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Stability Analysis and Hopf Bifurcation for ODE System of Predator-Prey Model with Mutual Interference
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
School of Mathematics and Statistics, Northeast Normal University, Changchun, China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
Department of Mathematics, School of Mathematics, University of Witwatersrand, Johannesburg, South Africa
Department of Mathematics and Physics, Faculty of Education, University of Gadarif, Gadarif, Sudan
- 1 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 2 School of Mathematics and Statistics, Northeast Normal University, Changchun, China
- 3 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 4 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 5 Department of Mathematics, School of Mathematics, University of Witwatersrand, Johannesburg, South Africa
- 6 Department of Mathematics and Physics, Faculty of Education, University of Gadarif, Gadarif, Sudan
Applied Mathematics·Volume 12 (2021)·Pages 793–802·Published 2 September 2021·DOI10.4236/am.2021.129053
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Abstract
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.
KeywordsPredator-Prey ModelMutual InterferenceHopf BifurcationFunctional Response
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