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Pattern Dynamics in a Predator‐Prey Model with Diffusion Network

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Listed:
  • Wenjie Yang
  • Qianqian Zheng
  • Jianwei Shen
  • Qing Hu

Abstract

Diffusion plays an essential role in the distribution of predator and prey. We mainly research the diffusion network’s effect on the predator‐prey model through bifurcation. First, it is found that the link probability and diffusion parameter can cause Turing instability in the network‐organized predator‐prey model. Then, the Turing stability region is obtained according to the sufficient condition of Turing instability and the eigenvalues’ distribution. Finally, the biological mechanism is explained through our theoretical results, which are also illustrated by numerical simulation.

Suggested Citation

  • Wenjie Yang & Qianqian Zheng & Jianwei Shen & Qing Hu, 2022. "Pattern Dynamics in a Predator‐Prey Model with Diffusion Network," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:9055480
    DOI: 10.1155/2022/9055480
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    References listed on IDEAS

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    1. Malbor Asllani & Timoteo Carletti & Duccio Fanelli, 2016. "Tune the topology to create or destroy patterns," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(12), pages 1-10, December.
    2. G. P. Samanta, 2010. "Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-18, March.
    3. Malbor Asllani & Joseph D. Challenger & Francesco Saverio Pavone & Leonardo Sacconi & Duccio Fanelli, 2014. "The theory of pattern formation on directed networks," Nature Communications, Nature, vol. 5(1), pages 1-9, December.
    4. Yansu Ji & Jianwei Shen, 2020. "Turing Instability of Brusselator in the Reaction-Diffusion Network," Complexity, Hindawi, vol. 2020, pages 1-12, October.
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