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The aim of this study is to analyze the integrability problem ofLotka--Volterra three species biological system. The system which considered inthis work is a biological plausibility or a chemical model. The system has acomplex dynamical behavior because it is chaotic system. We, first show thatthe system is a complete integrable when two of the involved parameters in thesystem are zero. Second, thorough invariant algebraic surfaces and exponentialfactors, the nonintegrability problems have been investigated. Particularly, weshow the non-existence of polynomial, rational, formal series, and Darbouxfirst integrals when parameters are strictly positive.

Integrability of a Family of Lotka--Volterra Three Species Biological System