摘要
在Dirichlet边界条件下研究一类具有HollingⅣ型功能反应函数的竞争模型平衡态正解的存在性和稳定性。利用特征值问题的主特征值得到平衡态正解存在的必要条件,通过椭圆型方程比较原理给出平衡态正解的先验估计。运用局部分歧理论和稳定性理论研究了平衡态正解的存在性和稳定性。通过数值模型验证了平衡态正解的存在性定理。结果表明,当两竞争物种的增长率满足一定条件时,两竞争物种可以共存且共存态是稳定的。
The existence and the stability of steady-state positive solutions of a competition model with Holling typeⅣfunctional response are studied under Dirichlet boundary conditions.The necessary conditions for the existence of the steady state positive solution of the model are obtained by using the principal eigenvalue of the eigenvalue problem,and a priori es-timate of the steady-state positive solution is given by using the comparison principle of the elliptic equation.The existence and the stability of steady-state positive solutions of the model are studied by using local bifurcation theory and stability theo-ry.The existence theorem of steady-state positive solution is verified by numerical simulation.The results show that when the growth rates of two competing species satisfy certain conditions,the two competing species can coexist and the coexis-tence state is stable.
作者
王利娟
白娜娜
武阳鸽
杨佳饶
WANG Lijuan;BAI Nana;WU Yangge;YANG Jiarao(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,China)
出处
《渭南师范学院学报》
2023年第5期87-94,共8页
Journal of Weinan Normal University
基金
陕西省自然科学基础研究计划面上项目:两类电流体宏观连续介质模型大解的定性理论研究(2022JM-034)
陕西省科技厅自然科学基础研究计划项目:具有自控能力的V-T捕食模型的Dirichlet问题研究(2018JQ1066)。
