Simplification of a reconstructed model

Abstract

We study a mathematical model in the form of a system of ordinary differential equations, with polynomial right-hand sides, obtained with a use of numerical methods. The paper deals with a simplification problem for such a model, since it can contain redundant terms. We propose a method to solve this problem without use of any numerical procedure. We show that the system can be simplified in such a way that the observed variable would not change. The simplification aims at reducing the number of nonzero coefficients in the right-hand side of the system. For this purpose, we use relations that connect a non-simplified model with a so-called differential model. The latter should be the same for all systems that have the same observable. This fact allows us to obtain a simplified system. The suggested approach, in general, permits to obtain several minimized systems that have identical time series for the observed variable. The researcher then can choose the system that better suits the physical process under consideration.