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arXiv · 2309.05979

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

Peter H. van der Kamp·Robert I. McLachlan·David I. McLaren·G. R. W. Quispel
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Abstract

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.

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Peter H. van der Kamp, Robert I. McLachlan, David I. McLaren, G. R. W. Quispel. 2023-09-12. Measure preservation and integrals for Lotka--Volterra tree-systems and their Kahan discretisation. https://doi.org/10.3934/jcd.2024011

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