Existence and global asymptotic stability of positive periodic solutions of a Lotka-Volterra type competition systems with delays and feedback controls

Abstract

The existence of positive periodic solutions of a periodic Lotka-Volterra type competition system with delays and feedback controls is studied by applying the continuation theorem of coincidence degree theory. By contracting a suitable Liapunov functional, a set of sufficient conditions for the global asymptotic stability of the positive periodic solution of the system is given. A counterexample is given to show that the result on the existence of positive periodic solution in [4] is incorrect.

Keywords

• Lotka-Volterra competition system
• time delay
• feedback control
• positive periodic solution
• global asymptotic stability
• continuation theorem