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Chen, Yaoping; Chen, Fengde; Li, Zhong

Dynamic behaviors of a general discrete nonautonomous system of plankton allelopathy with delays. (English) Zbl 1160.37432

Discrete Dyn. Nat. Soc. 2008, Article ID 310425, 22 p. (2008).
Summary: 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.

Cited in 2 Documents

MSC:

37N25 Dynamical systems in biology
92C80 Plant biology
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\textit{Y. Chen} et al., Discrete Dyn. Nat. Soc. 2008, Article ID 310425, 22 p. (2008; Zbl 1160.37432)
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