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Spatiotemporal complexity of a predator–prey system with constant harvest rate

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  • Zhang, Lei
  • Wang, Wenjuan
  • Xue, Yakui

Abstract

In this paper, we investigate the emergence of a predator–prey system with Michaelis–Menten-type predator–prey systems with reaction–diffusion and constant harvest rate. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. The results of spatial pattern analysis, via numerical simulations, typical spatial pattern formation is isolated groups, i.e., stripe-like, patch-like and so on. Our results show that modeling by reaction–diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.

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  • Zhang, Lei & Wang, Wenjuan & Xue, Yakui, 2009. "Spatiotemporal complexity of a predator–prey system with constant harvest rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 38-46.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:38-46
    DOI: 10.1016/j.chaos.2007.11.009
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    References listed on IDEAS

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    1. Li, Ping & Li, Zhong & Halang, Wolfgang A. & Chen, Guanrong, 2007. "Li–Yorke chaos in a spatiotemporal chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 335-341.
    2. Hutt, Axel & Atay, Fatihcan M., 2007. "Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 547-560.
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    Cited by:

    1. Zhang, Xue & Zhang, Qing-Ling & Liu, Chao & Xiang, Zhong-Yi, 2009. "Bifurcations of a singular prey–predator economic model with time delay and stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1485-1494.
    2. Wang, Yong & Zhou, Xu & Jiang, Weihua, 2023. "Bifurcations in a diffusive predator–prey system with linear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Kumar, Sachin & Kharbanda, Harsha, 2019. "Chaotic behavior of predator-prey model with group defense and non-linear harvesting in prey," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 19-28.
    4. Souna, Fethi & Lakmeche, Abdelkader & Djilali, Salih, 2020. "Spatiotemporal patterns in a diffusive predator-prey model with protection zone and predator harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Ghorai, Santu & Poria, Swarup, 2016. "Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 57-67.
    6. Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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