Trees and superintegrable Lotka-Volterra families

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.

16 pages, 3 figures, 22 references

Cited by in corpus (1)

• Linear Darboux polynomials for Lotka-Volterra systems, trees and superintegrable families