PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 11 | 1923-1931
Tytuł artykułu

Rings of constants of four-variable Lotka-Volterra systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
11
Strony
1923-1931
Opis fizyczny
Daty
wydano
2013-11-01
online
2013-08-23
Twórcy
Bibliografia
  • [1] Almeida M.A., Magalhães M.E., Moreira I.C., Lie symmetries and invariants of the Lotka-Volterra system, J. Math. Phys., 1995, 36(4), 1854–1867 http://dx.doi.org/10.1063/1.531362
  • [2] Bogoyavlenskiĭ O.I., Algebraic constructions of integrable dynamical systems - extension of the Volterra system, Russian Math. Surveys, 1991, 46(3), 1–64 http://dx.doi.org/10.1070/RM1991v046n03ABEH002801
  • [3] Cairó L., Llibre J., Darboux integrability for 3D Lotka-Volterra systems, J. Phys. A, 2000, 33(12), 2395–2406 http://dx.doi.org/10.1088/0305-4470/33/12/307
  • [4] Hegedűs P., The constants of the Volterra derivation, Cent. Eur. J. Math., 2012, 10(3), 969–973 http://dx.doi.org/10.2478/s11533-012-0024-8
  • [5] Kuroda S., Fields defined by locally nilpotent derivations and monomials, J. Algebra, 2005, 293(2), 395–406 http://dx.doi.org/10.1016/j.jalgebra.2005.06.011
  • [6] Moulin Ollagnier J., Nowicki A., Polynomial algebra of constants of the Lotka-Volterra system, Colloq. Math., 1999, 81(2), 263–270
  • [7] Nowicki A., Polynomial Derivations and their Rings of Constants, Uniwersytet Mikołaja Kopernika, Torun, 1994
  • [8] Nowicki A., Zielinski J., Rational constants of monomial derivations, J. Algebra, 2006, 302(1), 387–418 http://dx.doi.org/10.1016/j.jalgebra.2006.02.034
  • [9] Ossowski P., Zielinski 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
  • [10] Zielinski J., Factorizable derivations and ideals of relations, Comm. Algebra, 2007, 35(3), 983–997 http://dx.doi.org/10.1080/00927870601117639
  • [11] Zielinski J., The five-variable Volterra system, Cent. Eur. J. Math., 2011, 9(4), 888–896 http://dx.doi.org/10.2478/s11533-011-0032-0
  • [12] Zielinski J., Ossowski P., Rings of constants of generic 4D Lotka-Volterra systems, Czechoslovak Math. J., 2013, 63(138)(2), 529–538 http://dx.doi.org/10.1007/s10587-013-0035-z
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0300-2
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.