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Turing patterns in exploited predator–prey systems with habitat loss

Author

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  • Ramya Seenivasan

    (Vellore Institute of Technology)

  • Prosenjit Paul

    (Vellore Institute of Technology)

Abstract

In this study, we explore the emergence of spatial patterns in a predator–prey model influenced by habitat loss, incorporating the effects of linear diffusion. By examining the stability of the system through the Jacobian matrix, we derive conditions for the occurrence of both Hopf and Turing bifurcations using analytical and numerical approaches. Numerical simulations yield Hopf bifurcation diagrams, revealing the system’s dynamic responses to varying conditions. Our findings contribute to the understanding of how habitat loss and harvesting affect the spatial dynamics in predator–prey systems, which are described by partial differential equations (PDEs) under flux boundary conditions. We also investigate the impact of habitat loss due to harvesting on spatial patterns, identifying formations such as spots and stripes as a result of changes in harvesting efforts. We analytically derive the conditions for Turing instability, which are confirmed through numerical validation.

Suggested Citation

  • Ramya Seenivasan & Prosenjit Paul, 2024. "Turing patterns in exploited predator–prey systems with habitat loss," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(11), pages 1-15, November.
    • Handle: RePEc:spr:eurphb:v:97:y:2024:i:11:d:10.1140_epjb_s10051-024-00815-z
    DOI: 10.1140/epjb/s10051-024-00815-z
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    References listed on IDEAS

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    1. Ang, Tau Keong & Safuan, Hamizah M., 2019. "Harvesting in a toxicated intraguild predator–prey fishery model with variable carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 158-168.
    2. Wang, Weiming & Zhang, Lei & Wang, Hailing & Li, Zhenqing, 2010. "Pattern formation of a predator–prey system with Ivlev-type functional response," Ecological Modelling, Elsevier, vol. 221(2), pages 131-140.
    3. Ghorai, Santu & Poria, Swarup, 2016. "Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 421-429.
    4. Bhunia, Bidhan & Ghorai, Santu & Kar, Tapan Kumar & Biswas, Samir & Bhutia, Lakpa Thendup & Debnath, Papiya, 2023. "A study of a spatiotemporal delayed predator–prey model with prey harvesting: Constant and periodic diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
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