Geodesic
Rings of constants of generic 4D Lotka-Volterra systems
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 529-538 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10587-013-0035-z
Classification : 12H05, 13N15, 34A34, 92D25
Keywords: Lotka-Volterra derivation; polynomial constant; polynomial first integral; Darboux polynomial 
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     title = {Rings of constants of generic {4D} {Lotka-Volterra} systems},
     journal = {Czechoslovak Mathematical Journal},
     pages = {529--538},
     year = {2013},
     volume = {63},
     number = {2},
     doi = {10.1007/s10587-013-0035-z},
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Zieliński, Janusz; Ossowski, Piotr. Rings of constants of generic 4D Lotka-Volterra systems. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 529-538. doi: 10.1007/s10587-013-0035-z

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