On a diffusive predator-prey model with nonlinear harvesting

  • 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

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  • 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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    [1] Chaos Sol. and Fractals, 14 (2002), 1275-1293.
    [2] Appl. Math. Lett., 16 (2003), 1069-1075.
    [3] J. Math. Biol., 36 (1997), 149-168.
    [4] J. Diff. Eqns., 246 (2009), 3932-3956.
    [5] Springer, New-York, 1983.
    [6] Nonlinear Analysis: Real World Applications, 12 (2011), 2385-2395.
    [7] J. Math. Anal. Appl., 398 (2013), 278-295.
    [8] Appl. Math. Lett., 14 (2011), 697-699.
    [9] J. Comput. Appl Math., 185 (2006), 19-33.
    [10] Disc. Cont. Dyn. Syst. S, 1 (2008), 303-315.
    [11] Biometrika, 35 (1948), 213-245.
    [12] Princeton University Press, Princeton, NJ, 1974.
    [13] Nonlinear Anal. Real World Appl., 7 (2006), 1104-1118.
    [14] Bull. Math. Biol., 50 (1988), 379-409.
    [15] J. Math. Anal and Appl., 324 (2006), 14-29.
    [16] Science Press, Beijing, 1990.
    [17] Discrete Dyn. Nat. Soc., (2011), Art. ID 473949, 14 pp.
    [18] J. Math. Anal. Appl., 384 (2011), 400-408.
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