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Comparative analysis between prey-dependent and ratio-dependent predator–prey systems relating to patterning phenomenon

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  • Guin, Lakshmi Narayan
  • Baek, Hunki

Abstract

In this paper, we explore two different kinds of reaction–diffusion predator–prey systems with quadratic intra-predator interaction and linear prey harvesting. One has a Holling type II functional response, a typical type of prey dependence, and the other has a ratio-dependent functional response, a typical type of predator dependence. Firstly, by making use of the linear stability analysis and the bifurcation analysis, we obtain the conditions for a Hopf bifurcation of the nonspatial predator–prey systems and for the diffusion-driven instability, so called Turing bifurcation, of the reaction–diffusion systems in a two-dimensional spatial domain. Secondly, we investigate the effects of the intra-predator interaction and linear prey harvesting on these reaction–diffusion predator–prey systems in terms of spatiotemporal pattern formations caused by Turing bifurcation via numerical simulation. In fact, by choosing the intra-predator interaction and linear harvesting rate of the prey species as the bifurcation parameters, we show that these systems undergo a sequence of spatial patterns including typical Turing patterns such as spots, spots-stripes mixture, holes-stripes mixture, holes and labyrinthine pattern through diffusion-driven instability. Our results disclose that the intra-predator interaction and prey harvesting have a significant effect on the spatiotemporal pattern formations of predator–prey systems regardless of the type of functional responses.

Suggested Citation

  • Guin, Lakshmi Narayan & Baek, Hunki, 2018. "Comparative analysis between prey-dependent and ratio-dependent predator–prey systems relating to patterning phenomenon," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 100-117.
  • Handle: RePEc:eee:matcom:v:146:y:2018:i:c:p:100-117
    DOI: 10.1016/j.matcom.2017.10.015
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    Cited by:

    1. Wu, Daiyong & Yang, Youwei & Wu, Peng, 2023. "Impacts of prey-taxis and nonconstant mortality on a spatiotemporal predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 283-300.
    2. Yuan, Jun & Zhao, Lingzhi & Huang, Chengdai & Xiao, Min, 2021. "Stability and bifurcation analysis of a fractional predator–prey model involving two nonidentical delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 562-580.
    3. Kumar, Udai & Mandal, Partha Sarathi, 2022. "Role of Allee effect on prey–predator model with component Allee effect for predator reproduction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 623-665.

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