Stability of the boundary solution of a nonautonomous predator–prey system with the Beddington–DeAngelis functional response

The dynamics of a nonautonomous predator–prey system with the Beddington–DeAngelis functional response is studied from the perspective of extinction of the predator. With the help of a Fluctuation Lemma, we obtain a set of new sufficient conditions on the global asymptotic stability of the boundary solution (which means the extinction of the predator). The result not only improves but also complements some existing ones. Moreover, the result indicates that the effect of the parameters is accumulative rather than pointwise.