Nonpolynomial vector fields under the Lotka-Volterra normal form

TL;DR

This paper generalizes the Lotka-Volterra embedding to a broader class of flows using auxiliary variables, maintaining topological properties and expanding the applicability of Lotka-Volterra models.

Contribution

It introduces a method to embed nonpolynomial vector fields into Lotka-Volterra form using auxiliary variables, preserving topological features.

Findings

The generalized embedding is largely independent of auxiliary variable definitions.

Conservation of topological equivalence is demonstrated during the embedding process.

The method broadens the applicability of Lotka-Volterra models to more complex systems.

Abstract

We carry out the generalization of the Lotka-Volterra embedding to flows not explicitly recognizable under the Generalized Lotka-Volterra format. The procedure introduces appropiate auxiliary variables, and it is shown how, to a great extent, the final Lotka-Volterra system is independent of their specific definition. Conservation of the topological equivalence during the process is also demonstrated.