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Dynamical analysis of a delayed diffusive predator–prey model with schooling behaviour and Allee effect
Journal of Biological Dynamics ( IF 2.8 ) Pub Date : 2020-11-23
Xin-You Meng, Jiao-Guo Wang

In this paper, a delayed diffusive predator–prey model with schooling behaviour and Allee effect is investigated. The existence and local stability of equilibria of model without time delay and diffusion are given. Regarding the conversion rate as bifurcation parameter, Hopf bifurcation of diffusive system without time delay is obtained. In addition, the local stability of the coexistent equilibrium and existence of Hopf bifurcation of system with time delay are discussed. Moreover, the properties of Hopf bifurcation are studied based on the centre manifold and normal form theory for partial functional differential equations. Finally, some numerical simulations are also carried out to confirm our theoretical results.



中文翻译:

具有学习行为和Allee效应的时滞扩散捕食模型的动力学分析

本文研究了具有学习行为和Allee效应的时滞扩散捕食模型。给出了没有时间延迟和扩散的模型平衡点的存在性和局部稳定性。将转换率作为分岔参数,得到无时滞的扩散系统的Hopf分岔。此外,还讨论了共存均衡的局部稳定性以及具有时滞的系统的Hopf分支的存在性。此外,基于中心流形和偏形式微分方程的范式理论,研究了霍普夫分支的性质。最后,还进行了一些数值模拟以证实我们的理论结果。

更新日期:2020-11-23
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