作者:李萌，常笑源
Authors:LI Meng,CHANG Xiao yuan摘要:为了研究斑块环境下捕食者带有 Allee 效应的捕食者与食饵相互作用的种群扩散模型的动力学性质 , 分析了两个斑块环境下扩散对种群的影响 ,并给出了模型解的正性 ,最终有界性 , 以及平衡点的存在性和局部稳定性 。最终得出当扩散系数很大时 ,平衡点都是不稳定的 ; 当扩散系数很小时 ,存在两个平衡点是局部渐近稳定的 , 这个现象是由模型中的 Allee 效应产生的 。最后进行数值模拟 ,验证所得结果。
Abstract:In order to study the dynamics of the predator-prey model with Allee effect in two patch environments, the effects of diffusion on the population in two patch environments are analyzed. The positivity and the ultimate boundedness of the solutions are obtained , also the existence and the stability of the equilibrium points are proved. It is concluded that when the diffusion coefficient is large enough, the equilibrium points are unstable. However, when the diffusion coefficient is small enough, there are two equilibrium points which are both locally asymptotically stable, which phenomenon is caused by the Allee effect in this model. Finally, the numerical simulations are carried out to verify the obtained results.

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