Generation of phase trajectories of experimental data

Abstract

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.