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Extinction in two dimensional discrete Lotka-Volterra competitive system with the effect of toxic substances. (English) Zbl 1142.92044

Summary: We consider a nonautonomous discrete Lotka-Volterra system of two species with the effect of toxic substances. We prove that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete logistic equation under some conditions. For the periodic case, we also obtain another set of sufficient conditions which guarantee the extinction and the existence of a globally stable periodic solution. It is shown that toxic substances play an important role in the extinction of species.

MSC:

92D40 Ecology
39A11 Stability of difference equations (MSC2000)
34C60 Qualitative investigation and simulation of ordinary differential equation models
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