The five-variable Volterra system
Open Mathematics (2011)
- Volume: 9, Issue: 4, page 888-896
- ISSN: 2391-5455
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topJanusz Zieliński. "The five-variable Volterra system." Open Mathematics 9.4 (2011): 888-896. <http://eudml.org/doc/269519>.
@article{JanuszZieliński2011,
abstract = {We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.},
author = {Janusz Zieliński},
journal = {Open Mathematics},
keywords = {Volterra derivation; Lotka-Volterra derivation; Polynomial constant; Polynomial first integral; first integral; Volterra dynamical system},
language = {eng},
number = {4},
pages = {888-896},
title = {The five-variable Volterra system},
url = {http://eudml.org/doc/269519},
volume = {9},
year = {2011},
}
TY - JOUR
AU - Janusz Zieliński
TI - The five-variable Volterra system
JO - Open Mathematics
PY - 2011
VL - 9
IS - 4
SP - 888
EP - 896
AB - We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.
LA - eng
KW - Volterra derivation; Lotka-Volterra derivation; Polynomial constant; Polynomial first integral; first integral; Volterra dynamical system
UR - http://eudml.org/doc/269519
ER -
References
top- [1] Bogoyavlenskij O.I., Algebraic constructions of integrable dynamical systems - extension of the Volterra system, Uspekhi Mat. Nauk, 1991, 46(3), 3–48 (in Russian)
- [2] Bogoyavlenskij O.I., Integrable Lotka-Volterra systems, Regul. Chaotic Dyn., 2008, 13(6), 543–556 http://dx.doi.org/10.1134/S1560354708060051 Zbl1229.37097
- [3] Deveney J.K., Finston D.R., A proper G a action on C 5 which is not locally trivial, Proc. Amer. Math. Soc., 1995, 123(3), 651–655 Zbl0832.14036
- [4] Itoh Y., Integrals of a Lotka-Volterra system of odd number of variables, Progr. Theoret. Phys., 1987, 78(3), 507–510 http://dx.doi.org/10.1143/PTP.78.507
- [5] Maciejewski A.J., Moulin Ollagnier J., Nowicki A., Strelcyn J.-M., Around Jouanolounon-integrability theorem, Indag. Math., 2000, 11(2), 239–254 http://dx.doi.org/10.1016/S0019-3577(00)89081-3 Zbl0987.34005
- [6] Moulin Ollagnier J., Nowicki A., Polynomial algebra of constants of the Lotka-Volterra system, Colloq. Math., 1999, 81(2), 263–270 Zbl1004.12004
- [7] Nowicki A., Polynomial Derivations and their Rings of Constants, Uniwersytet Mikołaja Kopernika, Toruń, 1994 Zbl1236.13023
- [8] Nowicki A., The fourteenth problem of Hilbert for polynomial derivations, In: Differential Galois Theory, Bedlewo, 2001, Banach Center Publ., 58, Polish Academy of Sciences, Warsaw, 2002, 177–188 http://dx.doi.org/10.4064/bc58-0-13 Zbl1029.13015
- [9] Nowicki A., A factorisable derivation of polynomial rings in n variables (in press) Zbl1273.13048
- [10] Nowicki A., Zieliński J., Rational constants of monomial derivations, J. Algebra, 2006, 302(1), 387–418 http://dx.doi.org/10.1016/j.jalgebra.2006.02.034 Zbl1119.13021
- [11] Ossowski P., Zieliński J., Polynomial algebra of constants of the four variable Lotka-Volterra system, Colloq. Math., 2010, 120(2), 299–309 http://dx.doi.org/10.4064/cm120-2-9 Zbl1207.13016
- [12] Zieliński J., Factorizable derivations and ideals of relations, Comm. Algebra, 2007, 35(3), 983–997 http://dx.doi.org/10.1080/00927870601117639 Zbl1171.13013
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