Measure preservation and integrals for Lotka--Volterra tree-systems and their Kahan discretisation
Dynamical Systems
2024-03-01 v2 Numerical Analysis
Numerical Analysis
Abstract
We show that any Lotka--Volterra tree-system associated with an -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 -vertex subtree, we are able to construct rational integrals.
Keywords
Cite
@article{arxiv.2309.05979,
title = {Measure preservation and integrals for Lotka--Volterra tree-systems and their Kahan discretisation},
author = {Peter H. van der Kamp and Robert I. McLachlan and David I. McLaren and G. R. W. Quispel},
journal= {arXiv preprint arXiv:2309.05979},
year = {2024}
}
Comments
17 pages, 3 figures