Abstract
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.
Highlights
In 1953, Hadamard solved the Cauchy problem of Laplace’s equation by formulating the instability of the solution of the differential equation for the first time, and constructed the counterexample, which shows that the differential equation is sensitive to the initial value[1]
In this paper, based on the Lorenz system, we propose a new sudden change detection method for the field time series using geometric and topological methods
The path revolves around the left equilibrium point for six cycles, it runs through the boundary surface and enters the right equilibrium point region
Summary
In 1953, Hadamard solved the Cauchy problem of Laplace’s equation by formulating the instability of the solution of the differential equation for the first time, and constructed the counterexample, which shows that the differential equation is sensitive to the initial value[1]. In the middle of the20th century, Thom studied the singularity theory of a mapping on the differentiable manifold and classified the singularities of the function in Euclidian space to obtain a series of conclusions, which include the famous transversality theorem These conclusions form the mathematical foundation of sudden change theory[2]. Et al conducted research from the viewpoint of numerical weather transitional prediction and indicated the predictability of a sudden turn from drought to flood [16] This sudden turn is caused by the chaotic character of the atmosphere. Few researchers use geometric and topological methods to study the sudden change of the field time series. In this paper, based on the Lorenz system, we propose a new sudden change detection method for the field time series using geometric and topological methods. If we can obtain one sudden change detection method for the vector time series and apply it to the field time series, we can obtain a detection method for the sudden change of the field time series
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
