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Zheng, Wei School of Mathematics and Statistics, Northeast Normal University
Sugie, Jitsuro Department of Mathematics, Interdisciplinary Graduate School of Science and Engineering, ShimaneUniversity
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.
Global asymptotic stability
Lotka-Volterra predator-prey model
Weakly integrally positive
Nonlinear Analysis : Theory, Methods & Applications
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Interdisciplinary Graduate School of Science and Engineering