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Russian Mathematics

, Volume 61, Issue 4, pp 5–10 | Cite as

On global asymptotic stability of the equilibrium of “predator–prey” system in varying environment

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Abstract

This paper considers a predator–prey system of differential equations. This ecological system is a model of Lotka–Volterra type whose prey population receives time-variation of the environment. It is not assumed that the time-varying coefficient is weakly integrally positive. We obtain sufficient conditions of global asymptotic stability of the unique interior equilibrium if the time-variation is bounded.

Keywords

global asymptotic stability Lotka–Volterra predator–prey model 

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© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and MechanicsDonetskUkraine

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