scholarly journals A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1191
Author(s):  
Colin Shea-Blymyer ◽  
Subhradeep Roy ◽  
Benjamin Jantzen
Keyword(s):  
Dynamical Systems ◽  
Structural Changes ◽  
Time Series Data ◽  
Partial Information ◽  
Series Data ◽  
Deterministic System ◽  
Deterministic Systems ◽  
Dynamical Features ◽  
Dynamical Properties ◽  
Well Posed

Many problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data.

scholarly journals Magnetospheric chaos and dynamical complexity response during storm time disturbance

2020 ◽  
Author(s):  
Irewola Aaron Oludehinwa ◽  
Olasunkanmi Isaac Olusola ◽  
Olawale Segun Bolaji ◽  
Olumide Olayinka Odeyemi ◽  
Abdullahi Ndzi Njah
Keyword(s):  
Time Series ◽  
Solar Wind ◽  
Geomagnetic Storm ◽  
Time Series Data ◽  
Geomagnetic Storms ◽  
Approximate Entropy ◽  
Series Data ◽  
Dynamical Complexity ◽  
Significant Difference ◽  
Dynamical Features

Abstract. In this study, we examine the magnetospheric chaos and dynamical complexity response in the disturbance storm time (Dst) and solar wind electric field (VBs) during different categories of geomagnetic storm (minor, moderate and major geomagnetic storm). The time series data of the Dst and VBs are analyzed for the period of nine years using nonlinear dynamics tools (Maximal Lyapunov Exponent, MLE, Approximate Entropy, ApEn and Delay Vector Variance, DVV). We found a significant trend between each nonlinear parameter and the categories of geomagnetic storm. The MLE and ApEn values of the Dst indicate that chaotic and dynamical complexity response are high during minor geomagnetic storms, reduce at moderate geomagnetic storms and declined further during major geomagnetic storms. However, the MLE and ApEn values obtained in VBs indicate that chaotic and dynamical complexity response are high with no significant difference between the periods that are associate with minor, moderate and major geomagnetic storms. The test for nonlinearity in the Dst time series during major geomagnetic storm reveals the strongest nonlinearity features. Based on these findings, the dynamical features obtained in the VBs as input and Dst as output of the magnetospheric system suggest that the magnetospheric dynamics is nonlinear and the solar wind dynamics is consistently stochastic in nature.

scholarly journals Extracting Nonlinear Dynamics from Psychological and Behavioral Time Series Through HAVOK Analysis

2020 ◽  
Author(s):  
Robert Glenn Moulder ◽  
Elena Martynova ◽  
Steven M. Boker
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Data ◽  
Nonlinear Dynamical Systems ◽  
Series Data ◽  
Alternative View ◽  
Unified Framework ◽  
Nonlinear Dynamical ◽  
Depth Analysis ◽  
Analysis Of Time Series

Analytical methods derived from nonlinear dynamical systems, complexity, and chaos theories offer researchers a framework for in-depth analysis of time series data. However, relatively few studies involving time series data obtained from psychological and behavioral research employ such methods. This paucity of application is due to a lack of general analysis frameworks for modeling time series data with strong nonlinear components. In this article, we describe the potential of Hankel alternative view of Koopman (HAVOK) analysis for solving this issue. HAVOK analysis is a unified framework for nonlinear dynamical systems analysis of time series data. By utilizing HAVOK analysis, researchers may model nonlinear time series data in a linear framework while simultaneously reconstructing attractor manifolds and obtaining a secondary time series representing the amount of nonlinear forcing occurring in a system at any given time. We begin by showing the mathematical underpinnings of HAVOK analysis and then show example applications of HAVOK analysis for modeling time series data derived from real psychological and behavioral studies.

scholarly journals Brief Communication: Breeding vectors in the phase space reconstructed from time series data

2015 ◽  
Vol 2 (4) ◽  
pp. 1301-1315
Author(s):  
E. Lynch ◽  
D. Kaufman ◽  
A. S. Sharma ◽  
E. Kalnay ◽  
K. Ide
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Evolution Equations ◽  
Nearest Neighbor ◽  
Time Series Data ◽  
Series Data ◽  
Nonlinear Instability ◽  
Bred Vectors ◽  
Dynamical Properties ◽  
A New Technique

Abstract. Bred vectors characterize the nonlinear instability of dynamical systems and so far have been computed only for systems with known evolution equations. In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the standard and nearest-neighbor breeding are shown to be similar, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone.

