Periodic solution of a higher dimensional ecological system

The main purpose of this article is to study the periodicity of a Lotka-Volterra's competition system with feedback controls. Some new and interesting sufficient conditions are obtained for the global existence of positive periodic solutions. Our method is base on combining matrix's spectral theory and inequality |x(t)| ≤ x(t0) + ∫0ω |ẋ(t)|dt. Some examples and their simulations show the feasibility of our main result.