具有Holling II型响应函数的趋化器中捕食者-猎物模型

IF 0.4 Q4 MATHEMATICS, APPLIED Mathematics in applied sciences and engineering Pub Date : 2020-12-22 DOI:10.5206/mase/10842
T. Bolger, Brydon Eastman, Madeleine Hill, G. Wolkowicz
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引用次数: 2

摘要

考虑了具有Holling II型泛函和Monod或Michaelis-Menten形式的数值响应函数的趋化器中捕食者-猎物相互作用模型。证明了共存平衡点的局部渐近稳定性意味着它是全局渐近稳定的。还证明了当共存平衡存在但不稳定时,解收敛于唯一的、轨道渐近稳定的周期轨道。因此,趋化调节捕食者-猎物模型的动力学范围与具有Holling II型功能反应的类似的经典Rosenzweig-MacArthur捕食者-猎物模型相同。还给出了适用于其他功能响应的扩展。
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A Predator-Prey model in the chemostat with Holling Type II response function
A model of predator-prey interaction in a chemostat with Holling Type II functional and numerical response functions of the Monod or Michaelis-Menten form is considered. It is proved that local asymptotic stability of the coexistence equilibrium implies that it is globally asymptotically stable. It is also shown that when the coexistence equilibrium exists but is unstable, solutions converge to a unique, orbitally asymptotically stable periodic orbit. Thus the range of the dynamics of the chemostat predator-prey model is the same as for the analogous classical Rosenzweig-MacArthur predator-prey model with Holling Type II functional response. An extension that applies to other functional rsponses is also given.
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CiteScore
1.40
自引率
0.00%
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审稿时长
21 weeks
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