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

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Mathematics Discretization Measure (data warehouse) Tree (set theory) Vertex (graph theory) Applied mathematics Graph Combinatorics Mathematical analysis Computer science Database

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

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.3934/jcd.2024011 · OA: W4391987529

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.