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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    2. Fengrong Zhang, Yan Li, Stability and Hopf bifurcation of a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting, 2017, 88, 0924-090X, 1397, 10.1007/s11071-016-3318-8
    3. Nayana Mukherjee, S Ghorai, Malay Banerjee, Detection of turing patterns in a three species food chain model via amplitude equation, 2019, 69, 10075704, 219, 10.1016/j.cnsns.2018.09.023
    4. Lakshmi Narayan Guin, 2020, Chapter 24, 978-981-15-0421-1, 279, 10.1007/978-981-15-0422-8_24
    5. Xiaotao Han, Hua Liu, Yumei Wei, Chi-Hua Chen, Xuexia Ye, Hari Mohan Srivastava, 2022, Optimal control study of a predator-prey model with nonlinear prey harvesting, 9781510655195, 77, 10.1117/12.2638834
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    7. Samir Biswas, Lakpa Thendup Bhutia, Tapan Kumar Kar, Bidhan Bhunia, Esita Das, Spatiotemporal analysis of a modified Leslie–Gower model with cross-diffusion and harvesting, 2024, 470, 01672789, 134381, 10.1016/j.physd.2024.134381
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