scholarly journals Observation error covariance specification in dynamical systems for data assimilation using recurrent neural networks

2021 ◽  
Author(s):  
Sibo Cheng ◽  
Mingming Qiu
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Recurrent Neural Networks ◽  
Time Series Data ◽  
Series Data ◽  
Observation Data ◽  
Observation Error ◽  
Error Covariance

AbstractData assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modeling is an important element in data assimilation algorithms which can considerably impact the forecasting accuracy. The estimation of these covariances, which usually relies on empirical assumptions and physical constraints, is often imprecise and computationally expensive, especially for systems of large dimensions. In this work, we propose a data-driven approach based on long short term memory (LSTM) recurrent neural networks (RNN) to improve both the accuracy and the efficiency of observation covariance specification in data assimilation for dynamical systems. Learning the covariance matrix from observed/simulated time-series data, the proposed approach does not require any knowledge or assumption about prior error distribution, unlike classical posterior tuning methods. We have compared the novel approach with two state-of-the-art covariance tuning algorithms, namely DI01 and D05, first in a Lorenz dynamical system and then in a 2D shallow water twin experiments framework with different covariance parameterization using ensemble assimilation. This novel method shows significant advantages in observation covariance specification, assimilation accuracy, and computational efficiency.

scholarly journals Fuzzy Counter Propagation Neural Network Control for a Class of Nonlinear Dynamical Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Vandana Sakhre ◽  
Sanjeev Jain ◽  
Vilas S. Sapkal ◽  
Dev P. Agarwal
Keyword(s):  
Neural Network ◽  
Dynamical Systems ◽  
Time Series Data ◽  
Nonlinear Dynamical Systems ◽  
Back Propagation ◽  
Network Control ◽  
Series Data ◽  
Nonlinear Dynamical ◽  
Single Output ◽  
Propagation Network

Fuzzy Counter Propagation Neural Network (FCPN) controller design is developed, for a class of nonlinear dynamical systems. In this process, the weight connecting between the instar and outstar, that is, input-hidden and hidden-output layer, respectively, is adjusted by using Fuzzy Competitive Learning (FCL). FCL paradigm adopts the principle of learning, which is used to calculate Best Matched Node (BMN) which is proposed. This strategy offers a robust control of nonlinear dynamical systems. FCPN is compared with the existing network like Dynamic Network (DN) and Back Propagation Network (BPN) on the basis of Mean Absolute Error (MAE), Mean Square Error (MSE), Best Fit Rate (BFR), and so forth. It envisages that the proposed FCPN gives better results than DN and BPN. The effectiveness of the proposed FCPN algorithms is demonstrated through simulations of four nonlinear dynamical systems and multiple input and single output (MISO) and a single input and single output (SISO) gas furnace Box-Jenkins time series data.

scholarly journals The Structural Changes and Competitiveness of the Forest and Wood Sector in Baltic Countries within 1999-2016

2019 ◽  
Vol 25 (1) ◽  
Author(s):  
R Sirgmets ◽  
M Teder ◽  
Paavo Kaimre
Keyword(s):  
Time Series ◽  
Structural Changes ◽  
Time Series Data ◽  
Series Data ◽  
Total Output ◽  
Wood Processing ◽  
Baltic Countries ◽  
Primary Products ◽  
Introductory Part ◽  
Wood Sector

The structural changes and the competitiveness of forest and wood sector in three Baltic countries: Estonia, Latvia and Lithuania were analyzed in the period 1999-2016. Different concepts of competitiveness are discussed in the introductory part to find a proper approach for empirical analysis. Time series data of international trade from the Eurostat database were used to analyze the development of forest and wood sectors in Baltic countries. The relative trade advantage (RTA) index was applied for assessing the relative success of foreign trade, referred to aggregated EU28. The forest and wood sector of Baltic countries has mainly oriented to the mechanical wood processing, which formed 68% of Estonian, 64% of Latvian and 59% of Lithuanian total output value in 2015. However, the trends are dissimilar: the expanding of mechanical wood processing was remarkable in Estonia while in Latvia the forestry and logging, in Lithuania the paper and paper products increased their share.The value of exported goods by the forest and wood sector has increased more than 200% in Estonia and Latvia, and approximately 500% in Lithuania during the period from 1999 to 2016. At the same time the decrease of RTA index for primary products (forestry and logging) is common for all countries. Key words: forest and wood sector, competitiveness, Baltic countries, relative trade advantage index

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