A stage-structured predator-prey model of Beddington-Deangelis type
A stage-structured predator-prey model of Beddington-Deangelis type
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DOI：
10.1137/050630003
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发表时间：
2006-01-01
影响因子：
1.9
通讯作者：
Beretta, Edoardo
中科院分区：
文献类型：
--
作者：
Liu, Shengqiang;Beretta, Edoardo
构造并研究了一类具有Beddington-DeAngelis型功能反应的阶段结构捕食-食饵模型.时间延迟是指从出生到成熟所需的时间。Beddington-DeAngelis功能反应类似于Holling 2型功能反应，但包含一个描述捕食者相互干扰的额外术语。首先，我们证明了捕食者与猎物永久共存的充要条件是捕食者在猎物丰度峰值时的补充率大于其死亡率。其次，我们证明了如果系统是永久的，那么足够大的捕食者干扰度不仅可以稳定系统，而且还可以保证系统的稳定性对食饵的承载能力的增加和成年捕食者的出生率的增加。第三，我们分析和数值计算表明，随着成熟时滞的增加，内部平衡的稳定性可能会发生切换：稳定性可能会从稳定到不稳定，最终稳定，这意味着一个大的延迟可以稳定。
We formulate and study a robust stage structured predator-prey model of Beddington DeAngelis-type functional response. The time delay is the time taken from birth to maturity. The Beddington-DeAngelis functional response is similar to the Holling type 2 functional response but contains an extra term describing mutual interference by predators. First we show that the predator coexists with prey permanently if and only if the predator's recruitment rate at the peak of prey abundance is larger than its death rate. Second, we show that if the system is permanent, then a sufficiently large degree of the predator interference can not only stabilize the system but also guarantee the stability of the system against the increase of the carrying capacity of prey and the increase of birth rate of the adult predator. Third, we show both analytically and numerically that stability switches of interior equilibrium may occur as maturation time delay increases: stability may change from stable to unstable to finally stable, implying that a large delay can be stabilizing.