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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 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
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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.
Received: 29.12.2009
Revised: 30.05.2010
English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 10, Pages 1655–1669
DOI: https://doi.org/10.1134/S0965542510100039
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
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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