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

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.

Show me the PDF file (249 KB), TEX file, and other files for this article.

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

Return to the EJDE web page