Detection of a sudden change of the field time series based on the Lorenz system

We conducted an exploratory study of the detection of a sudden change of the field time series based on the numerical solution of the Lorenz system. First, the time when the Lorenz path jumped between the regions on the left and right of the equilibrium point of the Lorenz system was quantitatively...

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Bibliographic Details
Published in:PloS one 2017-01, Vol.12 (1), p.e0170720-e0170720
Main Authors: Da, ChaoJiu, Li, Fang, Shen, BingLu, Yan, PengCheng, Song, Jian, Ma, DeShan
Format: Article
Language:English
Subjects:
Alaska
Algorithms
Analysis
Applied mathematics
Atmosphere
Atmospheric sciences
Biology and life sciences
Change detection
Climate change
Computer and Information Sciences
Computer science
Drought
Dynamical systems
Earth Sciences
Equilibrium
Herbivores
Lorenz curves
Lorenz system
Numerical Analysis, Computer-Assisted
Physical Sciences
Precipitation
Research and analysis methods
Statistical methods
Studies
Temperature distribution
Test procedures
Time Factors
Time series
Time series analysis
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Summary:We conducted an exploratory study of the detection of a sudden change of the field time series based on the numerical solution of the Lorenz system. First, the time when the Lorenz path jumped between the regions on the left and right of the equilibrium point of the Lorenz system was quantitatively marked and the sudden change time of the Lorenz system was obtained. Second, the numerical solution of the Lorenz system was regarded as a vector; thus, this solution could be considered as a vector time series. We transformed the vector time series into a time series using the vector inner product, considering the geometric and topological features of the Lorenz system path. Third, the sudden change of the resulting time series was detected using the sliding t-test method. Comparing the test results with the quantitatively marked time indicated that the method could detect every sudden change of the Lorenz path, thus the method is effective. Finally, we used the method to detect the sudden change of the pressure field time series and temperature field time series, and obtained good results for both series, which indicates that the method can apply to high-dimension vector time series. Mathematically, there is no essential difference between the field time series and vector time series; thus, we provide a new method for the detection of the sudden change of the field time series.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0170720