Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 310425, 22 pages
doi:10.1155/2008/310425
Research Article
Dynamic Behaviors of a General Discrete Nonautonomous System of Plankton Allelopathy with Delays
College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China
Received 6 May 2008; Revised 8 September 2008; Accepted 22 November 2008
Academic Editor: Juan Jose Nieto
Copyright © 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.
Abstract
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.