Journal Article A necessary and sufficient condition for global asymptotic stability of time-varying Lotka-Volterra predator-prey systems

Zheng, Wei  ,  Sugie, Jitsuro

127pp.128 - 142 , 2015-11 , Elsevier
The purpose of this paper is to present a necessary and sufficient condition which guarantees that an interior equilibrium of a certain predator–prey system is globally asymptotically stable. This ecological system is a model of Lotka–Volterra type whose prey population receives time-variation of the environment. We assume that the time-varying coefficient is weakly integrally positive and has a weaker property than uniformly continuous. Our necessary and sufficient condition is expressed by an improper double integral on the time-varying coefficient. Our work is inspired by the study of the stability theory for damped linear oscillators.

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