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

09/12/2023

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by   Peter H. van der Kamp, et al.

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We show that any Lotka–Volterra T-system associated with an n-vertex tree T 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 T-systems factorises and preserves the same measure. As a consequence, for the Kahan maps of Lotka–Volterra systems related to the subclass of T-systems corresponding to graphs with more than one n-vertex subtree, we are able to construct rational integrals.