The Dynamics of a Flexible Levitated Droplet

2001 ◽  
Author(s):  
Mihai Dupac ◽  
Dan B. Marghitu ◽  
David G. Beale
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Time Series Data ◽  
Simulated Data ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Dynamics Analysis ◽  
Attractor Dimension ◽  
Levitated Droplet

Abstract In this paper, a nonlinear dynamics analysis of the simulated data was considered to study the time evolution of an electro-magnetically levitated flexible droplet. The main goals of this work are to study the behavior of the levitated droplet and to investigate its stability. Quantities characterizing time series data such as attractor dimension or largest Lyapunov exponent were computed.

Electromagnetic Levitation: A Nonlinear Analysis Approach

1999 ◽  
Author(s):  
Bogdan O. Ciocirlan ◽  
Dan B. Marghitu ◽  
David G. Beale ◽  
Ruel A. Overfelt
Keyword(s):  
Nonlinear Dynamics ◽  
Time Evolution ◽  
Time Series Data ◽  
Electromagnetic Levitation ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Attractor Dimension ◽  
Molten Droplet ◽  
Levitated Droplet ◽  
Electromagnetically Levitated

Abstract In this paper, a nonlinear dynamics approach for analyzing the time evolution of an electromagnetically levitated droplet is proposed. The analysis was performed on the experimental data acquired from a levitation instrument developed by Space Power Institute at Auburn University. Several nonlinear dynamics tools were applied in order to reveal whether the time evolution of the droplet is deterministic (periodic, quasiperiodic or chaotic) or random. Quantities characterizing time series data such as the attractor dimension or the largest Lyapunov exponent were computed. It was mainly found that the underlying dynamics of the molten droplet is in fact chaotic.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

Stability Analysis of a Levitated Droplet by Using Floquet Multipliers

2000 ◽  
Vol 122 (4) ◽  
pp. 399-408 ◽  
Author(s):  
Bogdan O. Ciocirlan ◽  
Dan B. Marghitu
Keyword(s):  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Time Series Data ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Attractor Dimension ◽  
Floquet Multipliers ◽  
Levitated Droplet ◽  
System Data ◽  
The Stability

In this paper, the analysis of the time evolution of a levitated droplet is proposed. The analysis is composed of two parts: in the first part, a nonlinear dynamics approach was considered to calculate quantities characterizing time series data such as attractor dimension or largest Lyapunov exponent. The number of degrees of freedom in the system was also assessed. Based on the results obtained in the first part, Floquet theory was applied in the second part of the analysis to investigate the stability of the system. Data acquired from a levitation instrument developed by Space Power Institute at Auburn University was used to perform the analysis. [S0739-3717(00)01903-6]

Changepoint Analysis of Binary and Ordinal Probit Models: An Application to Bank Rate Policy Under the Interwar Gold Standard

2011 ◽  
Vol 19 (2) ◽  
pp. 188-204 ◽  
Author(s):  
Jong Hee Park
Keyword(s):  
Time Series ◽  
Gold Standard ◽  
Time Series Data ◽  
Likelihood Function ◽  
Marginal Likelihood ◽  
Estimation Method ◽  
Simulated Data ◽  
Likelihood Method ◽  
Series Data ◽  
Ordinal Probit

In this paper, I introduce changepoint models for binary and ordered time series data based on Chib's hidden Markov model. The extension of the changepoint model to a binary probit model is straightforward in a Bayesian setting. However, detecting parameter breaks from ordered regression models is difficult because ordered time series data often have clustering along the break points. To address this issue, I propose an estimation method that uses the linear regression likelihood function for the sampling of hidden states of the ordinal probit changepoint model. The marginal likelihood method is used to detect the number of hidden regimes. I evaluate the performance of the introduced methods using simulated data and apply the ordinal probit changepoint model to the study of Eichengreen, Watson, and Grossman on violations of the “rules of the game” of the gold standard by the Bank of England during the interwar period.

scholarly journals The Dynamics of Philippine Foreign Exchange Rates (2013-2017): A Test for Chaos

2019 ◽  
Vol 8 (11) ◽  
pp. 486-489
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Lyapunov Exponent ◽  
Exchange Rates ◽  
Foreign Exchange ◽  
Chaotic Behavior ◽  
The Philippines ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Foreign Exchange Rates

