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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 603-617, October 2007




GLOBAL ATTRACTIVITY OF AN $ n$-SPECIES

NONAUTONOMOUS ``PURE-DELAY-TYPE''

COMPETITION SYSTEM


BY


FENGDE CHEN




Abstract. In this paper, we study a non-autonomous $ n$-species ``pure-delay-type'' competitive system, which can be seen as the generalization of the traditional ``pure-delay-type" Lotka-Volterra competition system. By constructing a suitable Lyapunov functional, some sufficient conditions which guarantee the global attractivity of the positive solutions of the system are obtained. An example shows the feasibility of our main result.

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Received October 1, 2005; revised February 19, 2007; May 23, 2007.

AMS Subject Classification. 34C25, 92D25, 34D20, 34D40.

Key words. non-autonomous, competition, pure-delay-type, Lyapunov functional, global attractivity.