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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:2411.18264 (nlin)
[Submitted on 27 Nov 2024 (v1), last revised 29 Nov 2024 (this version, v2)]

Title:Hypergraphs and homogeneous Lotka-Volterra systems with linear Darboux polynomials

Authors:Peter H. van der Kamp
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Abstract:We associate homogeneous $n$-component Lotka-Volterra systems which admit $k$ additional linear Darboux polynomials, with admissible 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 $n<9$.
Comments: 17 pages, 17 figures, 7 tables. Version 2: corrected a minus sign in equation (6) and related expressions
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Dynamical Systems (math.DS)
Cite as: arXiv:2411.18264 [nlin.SI]
  (or arXiv:2411.18264v2 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.2411.18264

Submission history

From: Peter van der Kamp [view email]
[v1] Wed, 27 Nov 2024 12:01:10 UTC (14 KB)
[v2] Fri, 29 Nov 2024 09:35:19 UTC (14 KB)
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