scholarly journals Local Functional Coefficient Autoregressive Model for Multistep Prediction of Chaotic Time Series

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Liyun Su ◽  
Chenlong Li
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Chaos Theory ◽  
Nearest Neighbor ◽  
Simulated Data ◽  
Real Data ◽  
Chaotic Time Series ◽  
Dimensional Phase Space ◽  
Local Functional ◽  
Functional Coefficient

A new methodology, which combines nonparametric method based on local functional coefficient autoregressive (LFAR) form with chaos theory and regional method, is proposed for multistep prediction of chaotic time series. The objective of this research study is to improve the performance of long-term forecasting of chaotic time series. To obtain the prediction values of chaotic time series, three steps are involved. Firstly, the original time series is reconstructed inm-dimensional phase space with a time delayτby using chaos theory. Secondly, select the nearest neighbor points by using local method in them-dimensional phase space. Thirdly, we use the nearest neighbor points to get a LFAR model. The proposed model’s parameters are selected by modified generalized cross validation (GCV) criterion. Both simulated data (Lorenz and Mackey-Glass systems) and real data (Sunspot time series) are used to illustrate the performance of the proposed methodology. By detailed investigation and comparing our results with published researches, we find that the LFAR model can effectively fit nonlinear characteristics of chaotic time series by using simple structure and has excellent performance for multistep forecasting.

scholarly journals Analysis of Dynamical Behavior for Epidemic Disease COVID-19 with Application

2021 ◽  
Vol 12 (4) ◽  
pp. 568-577
Author(s):  
Dr. Maysoon M. Aziz, Et. al.
Keyword(s):  
Time Series ◽  
Linear System ◽  
Power Spectrum ◽  
Dynamical Behavior ◽  
Simulated Data ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Disease ◽  
The World ◽  
Non Linear System

In this paper, we will use the differential equations of the SIR model as a non-linear system, by using the Runge-Kutta numerical method to calculate simulated values for known epidemiological diseases related to the time series including the epidemic disease COVID-19, to obtain hypothetical results and compare them with the dailyreal statisticals of the disease for counties of the world and to know the behavior of this disease through mathematical applications, in terms of stability as well as chaos in many applied methods. The simulated data was obtained by using Matlab programms, and compared between real data and simulated datd were well compatible and with a degree of closeness. we took the data for Italy as an application.  The results shows that this disease is unstable, dissipative and chaotic, and the Kcorr of it equal (0.9621), ,also the power spectrum system was used as an indicator to clarify the chaos of the disease, these proves that it is a spread,outbreaks,chaotic and epidemic disease .

scholarly journals Complex Network Construction of Univariate Chaotic Time Series Based on Maximum Mean Discrepancy

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 142
Author(s):  
Jiancheng Sun
Keyword(s):  
Time Series ◽  
Complex Network ◽  
Gaussian Mixture ◽  
Chaotic Time Series ◽  
Network Construction ◽  
Maximum Mean Discrepancy ◽  
Univariate Time Series ◽  
Dimensional Phase Space ◽  
The Common ◽  
The Lorenz System

The analysis of chaotic time series is usually a challenging task due to its complexity. In this communication, a method of complex network construction is proposed for univariate chaotic time series, which provides a novel way to analyze time series. In the process of complex network construction, how to measure the similarity between the time series is a key problem to be solved. Due to the complexity of chaotic systems, the common metrics is hard to measure the similarity. Consequently, the proposed method first transforms univariate time series into high-dimensional phase space to increase its information, then uses Gaussian mixture model (GMM) to represent time series, and finally introduces maximum mean discrepancy (MMD) to measure the similarity between GMMs. The Lorenz system is used to validate the correctness and effectiveness of the proposed method for measuring the similarity.

