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arXiv · 2311.15169

Trees and superintegrable Lotka-Volterra families

Peter H. van der Kamp·G. R. W. Quispel·D. I. McLaren
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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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Peter H. van der Kamp, G. R. W. Quispel, D. I. McLaren. 2024-10-29. Trees and superintegrable Lotka-Volterra families. https://arxiv.org/abs/2311.15169

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