| Title:
|
Rings of constants of generic 4D Lotka-Volterra systems (English) |
| Author:
|
Zieliński, Janusz |
| Author:
|
Ossowski, Piotr |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
529-538 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lotka-Volterra derivation |
| Keyword:
|
polynomial constant |
| Keyword:
|
polynomial first integral |
| Keyword:
|
Darboux polynomial |
| MSC:
|
12H05 |
| MSC:
|
13N15 |
| MSC:
|
34A34 |
| MSC:
|
92D25 |
| idZBL:
|
Zbl 06236429 |
| idMR:
|
MR3073976 |
| DOI:
|
10.1007/s10587-013-0035-z |
| . |
| Date available:
|
2013-07-18T15:07:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143330 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
