Algebraic approaches to Lotka-Volterra models and their generalisations

Project level: Honours, Masters, PhD

Lotka-Volterra models consist in systems of nonlinear ODEs and have applications to the description of various phenomena in different areas of science. They attracted attention from different perspectives in particular from the exact solvability and integrability point of view. The purpose of this project will be to obtain larger class of models via coproduct approach of Lie-Poisson algebras, Darboux integrals and other algebraic constructions. The project will also rely on constructing Casimir invariant, not necessarily in polynomial form via different methods to get insight into the models properties.