Hypergraphs and Lotka-Volterra systems with linear Darboux polynomials

Peter H. van der Kamp

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arXiv · 2411.18264

Hypergraphs and Lotka-Volterra systems with linear Darboux polynomials

Peter H. van der Kamp

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Abstract

We associate parametric classes of $n$-component Lotka-Volterra systems which admit $k$ additional linear Darboux polynomials, with admissible loopless hypergraphs of order $n$ and size $k$. We study the equivalence relation on admissible hypergraphs induced by linear transformations of the associated LV-systems, for $n\leq 5$. We present a new 13-parameter 5-component superintegrable Lotka-Volterra system, i.e. one that is not equivalent to a so-called tree-system. We conjecture that tree-systems associated with nonisomorphic trees are not equivalent, which we verified for $n<9$.

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Peter H. van der Kamp. 2024-11-27. Hypergraphs and Lotka-Volterra systems with linear Darboux polynomials. https://arxiv.org/abs/2411.18264

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