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

Autor:	van der Kamp, Peter H., McLachlan, Robert I., McLaren, David I., Quispel, G. R. W.
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems Mathematics - Numerical Analysis 34A05 39B99
Zdroj:	Journal of Computational Dynamics, 2024
Druh dokumentu:	Working Paper
DOI:	10.3934/jcd.2024011
Popis:	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. Comment: 17 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.05979 Zobrazit plný text záznamu View this record from Arxiv