Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 261, pp. 116.
Existence and global asymptotic stability of positive periodic solutions
of a LotkaVolterra type competition systems with delays and feedback controls
Anh Tuan Trinh
Abstract:
The existence of positive periodic solutions of a periodic
LotkaVolterra 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: LotkaVolterra 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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