Estimating the Lyapunov spectrum of time delay feedback systems from scalar time series

1999 ◽  
Vol 60 (2) ◽  
pp. 1563-1566 ◽  
Author(s):  
Rainer Hegger
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Lyapunov Spectrum ◽  
Feedback Systems ◽  
Scalar Time Series

scholarly journals Machine Learning of Time Series Using Time-Delay Embedding and Precision Annealing

2019 ◽  
Vol 31 (10) ◽  
pp. 2004-2024 ◽  
Author(s):  
Alexander J. A. Ty ◽  
Zheng Fang ◽  
Rivver A. Gonzalez ◽  
Paul. J. Rozdeba ◽  
Henry D. I. Abarbanel
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Time Delay ◽  
Global Minimum ◽  
Statistical Data ◽  
Dimensional Space ◽  
Network Models ◽  
Multilayer Perceptrons ◽  
Task Time ◽  
Scalar Time Series

Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. We borrow two techniques used in statistical data assimilation in order to accomplish this task: time-delay embedding to prepare our input data and precision annealing as a training method. The precision annealing approach identifies the global minimum of the action ([Formula: see text]). In this way, we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series [Formula: see text] and, using methods of nonlinear time series analysis, show how to produce a [Formula: see text]-dimensional time-delay embedding space in which the time series has no false neighbors as does the observed [Formula: see text] time series. In that [Formula: see text]-dimensional space, we explore the use of feedforward multilayer perceptrons as network models operating on [Formula: see text]-dimensional input and producing [Formula: see text]-dimensional outputs.

scholarly journals COMPUTING OF LYAPUNOV EXPONENTS TECHNIQUES USING NEURAL NETWORKS

2014 ◽  
pp. 93-98
Author(s):  
Vladimir Golovko ◽  
Yury Savitsky
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
Time Series ◽  
Lyapunov Exponents ◽  
Multilayer Perceptron ◽  
Lyapunov Spectrum ◽  
Scalar Time Series

The authors examine neural network techniques for computing of Lyapunov spectrum using observations from unknown dynamical system. Such an approach is based on applying of multilayer perceptron (MLP) for forecasting the next state of dynamical system from the previous one. It allows for evaluating the Lyapunov spectrum of unknown dynamical system accurately and efficiently only by using scalar time series. The results of experiments are discussed.

scholarly journals Time-Delay Identification Using Multiscale Ordinal Quantifiers

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 969
Author(s):  
Miguel C. Soriano ◽  
Luciano Zunino
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Real World ◽  
Propagation Speed ◽  
Real World Data ◽  
External Observer ◽  
The North ◽  
Weather Phenomenon ◽  
The North Atlantic Oscillation ◽  
Finite Propagation Speed

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.

Identification of Synchronicity in Deterministic Chaotic Attractors for the Downscaling Process in the Bogotá River Basin

2021 ◽  
Author(s):  
Santiago Duarte ◽  
Gerald Corzo ◽  
Germán Santos
Keyword(s):  
Time Series ◽  
Time Delay ◽  
River Basin ◽  
Spatial Scales ◽  
Climatic Variables ◽  
Chaotic Attractors ◽  
Multiple Attractors ◽  
Nearest Neighbours ◽  
Basin Scale ◽  
Non Linear

<p>Bogotá’s River Basin, it’s an important basin in Cundinamarca, Colombia’s central region. Due to the complexity of the dynamical climatic system in tropical regions, can be difficult to predict and use the information of GCMs at the basin scale. This region is especially influenced by ENSO and non-linear climatic oscillation phenomena. Furthermore, considering that climatic processes are essentially non-linear and possibly chaotic, it may reduce the effectiveness of downscaling techniques in this region. </p><p>In this study, we try to apply chaotic downscaling to see if we could identify synchronicity that will allow us to better predict. It was possible to identify clearly the best time aggregation that can capture at the best the maximum relations between the variables at different spatial scales. Aside this research proposes a new combination of multiple attractors. Few analyses have been made to evaluate the existence of synchronicity between two or more attractors. And less analysis has considered the chaotic behaviour in attractors derived from climatic time series at different spatial scales. </p><p>Thus, we evaluate general synchronization between multiple attractors of various climate time series. The Mutual False Nearest Neighbours parameter (MFNN) is used to test the “Synchronicity Level” (existence of any type of synchronization) between two different attractors. Two climatic variables were selected for the analysis: Precipitation and Temperature. Likewise, two information sources are used: At the basin scale, local climatic-gauge stations with daily data and at global scale, the output of the MPI-ESM-MR model with a spatial resolution of 1.875°x1.875° for both climatic variables (1850-2005). In the downscaling process, two RCP (Representative Concentration Pathways)  scenarios are used, RCP 4.5 and RCP 8.5.</p><p>For the attractor’s reconstruction, the time-delay is obtained through the  Autocorrelation and the Mutual Information functions. The False Nearest Neighbors method (FNN) allowed finding the embedding dimension to unfold the attractor. This information was used to identify deterministic chaos at different times (e.g. 1, 2, 3 and 5 days) and spatial scales using the Lyapunov exponents. These results were used to test the synchronicity between the various chaotic attractor’s sets using the MFNN method and time-delay relations. An optimization function was used to find the attractor’s distance relation that increases the synchronicity between the attractors.  These results provided the potential of synchronicity in chaotic attractors to improve rainfall and temperature downscaling results at aggregated daily-time steps. Knowledge of loss information related to multiple reconstructed attractors can provide a better construction of downscaling models. This is new information for the downscaling process. Furthermore, synchronicity can improve the selection of neighbours for nearest-neighbours methods looking at the behaviour of synchronized attractors. This analysis can also allow the classification of unique patterns and relationships between climatic variables at different temporal and spatial scales.</p>

scholarly journals Synchronization Measure Based on a Geometric Approach to Attractor Embedding Using Finite Observation Windows

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Inga Timofejeva ◽  
Kristina Poskuviene ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Time Delays ◽  
Geometric Approach ◽  
Optimal Time ◽  
Effective Algorithm ◽  
Geometrical Properties ◽  
Finite Observation

A simple and effective algorithm for the identification of optimal time delays based on the geometrical properties of the embedded attractor is presented in this paper. A time series synchronization measure based on optimal time delays is derived. The approach is based on the comparison of optimal time delay sequences that are computed for segments of the considered time series. The proposed technique is validated using coupled chaotic Rössler systems.

News Article Based Industry Risk Index Prediction for Industry-Specific Evaluation

2021 ◽  
Author(s):  
Kyungwon Kim ◽  
Kyoungro Yoon
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Evaluation Method ◽  
Time Series Data ◽  
Risk Index ◽  
News Article ◽  
Series Data ◽  
Specific Interest ◽  
Analysis Model ◽  
Long Time

The existing industry evaluation method utilizes the method of collecting the structured information such as the financial information of the companies included in the relevant industry and deriving the industrial evaluation index through the statistical analysis model. This method takes a long time to calculate the structured data and cause the time delay problem. In this paper, to solve this time delay problem, we derive monthly industry-specific interest and likability as a time series data type, which is a new industry evaluation indicator based on unstructured data. In addition, we propose a method to predict the industrial risk index, which is used as an important factor in industrial evaluation, based on derived industry-specific interest and likability time series data.

Sign in / Sign up

Export Citation Format

Share Document