Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 310425, 22 pages
doi:10.1155/2008/310425

Dynamic behaviors of a general discrete nonautonomous system of plankton allelopathy with delays

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.