Measure preservation and integrals for Lotka--Volterra tree-systems and their Kahan discretisation Article Swipe

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Peter H. van der Kamp , Robert I. McLachlan , David McLaren , G. Quispel ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2309.05979 · OA: W4386721721

We show that any Lotka--Volterra tree-system associated with an $n$-vertex tree, as introduced in Quispel et al., J. Phys. A 56 (2023) 315201, preserves a rational measure. We also prove that the Kahan discretisation of these tree-systems factorises and preserves the same measure. As a consequence, for the Kahan maps of Lotka--Volterra systems related to the subclass of tree-systems corresponding to graphs with more than one $n$-vertex subtree, we are able to construct rational integrals.