Displaying similar documents to “The five-variable Volterra system”

Rings of constants of generic 4D Lotka-Volterra systems

Janusz Zieliński, Piotr Ossowski (2013)

Czechoslovak Mathematical Journal

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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...

Rings of constants of four-variable Lotka-Volterra systems

Janusz Zieliński (2013)

Open Mathematics

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Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C 1, C 2, C 3, C 4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.

The constants of the Volterra derivation

Pál Hegedűs (2012)

Open Mathematics

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The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.