Rings of constants of generic 4D Lotka-Volterra systems

Title:

Rings of constants of generic 4D Lotka-Volterra systems

Creator:

Zieliński, Janusz and Ossowski, Piotr

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:b2463f96-b128-479e-9e20-8ca05be917d1
uuid:b2463f96-b128-479e-9e20-8ca05be917d1

Subject:

Lotka-Volterra derivation, polynomial constant, polynomial first integral, and Darboux polynomial

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We show that the rings of constants of generic four-variable Lotka-Volterra derivations are finitely generated polynomial rings. We explicitly determine these rings, and we give a description of all polynomial first integrals of their corresponding systems of differential equations. Besides, we characterize cofactors of Darboux polynomials of arbitrary four-variable Lotka-Volterra systems. These cofactors are linear forms with coefficients in the set of nonnegative integers. Lotka-Volterra systems have various applications in such branches of science as population biology and plasma physics, among many others.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

529-538

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:2

Harvested from:

CDK

Metadata only:

false