Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays

Yaoping Chen, Fengde Chen, and Zhong Li College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China Correspondence should be addressed to Fengde Chen, [email protected] Received 6 May 2008; Revised 8 September 2008; Accepted 22 November 2008 Recommended by Juan Jose Nieto We study the dynamic behaviors of a general discrete nonautonomous system of plankton allelopathy with delays. We first show that under some suitable assumption, the system is permanent. Next, by constructing a suitable Lyapunov functional, we obtain a set of sufficient conditions which guarantee the global attractivity of the two species. After that, by constructing an extinction-type Lyapunov functional, we show that under some suitable assumptions, one species will be driven to extinction. Finally, two examples together with their numerical simulations show the feasibility of the main results. Copyright q 2008 Yaoping Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.