Open AccessGeneration of phase trajectories of experimental data
Author(s) -
Kaloyan Yankov
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1031/1/012078
Subject(s) - spline (mechanical) , differential equation , trajectory , mathematics , thin plate spline , experimental data , ordinate , representation (politics) , phase plane , m spline , curve fitting , mathematical analysis , algorithm , spline interpolation , geometry , nonlinear system , physics , statistics , astronomy , quantum mechanics , politics , political science , law , bilinear interpolation , thermodynamics
The phase plane method (PPM) is a graph-analytical approach for studying the stability and long-time behavior of systems described by differential equations. In order to apply the PPM to experimental data, it is necessary to identify these data with a first-or second-order differential equation. This work presents a numerical-analytical algorithm for obtaining phase trajectories from experimental data avoiding identification with a differential equation. For this purpose, the data are interpolated with a cubic spline. The first derivative was obtained analytically from the spline. The abscissa coordinates are the values of the spline at a given point, and the ordinate is the analytical representation of the first derivative. As an example, the phase trajectory of the dose-dependent curve of the drug tubazid is constructed by two methods-with identification of the differential equation describing the process and with the algorithm proposed in the article. The approach is implemented with Korelia software.