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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 4: 807-821. doi: 10.3934/mbe.2014.11.807
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On a diffusive predator-prey model with nonlinear harvesting

  • 1.
    Department of Mathematics, Florida Gulf Coast University, 11501 FGCU Blvd. S., Fort Myers, FL 33965
  • Received: 01 August 2013 Accepted: 29 June 2018 Published: 01 March 2014

  • MSC : Primary: 35K40, 35K57, 35B36; Secondary: 35Q92.

  • In this paper, we study the dynamics of a diffusive Leslie-Gower model with a nonlinear harvesting term on the prey. We analyze the existence of positive equilibria and their dynamical behaviors. In particular, we consider the model with a weak harvesting term and find the conditions for the local and global asymptotic stability of the interior equilibrium. The global stability is established by considering a proper Lyapunov function. In contrast, the model with strong harvesting term has two interior equilibria and bi-stability may occur for this system. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

    Citation: Peng Feng. On a diffusive predator-prey model with nonlinear harvesting[J]. Mathematical Biosciences and Engineering, 2014, 11(4): 807-821. doi: 10.3934/mbe.2014.11.807

    Related Papers:

  • In this paper, we study the dynamics of a diffusive Leslie-Gower model with a nonlinear harvesting term on the prey. We analyze the existence of positive equilibria and their dynamical behaviors. In particular, we consider the model with a weak harvesting term and find the conditions for the local and global asymptotic stability of the interior equilibrium. The global stability is established by considering a proper Lyapunov function. In contrast, the model with strong harvesting term has two interior equilibria and bi-stability may occur for this system. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.


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  • © 2014 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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