Extinction of a Discrete Competitive System with Beddington-DeAngelis Functional Response and the Effect of Toxic Substances

Abstract

In this paper, we consider a discrete competitive system with Beddington-DeAngelis functional response and the effect of toxic substances. By constructing some suitable Lyapunov type extinction functions, sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. Our results not only supplement and improve but also generalize some existing ones. Numerical simulations show the feasibility of our results.