Stability Analysis and Hopf Bifurcation for ODE System of Predator-Prey Model with Mutual Interference  

作　　者：Khalid Ahmed Abbakar Yafei Yang Alhussein Mohamed Songchen Xia Mogahid Mamoon Abkar Omer Bushra Elfadil Hassan Khalid Ahmed Abbakar;Yafei Yang;Alhussein Mohamed;Songchen Xia;Mogahid Mamoon Abkar;Omer Bushra Elfadil Hassan(College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China;Department of Mathematics and Physics, Faculty of Education, University of Gadarif, Gadarif, Sudan;School of Mathematics and Statistics, Northeast Normal University, Changchun, China;Department of Mathematics, School of Mathematics, University of Witwatersrand, Johannesburg, South Africa)

机构地区：[1]College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China [2]Department of Mathematics and Physics, Faculty of Education, University of Gadarif, Gadarif, Sudan [3]School of Mathematics and Statistics, Northeast Normal University, Changchun, China [4]Department of Mathematics, School of Mathematics, University of Witwatersrand, Johannesburg, South Africa

出　　处：《Applied Mathematics》2021年第9期793-802,共10页应用数学（英文）

摘　　要：In this paper, the temporal and spatial patterns of a diffusive predator-prey model with mutual interference under homogeneous Neumann boundary conditions were studied. Specifically, first, taking the intrinsic growth rate of the predator as the parameter, we give a computational and theoretical analysis of Hopf bifurcation on the positive equilibrium for the ODE system. As well, we have discussed the conditions for determining the bifurcation direction and the stability of the bifurcating periodic solutions.In this paper, the temporal and spatial patterns of a diffusive predator-prey model with mutual interference under homogeneous Neumann boundary conditions were studied. Specifically, first, taking the intrinsic growth rate of the predator as the parameter, we give a computational and theoretical analysis of Hopf bifurcation on the positive equilibrium for the ODE system. As well, we have discussed the conditions for determining the bifurcation direction and the stability of the bifurcating periodic solutions.

关 键 词：Predator-Prey Model Mutual Interference Hopf Bifurcation Functional Response 

分 类 号：O17[理学—数学]