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

<div><p>We conducted an <a href="http://dict.youdao.com/w/exploratory/#keyfrom=E2Ctranslation" target="_blank">exploratory</a> 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 <i>t</i>-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.</p></div

Inner product time series structure and PDO index series: (a) inner product time series (b) PDO index series.

<p>Inner product time series structure and PDO index series: (a) inner product time series (b) PDO index series.</p

Sudden change detection using the sliding t-test method: (a) sudden change detection of the innerproduct time series(b) sudden change detection of the PDO index series.

<p>Sudden change detection using the sliding t-test method: (a) sudden change detection of the innerproduct time series(b) sudden change detection of the PDO index series.</p

Test results, where the gray line is the 0.05 significance test.

<p>(a) the inner-product time series (b) the Aleutian low time series.</p

Time series {<i>d</i>^(1,0,0)_<i>i</i>} of reference vector <i>β</i> = (1,0,0).

<p>Time series {<i>d</i>^(1,0,0)_<i>i</i>} of reference vector <i>β</i> = (1,0,0).</p

Innerproduct time series and the Aleutian low time series: (a) the inner-product time series (b) the Aleutian low time series.

<p>Innerproduct time series and the Aleutian low time series: (a) the inner-product time series (b) the Aleutian low time series.</p

Concept map of the detection method of a sudden change of the vector time series.

<p>Concept map of the detection method of a sudden change of the vector time series.</p

Time intervals detected according to reference vector <i>β</i> = (1,0,0).

<p>Time intervals detected according to reference vector <i>β</i> = (1,0,0).</p

Statistics <i>T</i>_statistics.

<p>Statistics <i>T</i>_statistics.</p