Linear Darboux polynomials of Lotka-Volterra systems correspond to admissible loopless hypergraphs, and for n≤5 these hypergraphs are classified up to linear equivalence, yielding a new non-tree 13-parameter superintegrable 5-component system.
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Hypergraphs and Lotka-Volterra systems with linear Darboux polynomials
Linear Darboux polynomials of Lotka-Volterra systems correspond to admissible loopless hypergraphs, and for n≤5 these hypergraphs are classified up to linear equivalence, yielding a new non-tree 13-parameter superintegrable 5-component system.