Taking the Singularly Perturbed System (SPS) as a model of ODE system separation into fast and slow subsystems by an arbitrarily small parameter, we state and prove a theorem on the decomposition of an Ordinary Differential Equations (ODE) system without the aforementioned arbitrarily small parameter. In accordance with the proven theorem, we implemented an algorithm to decompose an ODE system into fast and slow subsystems by coordinate transformation. A similar algorithm is called the Singular Perturbed Vector Field (SPVF) algorithm; however, it is not justified by any stated theorem. Since we have not found any theorem to propose a similar ODE decomposition in the literature, we have tried to fill the gap with our theorem and algorithm explanations through examples. Finally, we propose our concept on Marchuk’s infectious diseases model, which allows a different analysis of the original Marchuk’s ODE system with delay.
Bershadsky et al. (Wed,) studied this question.