Integrability and linearizability of the Lotka-Volterra systems |
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| Authors: | Changjian Liu Guoting Chen Chengzhi Li |
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| Institution: | a UFR de Mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq, France
b School of Mathematical Sciences, Peking University, 100871 Beijing, People's Republic of China |
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| Abstract: | Integrability and linearizability of the Lotka-Volterra systems are studied. We prove sufficient conditions for integrable but not linearizable systems for any rational resonance ratio. We give new sufficient conditions for linearizable Lotka-Volterra systems. Sufficient conditions for integrable Lotka-Volterra systems with 3:−q resonance are given. In the particular cases of 3:−5 and 3:−4 resonances, necessary and sufficient conditions for integrable systems are given. |
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| Keywords: | Integrability Linearizability Lotka-Volterra system Center problem |
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