Liouville integrability and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization

TL;DR

This paper demonstrates the Liouville and superintegrability of a generalized Lotka-Volterra system and its discretized version using Kahan's method, highlighting their integrable properties.

Contribution

It establishes the integrability and superintegrability of both the continuous and discretized systems, which was not previously known.

Findings

Proves Liouville integrability of the system

Establishes superintegrability of the system

Shows the Kahan discretization preserves integrability

Abstract

We prove the Liouville and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization.