# A new class of integrable Lotka-Volterra systems

## TL;DR

This paper introduces a new parameter-dependent class of Hamiltonian Lotka-Volterra systems, identifying conditions for integrability and exploring non-integrable cases through numerical analysis.

## Contribution

It defines a novel class of integrable and superintegrable Lotka-Volterra systems with specific parameter conditions for integrability.

## Key findings

- Contains Liouville integrable and superintegrable cases
- Provides sufficient conditions for integrability
- Numerically explores non-integrable parameter regimes

## Abstract

A parameter-dependent class of Hamiltonian (generalized) Lotka-Volterra systems is considered. We prove that this class contains Liouville integrable as well as superintegrable cases according to particular choices of the parameters. We determine sufficient conditions which result in integrable behavior, while we numerically explore the complementary cases, where these analytically derived conditions are not satisfied.