关于“受Allee效应影响的三营养食物链模型在有性生殖型顶级捕食者种群中的全局动态”的评论[Comp and Math Methods. 2019;《科学》,第2期,第1-23页。

IF 0.9 Q3 MATHEMATICS, APPLIED Computational and Mathematical Methods Pub Date : 2021-03-15 DOI:10.1002/cmm4.1159
Eric M. Takyi, Kwadwo Antwi-Fordjour, Said Kouachi, Rana D. Parshad
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引用次数: 1

摘要

Debnath et al.(2019)考虑了中间捕食者和顶级捕食者之间受Allee效应影响的猎物生长和Crowley-Martin感官功能反应的三营养食物链模型,其中顶级捕食者为有性生殖类型。在参数空间的一定限制下,该模型对所有正初始条件都有有界解,并且是耗散的。我们证明这是不正确的。特别是,对于充分选择的初始数据,即使在Debnath et al.(2019)导出的限制下,模型的解也可以在有限时间内爆炸。我们导出了一个新的消光边界。我们还推测了Allee阈值对模型爆破动力学的影响。所有的结果都通过数值模拟得到了验证。
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A remark on “ Global dynamics of a tritrophic food chain model subject to the Allee effects in the prey population with sexually reproductive generalized-type top predator” [Comp and Math Methods. 2019; E1079, pp. 1–23]

In Debnath et al. (2019), a tritrophic food chain model subject to a Allee effect on the prey growth and Crowley–Martin senses functional response between intermediate predator and top predator, with a top predator of sexually reproductive type is considered. It is claimed that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, and is dissipative. We show that this is not true. In particular, solutions to the model can blow-up in finite time, even under the restrictions derived in Debnath et al. (2019), for sufficiently chosen initial data. We derive a new extinction boundary for the system. We also conjecture on the effect of the Allee threshold on the blow-up dynamics in the model. All of our results are validated via numerical simulations.

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