Global asymptotic stability for predator-prey systems whose prey receives time-variation of the environment

Sugie, Jitsuro; Saito, Yasuhisa; Fan, Meng

doi:10.1090/S0002-9939-2011-11124-9

Global asymptotic stability for predator-prey systems whose prey receives time-variation of the environment
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by Jitsuro Sugie, Yasuhisa Saito and Meng Fan PDF

Proc. Amer. Math. Soc. 139 (2011), 3475-3483 Request permission

Abstract:

A predator-prey model with prey receiving time-variation of the environment is considered. Such a system is shown to have a unique interior equilibrium that is globally asymptotically stable if the time-variation is bounded and weakly integrally positive. In particular, the result tells us that the equilibrium point can be stabilized even by nonnegative functions that make the limiting system structurally unstable. The method that is used to obtain the result is an analysis of asymptotic behavior of the solutions of an equivalent system to the predator-prey model.

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