Liouville integrable Lotka-Volterra systems

TL;DR

The paper introduces new families of Liouville integrable Lotka-Volterra systems with specific parameter counts and explores their inhomogeneous variants.

Contribution

It presents explicit parameterized families of integrable Lotka-Volterra systems and analyzes their inhomogeneous forms.

Findings

Derived explicit formulas for the number of parameters in the families.

Established Liouville integrability of the proposed systems.

Explored properties of inhomogeneous versions.

Abstract

We present $\frac{m^{2}}{4}+\frac{m}{2}+\frac{1-\left(-1\right)^{m}}{8}$ homogeneous $(3m-2)$-parameter families of Liouville integrable $(2m)$- and $(2m-1)$-dimensional Lotka-Volterra systems. We also study inhomogeneous versions of these systems.