Algebraic decoupling of variables for systems of ODEs of quasipolynomial form

TL;DR

This paper extends an algebraic reduction technique for systems of ODEs, enabling broader applicability and providing simple criteria to identify reducible systems, thus advancing the analysis of quasipolynomial differential equations.

Contribution

It generalizes Gao and Liu's reduction method using algebraic approaches, allowing application to more complex flows and offering straightforward criteria for reducibility.

Findings

Extended reduction technique applicable to broader classes of ODEs.

Derived simple criteria for identifying reducible systems.

Enhanced algebraic methods facilitate analysis of quasipolynomial systems.

Abstract

A generalization of the reduction technique for ODEs recently introduced by Gao and Liu is given. It is shown that the use of algebraic methods allows the extension of the procedure to much more general flows, as well as the derivation of simple criteria for the identification of reducible systems.