Permanence and global stability for nonautonomous discrete model of plankton allelopathy. (English) Zbl 1067.39009

Huo, Hai-Feng; Li, Wan-Tong

Appl. Math. Lett. 17, No. 9, 1007-1013 (2004).

For the system \(x_i(k+ 1)= x_i(k)\exp\{r_i- a_{i1} x_1(k)- a_{i2} x_2(k)-b_i x_1(k)x_2(k)\}\) with variable coefficients, \(i= 1,2\), sufficient conditions are given such that it is permanent. In the case of periodic coefficients sufficient conditions are given such that a periodic solution exists, and that this solution is globally stable, in case it is positive.

Reviewer: Lothar Berg (Rostock)

MSC:

39A11	Stability of difference equations (MSC2000)
92D25	Population dynamics (general)
92D40	Ecology

Keywords:

plankton allelopathy; Periodic solution; Permanence; Global stability

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