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A predator-prey model with genetic differentiation both in the predator and prey

School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, China

Special Issues: Advances in Mathematical Modelling and Analysis of Bioprocesses

In this paper, we propose a predator-prey model with genetic differentiation both in the predator and prey. First, we analyze two special cases: a model without the predators and a model with one genotype in both the predator and prey, and for each model show that the positive equilibria are always globally stable when they exist, while the boundary equilibria are always unstable. Then, for the newly proposed model, we give the results that the positive equilibrium is always local stable when it exists, the boundary equilibrium at the origin is always unstable, and the stability of another boundary equilibrium is determined by the existence of the positive equilibrium. Moreover, our discussions show the existence of local center manifolds near the equilibria. Finally, we give some examples to illustrate our results.
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Keywords predator-prey model; genotypes; equilibrium; stability; center manifold

Citation: Lisha Wang, Jiandong Zhao. A predator-prey model with genetic differentiation both in the predator and prey. Mathematical Biosciences and Engineering, 2020, 17(3): 2616-2635. doi: 10.3934/mbe.2020143


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