Trees and superintegrable Lotka-Volterra families

2023/11/26 by Peter H. van der Kamp, van der Kamp, Peter H., G. Quispel +3
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2311.15169

Abstract

To any tree on n vertices we associate an n-dimensional Lotka-Volterra system with 3n-2 parameters and, for generic values of the parameters, prove it is superintegrable, i.e. it admits n-1 functionally independent integrals. We also show how these systems can be reduced to an (n-1)-dimensional system which is superintegrable and solvable by quadratures.

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