scholarly journals Reconstructing bifurcation diagrams only from time-series data generated by electronic circuits in discrete-time dynamical systems

2020 ◽  
Vol 30 (1) ◽  
pp. 013128
Author(s):  
Y. Itoh ◽  
S. Uenohara ◽  
M. Adachi ◽  
T. Morie ◽  
K. Aihara
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Discrete Time ◽  
Time Series Data ◽  
Series Data ◽  
Electronic Circuits ◽  
Bifurcation Diagrams ◽  
Discrete Time Dynamical Systems

Analysis of Degenerate Chenciner Bifurcation

2020 ◽  
Vol 30 (16) ◽  
pp. 2050245
Author(s):  
G. Tigan ◽  
S. Lugojan ◽  
L. Ciurdariu
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Bifurcation Diagrams ◽  
Discrete Time Dynamical Systems

Degenerate Chenciner bifurcation in generic discrete-time dynamical systems is studied in this work. While the nondegenerate Chenciner bifurcation can be described by two bifurcation diagrams, the degeneracy we studied in this work gives rise to 32 different bifurcation diagrams.

scholarly journals Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London

2008 ◽  
Vol 5 (25) ◽  
pp. 885-897 ◽  
Author(s):  
Simon Cauchemez ◽  
Neil M Ferguson
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Continuous Time ◽  
Generation Time ◽  
Data Augmentation ◽  
Time Series Data ◽  
Observation Interval ◽  
Series Data ◽  
Time Model ◽  
Similar Time

We present a new statistical approach to analyse epidemic time-series data. A major difficulty for inference is that (i) the latent transmission process is partially observed and (ii) observed quantities are further aggregated temporally. We develop a data augmentation strategy to tackle these problems and introduce a diffusion process that mimicks the susceptible–infectious–removed (SIR) epidemic process, but that is more tractable analytically. While methods based on discrete-time models require epidemic and data collection processes to have similar time scales, our approach, based on a continuous-time model, is free of such constraint. Using simulated data, we found that all parameters of the SIR model, including the generation time, were estimated accurately if the observation interval was less than 2.5 times the generation time of the disease. Previous discrete-time TSIR models have been unable to estimate generation times, given that they assume the generation time is equal to the observation interval. However, we were unable to estimate the generation time of measles accurately from historical data. This indicates that simple models assuming homogenous mixing (even with age structure) of the type which are standard in mathematical epidemiology miss key features of epidemics in large populations.

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 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.

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