MEASURE PRESERVATION AND INTEGRALS FOR LOTKA-VOLTERRA TREE-SYSTEMS AND THEIR KAHAN DISCRETISATION

被引：0

作者：

van der Kamp, Peter H. ^{[1
]}

McLachlan, Robert I. ^{[2
]}

McLaren, David I. ^{[1
]}

Quispel, G. R. W. ^{[1
]}

机构：

[1] La Trobe Univ, Bundoora, Vic, Australia

[2] Massey Univ, Palmerston North, New Zealand

来源：

JOURNAL OF COMPUTATIONAL DYNAMICS | 2024年 / 11卷 / 04期

关键词：

Measure preservation; integrals; Lotka-Volterra; tree-systems; Kahan discretisation; INTEGRABILITY;

D O I：

10.3934/jcd.2024011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：468 / 484

页数：17

共 15 条

[1] Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
Celledoni, E.
Evripidou, C.
McLaren, D., I
Owren, B.
Quispel, G. R. W.
Tapley, B. K.
van der Kamp, P. H.
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2019, 52 (31)
[2] DETECTING AND DETERMINING PRESERVED MEASURES AND INTEGRALS OF BIRATIONAL MAPS
Celledoni, Elena
Evripidou, Charalambos
McLaren, David, I
Owren, Brynjulf
Quispel, G. R. W.
Tapley, Benjamin K.
[J]. JOURNAL OF COMPUTATIONAL DYNAMICS, 2022, : 553 - 574
[3] Geometric properties of Kahan's method
Celledoni, Elena
McLachlan, Robert I.
Owren, Brynjulf
Quispel, G. R. W.
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2013, 46 (02)
[4] Collins C.B., 1996, Japan J. Indust. Appl. Math., V13, P63
[5] A Darboux-type theory of integrability for discrete dynamical systems
Gasull, A
Mañosa, V
[J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2002, 8 (12) : 1171 - 1191
[6] Goriely A., 2001, INTEGRABILITY NONINT
[7] Harary F., 1963, CAN MATH BULLETIN, V6, P1, DOI 10.4153/CMB-1963-001-x
[8] Kahan W., 1993, Unconventional numerical methods for trajectory calculations
[9] Discretization of the Lagrange top
Kimura, K
Hirota, R
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2000, 69 (10) : 3193 - 3199
[10] Liouville integrability and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization
Kouloukas, T. E.
Quispel, G. R. W.
Vanhaecke, P.
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2016, 49 (22)

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