Building superintegrable Lotka–Volterra systems using Darboux Polynomials
Reinout Quispel
(La Trobe University)
In this talk we show how to construct large classes of Lotka–Volterra ODEs in \(\mathbb{R}^n\) with \(n−1\) first integrals. The building blocks we use will be linear Darboux Polynomials of the ODE. The talk will also feature a novel application of (free) trees to Lotka-Volterra systems. The trees here represent the set of Darboux polynomials of the ODEs. In the talk these concepts will be defined, and the procedure explained.