Prediction of Chaotic Time Series of Bridge Monitoring System Based on Multi-Step Recursive BP Neural Network

2010 ◽  
Vol 159 ◽  
pp. 138-143 ◽  
Author(s):  
Jian Xi Yang ◽  
Jian Ting Zhou
Keyword(s):  
Neural Network ◽  
Time Series ◽  
Phase Space ◽  
Bp Neural Network ◽  
Chaotic Time Series ◽  
Effective Theory ◽  
Maximum Lyapunov Exponent ◽  
Space Correlation ◽  
Bridge Monitoring System ◽  
Monitoring Information

BHM is an important means to assess and predict the safety operation of large bridge in service around the world. Given the missing of real-time monitoring information for some time and the lack of effective theory and technique to capture the missing information and even to predict the evolution of structure, this paper made an attempt to predict the evolution of monitoring information using time series and chaotic theory. Firstly, maximum Lyapunov exponent of available monitoring information is calculated to assess the chaos of the bridge structure. The parameters of reconstructed phase space, correlation dimension and time delay, are calculated by C-C algorithm and G-P algorithm respectively. According to empirical formula, one 3-layer BP neural network is established Ten recursions are carried out. The results show that multi-layer recursive BP neural network is able to predict BHM information. Using chaotic time series to reconstruct phase space and applying multi-layer recursive BP neural network to predict BHM information facilitates further estimation and prediction of bridge safety condition by means of chaotic nonlinear characteristics.

Analysis of Myograms Acording to the Stochastics and the Chaos Theory – Self-Organization

2015 ◽  
Vol 22 (2) ◽  
pp. 32-38
Author(s):  
Григоренко ◽  
V. Grigorenko ◽  
Горбунов ◽  
D. Gorbunov ◽  
Еськов ◽  
...  
Keyword(s):  
Phase Space ◽  
Shannon Entropy ◽  
Chaos Theory ◽  
The State ◽  
Biomechanical Analysis ◽  
Self Organization ◽  
Biological Research ◽  
Dimensional Phase Space ◽  
Low Load ◽  
Little Finger

The paper shows the feasibility of applying the method of multi-dimensional phase space as a quantitative measure for the evaluation of chaotic dynamics on the example of the muscles (flexor of the little finger). The method of multi-dimensional phase space was used. In the study and modeling of complex biological objects (complexity) there is the possibility of introducing traditional physical methods in biological research and new methods based on the chaos theory and self-organization. As a measure of the state of the neuromuscular system of the person (weak muscle tension and strong, almost the maximum force), the authors used quasi-attractors volumes of multidimensional phase space. This enables identification of the actual measurements of the parameters of the functional state with weak muscles (Fi = 5 daN) and strong (Fi = 10 daN) static stress. The authors built a timebase signal received from the electromyograph and the autocorrelation function A(t) of signal. A biomechanical analysis of the state of the system is carried out on the basis of comparison of the volume VG quasi attractor, as well as on the basis of the analysis of the Shannon entropy E. Volume of quasi attractor VG displacements under low load is slightly less than the same volume displacement VG with strong exertion of the muscles of the flexor of the little finger, exactly the same as the values of the Shannon entropy under a heavy load increases compared to the values obtained under low load the muscles.

Understanding the Unpredictability of Cancer using Chaos Theory and Modern Art Techniques

Leonardo ◽  
2016 ◽  
Vol 49 (1) ◽  
pp. 66-67
Author(s):  
Dhruba Deb
Keyword(s):  
Phase Space ◽  
Conceptual Model ◽  
Chaotic System ◽  
Chaos Theory ◽  
Strange Attractor ◽  
Model Building ◽  
Modern Art ◽  
System Level ◽  
Abstract Expressionist ◽  
Dimensional Phase Space

The unpredictability of cancer poses a threat to personalized cures. Although cancer is studied as a chaotic system, the shape of its unpredictability, known as the strange attractor, is unclear. In this article, the author discusses a conceptual model, building on the strange attractor in cancer phase space. Using techniques of cubism, the author defines the 10-dimensional phase space and then, using an abstract expressionist approach, represents the strange attractor, which twists and turns in multi dimensions, indicating the unpredictability of cancer. This conceptual model motivates the identification of specific experiments for a system-level understanding of cancer.

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