Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay
Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay
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DOI：
10.1155/2019/7296461
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发表时间：
2019-08
影响因子：
1.2
通讯作者：
Yong Ye;Hua Liu;Yumei Wei;Ming Ma;Kai Zhang
中科院分区：
文献类型：
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作者：
Yong Ye;Hua Liu;Yumei Wei;Ming Ma;Kai Zhang
本文详细研究了猎物-捕食者模型和猎物生长中的弱Allee效应及其动态行为。定性讨论了模型平衡点的存在性、有界性和稳定性。还考虑了分岔分析。结合搜索延迟和消化延迟后，我们建立了具有 Allee 效应的延迟捕食者-被捕食系统。结果表明，当时延跨越一组临界值时，存在稳定性开关，并且发生Hopf分岔。最后，我们提出一些数值模拟来说明我们的理论分析。
In this paper, a prey-predator model and weak Allee effect in prey growth and its dynamical behaviors are studied in detail. The existence, boundedness, and stability of the equilibria of the model are qualitatively discussed. Bifurcation analysis is also taken into account. After incorporating the searching delay and digestion delay, we establish a delayed predator-prey system with Allee effect. The results show that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values. Finally, we present some numerical simulations to illustrate our theoretical analysis.