Imperfect and Bogdanov–Takens bifurcations in biological models: from harvesting of species to isolation of infectives
Imperfect and Bogdanov–Takens bifurcations in biological models: from harvesting of species to isolation of infectives
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DOI：
10.1007/s00285-023-01951-3
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发表时间：
2023-06
影响因子：
1.9
通讯作者：
S. Ruan;Dongmei Xiao
中科院分区：
文献类型：
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作者：
S. Ruan;Dongmei Xiao
自然界生物系统在人为干预下可能会表现出复杂的动力学行为，这可能导致系统的崩溃或稳定。分岔理论通过对生物系统的建模和分析，在理解这一进化过程中起着重要的作用。在本文中，我们研究了两种类型的生物模型，弗雷德布劳尔作出了先驱性的贡献：捕食者-食饵模型与放养/收获和传染病模型与进口/隔离。首先考虑具有Holling Ⅱ型功能性反应的捕食者-食饵模型，其动力学和分支是很好理解的。通过考虑人类的干预，如捕食者的不断收获或放养，我们证明了系统在人类的干预下经历了不完美分支和Bogdanov-Takens分支，这导致了更丰富的动力学行为，如极限环或同宿环的存在.然后我们考虑一个带有常数输入/隔离的传染病模型，当常数输入/隔离率变化时，观察到类似的不完全分支和Bogdanov-Takens分支.
A natural biological system under human interventions may exhibit complex dynamical behaviors which could lead to either the collapse or stabilization of the system. The bifurcation theory plays an important role in understanding this evolution process by modeling and analyzing the biological system. In this paper, we examine two types of biological models that Fred Brauer made pioneer contributions: predator–prey models with stocking/harvesting and epidemic models with importation/isolation. First we consider the predator–prey model with Holling type II functional response whose dynamics and bifurcations are well-understood. By considering human interventions such as constant harvesting or stocking of predators, we show that the system under human interventions undergoes imperfect bifurcation and Bogdanov-Takens bifurcation, which induces much richer dynamical behaviors such as the existence of limit cycles or homoclinic loops. Then we consider an epidemic model with constant importation/isolation of infective individuals and observe similar imperfect and Bogdanov-Takens bifurcations when the constant importation/isolation rate varies.