Pseudo-periodic surrogate test to sample time series in stochastic softening Duffing oscillator

2006 ◽  
Vol 357 (3) ◽  
pp. 204-208 ◽  
Author(s):  
Chunbiao Gan
Keyword(s):  
Time Series ◽  
Duffing Oscillator ◽  
Sample Time

scholarly journals Periodicity Detection Method for Small-Sample Time Series Datasets

2010 ◽  
Vol 4 ◽  
pp. BBI.S5983 ◽  
Author(s):  
Daisuke Tominaga
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Small Sample ◽  
Detection Methods ◽  
Series Data ◽  
Computational Time ◽  
Signal Pathways ◽  
Periodicity Detection ◽  
Sampling Points ◽  
Sample Time

Time series of gene expression often exhibit periodic behavior under the influence of multiple signal pathways, and are represented by a model that incorporates multiple harmonics and noise. Most of these data, which are observed using DNA microarrays, consist of few sampling points in time, but most periodicity detection methods require a relatively large number of sampling points. We have previously developed a detection algorithm based on the discrete Fourier transform and Akaike's information criterion. Here we demonstrate the performance of the algorithm for small-sample time series data through a comparison with conventional and newly proposed periodicity detection methods based on a statistical analysis of the power of harmonics. We show that this method has higher sensitivity for data consisting of multiple harmonics, and is more robust against noise than other methods. Although “combinatorial explosion” occurs for large datasets, the computational time is not a problem for small-sample datasets. The MATLAB/GNU Octave script of the algorithm is available on the author's web site: http://www.cbrc.jp/%7Etominaga/piccolo/ .

scholarly journals Synchronisation phenomenon in three blades rotor driven by regular or chaotic oscillations

2018 ◽  
Vol 148 ◽  
pp. 06002
Author(s):  
Zofia Szmit ◽  
Jerzy Warmiński
Keyword(s):  
Time Series ◽  
Numerical Calculation ◽  
Duffing Oscillator ◽  
Equations Of Motion ◽  
Composite Beams ◽  
Chaotic Oscillations ◽  
Rotating System ◽  
Chaotic Motions ◽  
Structural Differences ◽  
Different Types

The goal of the paper is to analysed the influence of the different types of excitation on the synchronisation phenomenon in case of the rotating system composed of a rigid hub and three flexible composite beams. In the model is assumed that two blades, due to structural differences, are de-tuned. Numerical calculation are divided on two parts, firstly the rotating system is exited by a torque given by regular harmonic function, than in the second part the torque is produced by chaotic Duffing oscillator. The synchronisation phenomenon between the beams is analysed both either for regular or chaotic motions. Partial differential equations of motion are solved numerically and resonance curves, time series and Poincaré maps are presented for selected excitation torques.

Finding Unstable Fixed Points From Time Series Data

2003 ◽  
Author(s):  
Takaaki Maehara ◽  
Mikio Nakai
Keyword(s):  
Time Series ◽  
Fixed Points ◽  
Time Series Data ◽  
Piecewise Linear ◽  
Duffing Oscillator ◽  
Conley Index ◽  
Series Data ◽  
Experimental Time ◽  
Index Pairs ◽  
Experimental Time Series

This study employs topological methods to extract unstable fixed points in phase space from both numerical and experimental time series data. Conley index of an isolated invariant subset and the R-B method can determine unstable fixed points contained in strange attractor from numerical time series data. For experimental time series data, the theorem for the relationship between index pairs and Conley index enables one to predict them with acceptable accuracy. As a corollary, some results for Duffing oscillator and piecewise linear system are shown.

Regular nonlinear response of the driven Duffing oscillator to chaotic time series

2009 ◽  
Vol 18 (3) ◽  
pp. 958-968 ◽  
Author(s):  
Yuan Ye ◽  
Li Yue ◽  
Danilo P Mandic ◽  
Yang Bao-Jun
Keyword(s):  
Time Series ◽  
Nonlinear Response ◽  
Duffing Oscillator ◽  
Chaotic Time Series

scholarly journals Time Series Experiment Design Under One-Shot Sampling: The Importance of Condition Diversity

2019 ◽  
Author(s):  
Xiaohan Kang ◽  
Bruce Hajek ◽  
Faqiang Wu ◽  
Yoshie Hanzawa
Keyword(s):  
Time Series ◽  
Biological Data ◽  
Data Sets ◽  
Ratio Test ◽  
Single Individual ◽  
Individual Organism ◽  
Condition Effect ◽  
Multiple Samples ◽  
Sample Time ◽  
Multiple Conditions

AbstractMany biological data sets are prepared using one-shot sampling, in which each individual organism provides only one sample. Time series therefore do not follow trajectories of individuals over time. However, samples collected at different times from individuals grown/raised under the same conditions share the same perturbations of the biological processes, and hence behave as surrogates for multiple samples from a single individual at different times. This implies the importance of growing/raising individuals under multiple conditions if one-shot sampling is used. This paper models the condition effect explicitly by correlated perturbations in the variations driving the expression dynamics, quantifies the performance of the generalized likelihood-ratio test for network structure, and illustrates the difficulty in network reconstruction under one-shot sampling when the condition effect is absent.

scholarly journals Determining the Pension Benefit Obligation of a Defined Benefit Plan: Applying a Multivariate ARIMA Stochastic Model

2022 ◽  
Vol 17 (4) ◽  
pp. 145
Author(s):  
Jeffrey Tim Query ◽  
Evaristo Diz
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Pension Benefit ◽  
Defined Benefit ◽  
Data Set ◽  
Autoregressive Integrated Moving Average ◽  
Statistical Estimates ◽  
Moving Average Model ◽  
Series Type ◽  
Sample Time

<p>In this study we examine the robustness of fit for a multivariate and an autoregressive integrated moving average model to a data sample time series type.  The sample is a recurrent actuarial data set for a 10-year horizon.  We utilize this methodology to contrast with stochastic models to make projections beyond the data horizon. Our key results suggest that both types of models are useful for making predictions of actuarial liability levels given by PBO Projected Benefit Obligations on and off the horizon of the sample time series.  As we have seen in prior research, the use of multivariate models for control and auditing purposes is widely recommended.  Fast and reliable statistical estimates are desirable in all cases, whether for audit purposes or to verify and validate miscellaneous actuarial results.</p>

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