Solving the problem of mathematical models overparameterization for some nonlinear oscillating systems

Abstract

This study proposes a numerical-analytical method that allows us to simplify the model, which is obtained on the basis of the single observable variable of an object under the study, and which may be overparameterized. As a model, we consider a system of ordinary differential equations with polynomial right-hand sides. To solve this problem, the so-called differential model is used, that is, a system in which unknown variables are replaced by derivatives of the observed variable, and which is derived on the basis of a system under the study so that the observed variables of these systems coincide. The method of simplification of a system under the study is based on the fact that using a numerical method, a simpler differential model can be obtained. Next, an analytical transition from a simplified differential model to a simplified original system is performed. In this case, the time series error remains within given limits even for systems with deterministic chaos, despite their high sensitivity to the initial conditions.