Dynamical analysis of a delayed diffusive predator-prey model with schooling behaviour and Allee effect
Dynamical analysis of a delayed diffusive predator-prey model with schooling behaviour and Allee effect
复制标题
具有学校行为和 Allee 效应的延迟扩散捕食者-被捕食者模型的动力学分析
DOI：
10.1080/17513758.2020.1850892
复制
发表时间：
2020
影响因子：
2.8
通讯作者：
Wang Jiao Guo
中科院分区：
文献类型：
--
作者：
Meng Xin You;Wang Jiao Guo
研究了一类具有学习行为和Allee效应的时滞扩散捕食者-食饵模型。给出了无时滞扩散模型平衡点的存在性和局部稳定性。以转化率为分支参数，得到了扩散系统的无时滞Hopf分支。此外，还讨论了时滞系统共存平衡点的局部稳定性和Hopf分支的存在性。此外，基于偏泛函微分方程的中心流形和规范型理论，研究了其Hopf分支的性质。最后，还进行了一些数值模拟，以验证我们的理论结果。
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.