In most studies on dynamics of time series financial data, the absence of chaotic behavior is generally observed. However, this theory is not yet established in the dynamics of foreign exchange rates. Conflicting claims of presence and absence of chaos in foreign exchange rates open door for further investigation considering various deterministic factors. This work examines the dynamics of exchange rate of the Philippine Peso against selected foreign currencies. Time series data were collected for eight (8) of Philippine’s top trading partners as categorized according to economic condition. The data obtained with permission from the Central Bank of the Philippines covered the years 2013 to 2017. Data sets were plotted revealing non-linear movement of Philippine exchange rates against time. The foreign exchange rate time series obtained per currency were examined for chaotic behavior by computing the Largest Lyapunov Exponents (LLE). A positive Lyapunov exponent is an indication of sensitivity dependence, i.e, a chaotic dynamics; whereas, a negative Lyapunov exponent indicates otherwise. Computed LLE’s varied per currency but all were found to be negative. Therefore, using the Largest Lyapunov Exponent Test (LLE), analysis of the time series of Philippine foreign exchange rates shows little evidence of chaotic patterns.

scholarly journals Machine learning methods trained on simple models can predict critical transitions in complex natural systems

2021 ◽  
Author(s):  
Smita Deb ◽  
Sahil Sidheekh ◽  
Christopher F. Clements ◽  
Narayanan C. Krishnan ◽  
Partha S. Dutta
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Complex Systems ◽  
Time Series Data ◽  
High Reliability ◽  
Stable State ◽  
Simulated Data ◽  
Series Data ◽  
Underlying Structure ◽  
Critical Transitions

Abstract1. Sudden transitions from one stable state to a contrasting state occur in complex systems ranging from the collapse of ecological populations to climatic change, with much recent work seeking to develop methods to predict these unexpected transitions from signals in time series data. However, previously developed methods vary widely in their reliability, and fail to classify whether an approaching collapse might be catastrophic (and hard to reverse) or non-catastrophic (easier to reverse) with significant implications for how such systems are managed.2. Here we develop a novel detection method, using simulated outcomes from a range of simple mathematical models with varying nonlinearity to train a deep neural network to detect critical transitions - the Early Warning Signal Network (EWSNet).3. We demonstrate that this neural network (EWSNet), trained on simulated data with minimal assumptions about the underlying structure of the system, can predict with high reliability observed real-world transitions in ecological and climatological data. Importantly, our model appears to capture latent properties in time series missed by previous warning signals approaches, allowing us to not only detect if a transition is approaching but critically whether the collapse will be catastrophic or non-catastrophic.4. The EWSNet can flag a critical transition with unprecedented accuracy, overcoming some of the major limitations of traditional methods based on phenomena such as Critical Slowing Down. These novel properties mean EWSNet has the potential to serve as a universal indicator of transitions across a broad spectrum of complex systems, without requiring information on the structure of the system being monitored. Our work highlights the practicality of deep learning for addressing further questions pertaining to ecosystem collapse and have much broader management implications.

DETECTING NONLINEAR DETERMINISM IN VOICED SOUNDS OF JAPANESE VOWEL /a/

2000 ◽  
Vol 10 (08) ◽  
pp. 1973-1979 ◽  
Author(s):  
TAKAYA MIYANO ◽  
AKIRA NAGAMI ◽  
ISAO TOKUDA ◽  
KAZUYUKI AIHARA
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Time Series Analysis ◽  
Basis Function ◽  
Speech Signal ◽  
Time Series Data ◽  
Series Data ◽  
Radial Basis Function Networks ◽  
Data Points ◽  
Surrogate Method

Nonlinear determinism in voiced sounds of the Japanese vowel /a/ is tested by the time series analysis associated with the surrogate method. To capture nonlinear dynamics underlying the speech signal, we apply the generalized radial basis function networks as nonlinear predictors to the time series data. The optimized network parameters may show a trail of the nonlinear dynamics though not conspicuously. This may be due to paucity of data points.

Inferring dynamic gene regulatory networks with low-order conditional independencies – an evaluation of the method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hamda B. Ajmal ◽  
Michael G. Madden
Keyword(s):  
Time Series ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Time Series Data ◽  
Simulated Data ◽  
Dynamic Bayesian Networks ◽  
Series Data ◽  
Gene Regulatory ◽  
Lasso Method ◽  
Low Order

AbstractOver a decade ago, Lèbre (2009) proposed an inference method, G1DBN, to learn the structure of gene regulatory networks (GRNs) from high dimensional, sparse time-series gene expression data. Their approach is based on concept of low-order conditional independence graphs that they extend to dynamic Bayesian networks (DBNs). They present results to demonstrate that their method yields better structural accuracy compared to the related Lasso and Shrinkage methods, particularly where the data is sparse, that is, the number of time measurements n is much smaller than the number of genes p. This paper challenges these claims using a careful experimental analysis, to show that the GRNs reverse engineered from time-series data using the G1DBN approach are less accurate than claimed by Lèbre (2009). We also show that the Lasso method yields higher structural accuracy for graphs learned from the simulated data, compared to the G1DBN method, particularly when the data is sparse ($n{< }{< }p$). The Lasso method is also better than G1DBN at identifying the transcription factors (TFs) involved in the cell cycle of Saccharomyces cerevisiae.

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