Integrability of Lotka-Volterra type systems of degree 4

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Original languageEnglish
Pages (from-to)1107-1116
Journal / PublicationJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Apr 2012


We study the integrability of the Lotka-Volterra type systems with 1. :. - (3. q- 1) resonances. We prove some sufficient conditions for the integrabilities of the systems and give some necessary conditions by studying the first two saddle values of the system. In the particular cases of 1. :. - 2, 1. :. - 5 and 1. :. - 8 resonances, we derive necessary and sufficient conditions for the integrabilities of the systems. © 2011 Elsevier Inc.

Research Area(s)

  • Center problem, Integrability, Lotka-Volterra type system, Saddle value