نبذة مختصرة : In this paper we study the Lotka-Volterra complex cubic systems. We obtain necessary conditions of integrability for these systems with some restriction on the parameters. The sufficiency is proved for all conditions, except one which remains open, using different methods. ; The research of this paper was done during the three months visit of first author in Lleida. She obtained Slovenian scholarship for the Research Cooperation of Doctoral Students Abroad in Year 2013 and is partially supported by Slovenian research Agency and the 7th European Community Framework Programme, FP7-PEOPLE-2012-IRSES-316338. The second author is partially supported by a MINECO/ FEDER grant number MTM2014-53703-P and by an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204.
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