一类具有食饵恐惧和避难所的反应扩散捕食模型的稳定性与Hopf分支  

Stability and Hopf Bifurcation of a Reaction Diffusion Predator-prey Model with Prey Fear and Refuge

作　　者：陈清婉 柳文清 CHEN Qingwan;LIU Wenqing(College of General Education,Minnan Science and Technology Institute,Quanzhou 362300)

机构地区：[1]闽南科技学院通识教育学院,泉州362300

出　　处：《工程数学学报》2022年第3期495-501,共7页Chinese Journal of Engineering Mathematics

基　　金：福建省中青年教师教育科研项目(JAT210616,JAT191035,JAT191044);福建省教育科学“十四五”规划课题(FJJKBK21-100)。

摘　　要：在捕食生态系统中,恐惧因子和食饵避难所都有重要的作用。为此,对一类带恐惧因子和食饵避难所的捕食-食饵反应扩散模型进行了研究。通过分析平衡点特征方程,得到了平衡点的局部渐近稳定性;将不受保护食饵比例作为分支参数,给出了正平衡点Hopf分支存在的条件。结果表明:避难所的存在会导致Hopf分支,产生空间齐次周期解。扩散的加入会产生新的Hopf分支点,产生空间非齐次周期解。这说明通过设立适当的食饵避难所或者减小捕食者的扩散,有助于物种共存。最后,利用Matlab进行数值模拟验证了所得的结论。Both fear factors and prey refuge have important effects in predation on the ecosystems. A class of reaction diffusion predator-prey models with fear effect and prey refuge is studied. We first provide the local asymptotic stability of the equilibrium point by using the linearization method and local bifurcation theory. Next, the existence of Hopf bifurcation and limit cycle is examined by choosing the ratio of un-protected prey as the bifurcation parameter.The results show that the existence of the refuge leads to Hopf bifurcation and spatially homogeneous periodic solution, and the addition of diffusion leads to new Hopf bifurcation points and inhomogeneous periodic solutions. This shows that the biological population can coexist by setting up an appropriate prey refuge or reducing the diffusion of predators. Finally, the conclusions are verified through numerical simulation.

关 键 词：恐惧因子 避难所 HOPF分支 稳定性 

分 类 号：O175.26[理学—数学]