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 Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 10, Pages 1741–1757 (Mi zvmmf4945)

Algebraic features of some generalizations of the Lotka–Volterra system

Yu. V. Bibik, D. A. Sarancha

Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: For generalizations of the Lotka–Volterra system, an integration method is proposed based on the nontrivial algebraic structure of these generalizations. The method makes use of an auxiliary first-order differential equation derived from the phase curve equation with the help of this algebraic structure. Based on this equation, a Hamiltonian approach can be developed and canonical variables (moreover, action-angle variables) can be constructed.

Key words: Lotka–Volterra system, Hamiltonian approach, action-angle variables.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:10, 1655–1669

Bibliographic databases:

UDC: 519.62
Revised: 30.05.2010

Citation: Yu. V. Bibik, D. A. Sarancha, “Algebraic features of some generalizations of the Lotka–Volterra system”, Zh. Vychisl. Mat. Mat. Fiz., 50:10 (2010), 1741–1757; Comput. Math. Math. Phys., 50:10 (2010), 1655–1669

Citation in format AMSBIB
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