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Mathematical Biosciences and Engineering

2020, Volume 17, Issue 3: 2616-2635. doi: 10.3934/mbe.2020143
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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
  • Received: 27 November 2019 Accepted: 26 February 2020 Published: 04 March 2020

  • 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.

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

    Related Papers:

  • 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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