Trees and Superintegrable Lotka–Volterra Families

期刊论文
发表日期：

2024年11月26日

查看全文

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

摘要

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