Volume 4,  Issue 5, 2003

Article 89

EXISTENCE AND GLOBAL ATTRACTIVITY OF PERIODIC SOLUTIONS IN n-SPECIES FOOD-CHAIN SYSTEM WITH TIME DELAYS

QIMING LIU AND HAIYUN ZHOU

DEPARTMENT OF MATHEMATICS
SHIJIAZHUANG INSTITUTE OF MECHANICAL ENGINEERING
NO. 97 HEPING WEST ROAD
SHIJIAZHUANG 050003, HEBEI
P.R. CHINA.
E-Mail: llqm2002@yahoo.com.cn

Received 21 August, 2003; Accepted 10 October, 2003.
Communicated by: R.P. Agarwal

ABSTRACT.   A delayed periodic n-species simple food-chain system with Holling type-II functional response is investigated. By means of Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing appropriate Lyapunov functionals, sufficient conditions are obtained for the existence and global attractivity of positive periodic solutions of the system.
Key words:
Time delay, Periodic solution, Global attractivity.

2000 Mathematics Subject Classification:
34K13, 92D25.

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