An integrating factor matrix method to find first integrals

TL;DR

This paper introduces a new integrating factor matrix method to determine first integrals in dynamical systems, specifically applied to Lotka-Volterra models, providing a systematic approach to find conserved quantities.

Contribution

The paper presents a novel integrating factor matrix method for deriving first integrals, extending analysis to Lotka-Volterra systems with constant terms.

Findings

Derived conditions for first integrals in 2D and 3D Lotka-Volterra systems

Compared new method results with previous approaches

Enhanced understanding of conserved quantities in ecological models

Abstract

In this paper we developed an integrating factor matrix method to derive conditions for the existence of first integrals. We use this novel method to obtain first integrals, along with the conditions for their existence, for two and three dimensional Lotka-Volterra systems with constant terms. The results are compared to previous results obtained by other methods.