Trees and Superintegrable Lotka–Volterra Families.

To any tree on n vertices we associate an n-dimensional Lotka–Volterra system with 3 n - 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 each system can be reduced to an ( n - 1 )-dimensional system which is superintegrable and solvable by quadratures. [ABSTRACT FROM AUTHOR]