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