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Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances. (English) Zbl 1113.92065

Summary: We consider a nonautonomous competitive Lotka-Volterra system of two species with the effect of toxic substances. It is shown that toxic substances play an important role in the extinction of species. We prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation under some conditions.

MSC:

92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
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