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Pattern Formation in a Predator–Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks

Author

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  • Lei Shi

    (School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China
    These authors contributed equally to this work.)

  • Jiaying Zhou

    (School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
    These authors contributed equally to this work.)

  • Yong Ye

    (School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China)

Abstract

With the rapid development of network science, Turing patterns on complex networks have attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator–prey model with Allee effect and hyperbolic mortality as an example. In theory, the threshold condition for generating Turing patterns is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing patterns. The factors considered include model parameters, diffusion rate, average degree of the network, and differences in the average degree of different layers. The results indicate that the importance of diffusion rate and network average degree for Turing patterns is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing patterns, which are not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing patterns and spatiotemporal patterns. We believe that these findings contribute to a better understanding of self-organization on complex networks.

Suggested Citation

  • Lei Shi & Jiaying Zhou & Yong Ye, 2023. "Pattern Formation in a Predator–Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks," Mathematics, MDPI, vol. 11(15), pages 1-15, July.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3339-:d:1206481
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    References listed on IDEAS

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    1. Yong Ye & Hua Liu & Yu-mei Wei & Ming Ma & Kai Zhang, 2019. "Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-15, August.
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    3. Hua Liu & Yong Ye & Yumei Wei & Weiyuan Ma & Ming Ma & Kai Zhang, 2019. "Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay," Complexity, Hindawi, vol. 2019, pages 1-14, November.
    4. Yansu Ji & Jianwei Shen, 2020. "Turing Instability of Brusselator in the Reaction-Diffusion Network," Complexity, Hindawi, vol. 2020, pages 1-12, October.
    5. Ye, Yong & Zhao, Yi & Zhou, Jiaying, 2022. "Promotion of cooperation mechanism on the stability of delay-induced host-generalist parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    6. Hu, Junlang & Zhu, Linhe, 2021. "Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
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