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Partial survival and extinction of species in discrete nonautonomous Lotka-Volterra systems. (English) Zbl 1081.39014
Consider the following discrete model of a nonautonomous Lotka-Volterra system, \[ N_i(p+1)=N_i(p)\exp \biggl\{c_i(p)-\sum_{j=1}^n \sum_{l=0}^m a_{ij}^l (p)N_j(p-k_l)\biggr\}, \quad p\geq 0, \;1\leq i\leq n, \] with \[ N_i(p)=N_{ip}\geq 0, \;p\leq 0, \quad \text{and}\quad N_{i0}>0, \;1\leq i\leq n, \] which is the discrete version of the system considered by Y. Muroya [Dyn. Syst. Appl. 12, No. 3–4, 295–306 (2003; Zbl 1044.92049)]. The author studies the partial survial and extinction of species. These results extend those of S. Ahmad [Proc. Am. Math. Soc. 127, No. 10, 2905–2910 (1999; Zbl 0924.34040)] to discrete nonautonomous Lotka-Volterra systems.

MSC:
39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
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