external forces, which involves synchronization of self-sustained oscillators and their phase, and its applications in oscillatory media and complex systems.
Abstract: Preface 1. Introduction Part I. Synchronization Without Formulae: 2. Basic notions: the self-sustained oscillator and its phase 3. Synchronization of a periodic oscillator by external force 4. Synchronization of two and many oscillators 5. Synchronization of chaotic systems 6. Detecting synchronization in experiments Part II. Phase Locking and Frequency Entrainment: 7. Synchronization of periodic oscillators by periodic external action 8. Mutual synchronization of two interacting periodic oscillators 9. Synchronization in the presence of noise 10. Phase synchronization of chaotic systems 11. Synchronization in oscillatory media 12. Populations of globally coupled oscillators Part III. Synchronization of Chaotic Systems: 13. Complete synchronization I: basic concepts 14. Complete synchronization II: generalizations and complex systems 15. Synchronization of complex dynamics by external forces Appendix 1. Discovery of synchronization by Christiaan Huygens Appendix 2. Instantaneous phase and frequency of a signal References Index.
6,438 citations
"Recurrence plots for the analysis o..." refers background or methods or result in this paper
...This is in agreement with the criterion for PS via Lyapunov exponents i [133]: 4 becomes negative at ≈ 0....
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...Increasing the coupling strength, PS can be obtained by the transition of one of the zero Lyapunov exponents to negative values, indicating the establishment of a relationship between the phases [133]....
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..., the analytical signal approach [133] and compare them with sj i = | xi − sj yi |....
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...33; the mean frequencies 1 and 2 are calculated as proposed in [133])....
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...Then the phase can be identified with the angle of rotation [133,148]...
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