The search for Invariants for 3D Systems of 1ODEs - a new Method and Integrability Analysis

TL;DR

This paper introduces a new, more efficient method for finding elementary invariants in 3D systems of first-order rational differential equations and analyzes their integrability, especially with free parameters.

Contribution

It presents novel theoretical results that improve the process of identifying invariants and enables integrability analysis for parameterized systems.

Findings

New theoretical approach for invariant detection

Enhanced algorithm for invariants in 3D systems

Integrability analysis with free parameters

Abstract

In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce new theoretical results that will lead to a novel, more efficient, approach to determine these invariants. Furthermore, one important aspect of such dynamical systems is that the integrability can be an issue. We will show that the present theoretical development allows for an Integrability analysis in the case where the system has free parameters.