Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory

2011 ◽  
Vol 56 (7) ◽  
pp. 2161-2181 ◽  
Author(s):  
D K Tewatia ◽  
R P Tolakanahalli ◽  
B R Paliwal ◽  
W A Tomé
Keyword(s):  
Dynamical System ◽  
Lung Cancer ◽  
System Theory ◽  
Time Series ◽  
Nonlinear Dynamical System ◽  
Dynamical System Theory ◽  
Breathing Patterns ◽  
Nonlinear Dynamical ◽  
Lung Cancer Patients ◽  
Time Series Analyses

DYNAMICAL ESTIMATION OF CALENDAR EFFECTS

2006 ◽  
Vol 06 (01) ◽  
pp. L7-L15
Author(s):  
ALEXANDROS LEONTITSIS
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Noise Level ◽  
Nonlinear Dynamical System ◽  
Main Tool ◽  
Experimental Results ◽  
Accurate Estimation ◽  
Nonlinear Dynamical ◽  
Correlation Integral ◽  
Calendar Effects

The paper introduces a method for estimation and reduction of calendar effects from time series, which their fluctuations are governed by a nonlinear dynamical system and additive normal noise. Calendar effects can be considered deviations of the distribution(s) of particular group(s) of observations that have a common characteristic related to the calendar. The concept of this method is the following: since the calendar effects are not related to the dynamics of the time series, the accurate estimation and reduction will result a time series with a smaller amount of noise level (i.e. more accurate dynamics). The main tool of this method is the correlation integral, due to its inherit capability of modeling both the dynamics and the additive normal noise. Experimental results are presented on the Nasdaq Cmp. index.

Approach to Forecasting Occurrence of Slope Failure with Nonlinear Dynamical System

2013 ◽  
Vol 438-439 ◽  
pp. 1597-1602
Author(s):  
Han Dong Liu
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Time Scale ◽  
Slope Failure ◽  
Time Series Data ◽  
Nonlinear Dynamical System ◽  
Series Data ◽  
Geologic Hazard ◽  
Nonlinear Dynamical ◽  
Short Term Prediction

Landslides constitute a major geologic hazard because they are widespread and commonly occur in connection with other major natural disasters such as earthquakes, rainstorms, wildfires and floods. Nonlinear dynamical system (NDS) techniques have been developed to analyze chaotic time series data. According to NDS theory, the correlation dimension and predictable time scale are evaluated from a single observed time series. The Xintan landslide case study is presented to demonstrate that chaos exists in the evolution of a landslide and the predictable time scale must be considered. The possibility for long-term, medium-term and short-term prediction of landslide is discussed.

scholarly journals Dynamical System Analysis of Interacting Hessence Dark Energy inf(T)Gravity

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Jyotirmay Das Mandal ◽  
Ujjal Debnath
Keyword(s):  
Dynamical System ◽  
Autonomous System ◽  
System Analysis ◽  
Nonlinear Dynamical System ◽  
Computational Method ◽  
Dynamical Analysis ◽  
Dynamical System Theory ◽  
Nonlinear Dynamical ◽  
The Stability ◽  
The Universe

We have carried out dynamical system analysis of hessence field coupling with dark matter inf(T)gravity. We have analysed the critical points due to autonomous system. The resulting autonomous system is nonlinear. So, we have applied the theory of nonlinear dynamical system. We have noticed that very few papers are devoted to this kind of study. Maximum works in literature are done treating the dynamical system as done in linear dynamical analysis, which are unable to predict correct evolution. Our work is totally different from those kinds of works. We have used nonlinear dynamical system theory, developed till date, in our analysis. This approach gives totally different stable solutions, in contrast to what the linear analysis would have predicted. We have discussed the stability analysis in detail due to exponential potential through computational method in tabular form and analysed the evolution of the universe. Some plots are drawn to investigate the behaviour of the system(this plotting technique is different from usual phase plot and that devised by us). Interestingly, the analysis shows that the universe may resemble the “cosmological constant” like evolution (i.e.,ΛCDM model is a subset of the solution set). Also, all the fixed points of our model are able to avoid Big Rip singularity.

scholarly journals Predicting Variable Star Light Curves

1993 ◽  
Vol 134 ◽  
pp. 145-147
Author(s):  
T. Serre
Keyword(s):  
Dynamical System ◽  
System Theory ◽  
Time Series ◽  
Variable Star ◽  
Prediction Method ◽  
Nonlinear Behavior ◽  
Light Curves ◽  
Dynamical System Theory ◽  
Embedding Dimension ◽  
Pulsating Stars

AbstractI present a new method to test determinism, in particular the nonlinear behavior, in observed time series of pulsating stars, based on a recent prediction method which exploits the dynamical system theory. A method for filling gaps in data has thereby been constructed. Estimated bounds to the necessary embedding dimension can be obtained and chaotic divergences can be estimated.

NOISE REDUCTION BY GRADIENT DESCENT

1993 ◽  
Vol 03 (01) ◽  
pp. 113-118 ◽  
Author(s):  
MIKE DAVIES
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Gradient Descent ◽  
Nonlinear Dynamical System ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Gradient Descent Method ◽  
Local Minima ◽  
Nonlinear Dynamical ◽  
The Stability

The problem of reducing noise in a time series from a nonlinear dynamical system can be formulated as a nonlinear minimisation process. This paper demonstrates that this can be easily solved using a steepest descent method without any of the stability problems that have been associated with using a Newton method [Hammel, 1990; Farmer & Sidorowich, 1991]. The optimisation function to be minimised is also shown not to contain any local minima if the trajectory is always hyperbolic. So that in this case this method will converge eventually to a purely deterministic trajectory. Finally this method is compared with a recently proposed algorithm [Schreiber & Grassberger, 1991], which can be viewed as an alternative gradient descent method.

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