具有时滞和基于比率的三种群捕食系统的持久性与全局渐近稳定性

徐瑞;陈兰荪

系统科学与数学 ›› 2001, Vol. 21 ›› Issue (2) : 204-212.

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系统科学与数学 ›› 2001, Vol. 21 ›› Issue (2) : 204-212. DOI: 10.12341/jssms09682
论文

具有时滞和基于比率的三种群捕食系统的持久性与全局渐近稳定性

    徐瑞(1),陈兰荪(2)
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PERSISTENCE AND GLOBAL STABILITY FOR THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME DELAYS

    Rui XU(1),Lan Sun CHEN(2)
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摘要

研究一类具有时滞和基于比率的三种群食物链捕食-被捕食动力学模型.证明了该系统在适当条件下的一致持久性;通过构造Lyapunov泛函,得到了该系统正平衡点全局渐近稳定的充分条件.

Abstract

A three-species ratio-dependent predator-prey food chain model with time delays is investigated.It is shown that the system is uniformly persistent under some appropriate conditions,and sufficient conditions are obtained for the global stability of the positive equilibrium of the system.

关键词

时滞 / 持久性 / Lyapunov泛函 / 全局渐近稳定性

Key words

Delay / persistence / global asymptotic stability

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徐瑞 , 陈兰荪. 具有时滞和基于比率的三种群捕食系统的持久性与全局渐近稳定性. 系统科学与数学, 2001, 21(2): 204-212. https://doi.org/10.12341/jssms09682
Rui XU , Lan Sun CHEN. PERSISTENCE AND GLOBAL STABILITY FOR THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME DELAYS. Journal of Systems Science and Mathematical Sciences, 2001, 21(2): 204-212 https://doi.org/10.12341/jssms09682
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