Global attractivity of multiple species competition Lotka-Volterra system with toxicants effect and feedback controls

By means of species dynamic theory, a nonautonomous Lotka-Volterra multiple species competition system with toxicants effect and feedback controls was established, and the high order nonlinear function was used in the construction of the feedback control variables. By means of Continuation Theorem based on Gaines and Mawhin coincidence degree theory, Barbalat Lemma and constructing an appropriate Lyapunov function, the sufficient conditions for the uniqueness and global attractivity of positive periodic solutions of the system were obtained.