Measure preservation and integrals for Lotka-Volterra tree-systems and their Kahan discretisation
DOI10.3934/jcd.2024011MaRDI QIDQ6616290
David I. McLaren, Peter H. van der Kamp, Robert I. McLachlan, G. R. W. Quispel
Publication date: 9 October 2024
Published in: Journal of Computational Dynamics (Search for Journal in Brave)
Nonlinear ordinary differential equations and systems (34A34) Population dynamics (general) (92D25) Explicit solutions, first integrals of ordinary differential equations (34A05) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) General groups of measure-preserving transformations and dynamical systems (37A15) Boundary value problems on graphs and networks for ordinary differential equations (34B45)
Cites Work
- On integrability of Hirota-Kimura type discretizations
- Algebraic classification of homogeneous polynomial vector fields in the plane
- Detecting and determining preserved measures and integrals of birational maps
- Discretization of the Lagrange top.
- Integrability and nonintegrability of dynamical systems
- Growth of degrees of integrable mappings
- T-systems andY-systems in integrable systems
- Liouville integrability and superintegrability of a generalized Lotka–Volterra system and its Kahan discretization
- A Characterization of Block-Graphs
- A Darboux-type Theory of Integrability for Discrete Dynamical Systems
- Geometric properties of Kahan's method
- Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
- New classes of quadratic vector fields admitting integral-preserving Kahan–Hirota–Kimura discretizations
- Birational maps from polarization and the preservation of measure and integrals
- Linear Darboux polynomials for Lotka–Volterra systems, trees and superintegrable families
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