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Optimality for a diffusive predator-prey system in a spatially heterogeneous environment incorporating a prey refuge

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  • Liu, Guodong
  • Chang, Zhengbo
  • Meng, Xinzhu
  • Liu, Siyu

Abstract

In this paper, we consider the optimal harvesting controls for a diffusive predator-prey system, which is formulated by prey refuge and modified Leslie-Gower functional response. The locally and globally asymptotic stability of unique positive constant steady state is discussed under homogeneous Neumann boundary condition. The nonexistence and existence of nonconstant steady states are obtained by Leray-Schauder degree theory. Also, the optimal harvesting strategies to get maximum sustainable yield (MSY) and maximum economic yield (MEY) are correspondingly given.

Suggested Citation

  • Liu, Guodong & Chang, Zhengbo & Meng, Xinzhu & Liu, Siyu, 2020. "Optimality for a diffusive predator-prey system in a spatially heterogeneous environment incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    • Handle: RePEc:eee:apmaco:v:384:y:2020:i:c:s0096300320303489
    DOI: 10.1016/j.amc.2020.125385
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    References listed on IDEAS

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    1. Legović, Tarzan & Klanjšček, Jasminka & Geček, Sunčana, 2010. "Maximum sustainable yield and species extinction in ecosystems," Ecological Modelling, Elsevier, vol. 221(12), pages 1569-1574.
    2. Liu, Guodong & Meng, Xinzhu, 2019. "Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
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    Cited by:

    1. Arellano-García, María Evarista & Camacho-Gutiérrez, José Ariel & Solorza-Calderón, Selene, 2021. "Machine learning approach for higher-order interactions detection to ecological communities management," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. Ma, Tingting & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2021. "Stability analysis and optimal harvesting control of a cross-diffusion prey-predator system," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Jang, Geunsoo & Cho, Giphil, 2022. "Optimal harvest strategy based on a discrete age-structured model with monthly fishing effort for chub mackerel, Scomber japonicus, in South Korea," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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