1. Rings of constants of generic 4D Lotka-Volterra systems
- Creator:
- Zieliński, Janusz and Ossowski, Piotr
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Lotka-Volterra derivation, polynomial constant, polynomial first integral, and Darboux polynomial
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public