Electron. J. Diff. Equ., Vol. 2013 (2013), No. 261, pp. 1-16.

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

Anh Tuan Trinh

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.

Submitted January 8, 2013. Published November 26, 2013.
Math Subject Classifications: 34K13, 92B05, 92D25, 93B52.
Key Words: Lotka-Volterra competition system; time delay; feedback control; positive periodic solution; global asymptotic stability; continuation theorem.

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Anh Tuan Trinh
Department of Mathematics
Hanoi National University of Education
136 Xuan Thuy Road, Hanoi, Vietnam
email: anhtt@hnue.edu.vn

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