Rings of constants of generic 4D Lotka-Volterra systems

Janusz Zieliński; Piotr Ossowski

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 2, page 529-538
  • ISSN: 0011-4642

Abstract

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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 systems have various applications in such branches of science as population biology and plasma physics, among many others.

How to cite

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Zieliński, Janusz, and Ossowski, Piotr. "Rings of constants of generic 4D Lotka-Volterra systems." Czechoslovak Mathematical Journal 63.2 (2013): 529-538. <http://eudml.org/doc/260685>.

@article{Zieliński2013,
abstract = {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.},
author = {Zieliński, Janusz, Ossowski, Piotr},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lotka-Volterra derivation; polynomial constant; polynomial first integral; Darboux polynomial; Lotka-Volterra derivation; polynomial constant; polynomial first integral; Darboux polynomial},
language = {eng},
number = {2},
pages = {529-538},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Rings of constants of generic 4D Lotka-Volterra systems},
url = {http://eudml.org/doc/260685},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Zieliński, Janusz
AU - Ossowski, Piotr
TI - Rings of constants of generic 4D Lotka-Volterra systems
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 529
EP - 538
AB - 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.
LA - eng
KW - Lotka-Volterra derivation; polynomial constant; polynomial first integral; Darboux polynomial; Lotka-Volterra derivation; polynomial constant; polynomial first integral; Darboux polynomial
UR - http://eudml.org/doc/260685
ER -

References

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  9. Ossowski, P., Zieliński, J., 10.4064/cm120-2-9, Colloq. Math. 120 (2010), 299-309. (2010) Zbl1207.13016MR2672276DOI10.4064/cm120-2-9
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