Trees and superintegrable Lotka-Volterra families

Author:

Peter H. van der Kamp, G. R. W. Quispel, D. I. McLaren

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Dynamical Systems (math.DS)

journal:

date:

2023-11-26 00:00:00

Abstract

To any tree on $n$ vertices we associate an $n$-dimensional Lotka-Volterra system with $3n-2$ parameters and 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.

PDF: Trees and superintegrable Lotka-Volterra families.pdf