一类带有Holling-Ⅲ功能反应函数的Leslie-Gower捕食-食饵模型平衡态正解分析  

Analysis of positive steady-state solutions for a class of Leslie-Gower predator-prey model with Holling-Ⅲfunctional response

作　　者：康子月 姜洪领 赵艺 卢晨萧 KANG Zi-yue;JIANG Hong-ling;ZHAO Yi;LU Chen-xiao(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）》2024年第3期5-10,36,共7页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金项目(12061081);陕西省科技厅自然科学基础研究计划项目(2018JQ1066)。

摘　　要：目的研究一类带有HollingⅢ功能反应函数的Leslie-Gower捕食-食饵模型平衡态正解的存在性与稳定性,并通过数值模拟验证已得到的理论结果。方法利用反应扩散方程理论对平衡态正解进行定性分析,使用数值模拟技术进行定量分析。结果建立了平衡态正解存在以及稳定的条件,给出了物种生长率对平衡态正解的影响。结论适当大的生长率可以使捕食者和食饵共存。同时数值模拟表明,食饵生长率较高时,捕食者数量关于其生长率不是严格递增的。Purposes—To investigate the existence and stability of positive steady-state solutions for a Leslie-Gower predator-prey model with HollingⅢfunctional response,and verify the obtained theoretical results by numerical simulations.Methods—The qualitative analysis of positive steady-state solutions is carried out by using the theory of reaction-diffusion equation,and so is the quantitative analysis by using the numerical simulations technique.Results—The conditions for the existence and stability of positive steady-state solutions are established,with the effects of the species growth rate on positive steady-state solutions given.Conclusions—An appropriate high growth rate can make predator and prey coexist.At the same time,numerical simulations show that when prey growth rate is high,the numbers of predator are not strictly increasing with respect to their growth rate.

关 键 词：Holling-Ⅲ功能反应函数 Leslie-Gower捕食-食饵模型 分歧 数值模拟 

分 类 号：O175.26[理学—数学]