具有非线性增长率和Ivlev功能函数的捕食-食饵模型平衡态正解的存在性及稳定性  

The existence and stability of the steady-state positive solutions of a predator-prey model with nonlinear growth rate and Ivlev-type functional response

作　　者：井苗苗 姜洪领 康子月 JING Miao-miao;JIANG Hong-ling;KANG Zi-yue(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2023年第2期13-18,共6页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：陕西省科技厅自然科学基础研究计划项目(2018JQ1066);陕西省教育厅专项科学研究计划项目(18JK0043)。

摘　　要：目的在齐次Dirichlet边界条件下,研究一类带Ivlev型功能反应函数和非线性增长率的捕食-食饵扩散模型的平衡态正解性质。方法利用上下解方法和强极值原理研究平衡态正解的先验估计,利用简单特征值分歧理论和扰动理论研究平衡态正解的存在性与稳定性。结果给出捕食-食饵模型存在平衡态正解以及稳定的条件。结论在适当条件下,捕食者和食饵不但共存,而且共存模式是稳定的。Purposes—To study the properties of positive solutions of a predator-prey diffusion model with Ivlev-type functional response and nonlinear growth rate under the homogeneous Dirichlet boundary condition.Methods—The upper and lower solution method and the strong extremum principle are used to study the prior estimation of steady-state positive solutions,and bifurcation theory and perturbation theory of the simple eigenvalue are used to study the existence and stability of steady-state positive solution.Result—The conditions of the existence and stability for steady-state positive solutions of the predator-prey model are established.Conclusion—Under appropriate conditions,predator and prey coexist and coexistence is stable.

关 键 词：捕食-食饵模型 Ivlev型功能反应函数 非线性增长率 平衡态正解 

分 类 号：O175.26[理学—数学]