A family of planar Lotka--Volterra systems with invariant algebraic curves of arbitrary degree

TL;DR

This paper introduces a new family of planar Lotka-Volterra systems that possess explicit invariant algebraic curves of any degree, expanding the understanding of their geometric properties.

Contribution

It presents a novel family of Lotka-Volterra systems with explicitly constructed high-degree invariant algebraic curves, which was not previously known.

Findings

Existence of explicit invariant algebraic curves of arbitrary degree

New family of Lotka-Volterra systems with these properties

Enhanced understanding of system geometric structure

Abstract

We introduce a new family of planar Lotka--Volterra systems admitting explicit invariant algebraic curves of arbitrarily high degree.