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Cross-diffusion-driven instability in an interacting species model with prey refuge

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  • Guin, Lakshmi Narayan
  • Djilali, Salih
  • Chakravarty, Santabrata

Abstract

The present study appertains to a reaction-diffusion system embracing two-dimensional continuous Beddington-DeAngelis predator-prey model incorporating intra-specific competition among predators and prey refuge in proportion to both the species as well. The existence of all conceivable ecologically significant equilibria is explored and consequently the diffusion-driven instability around the coexistence equilibrium position is reviewed. Numerical simulation with zero-flux boundary conditions discloses that the system under consideration experiences the occurrence of diffusion-driven instability. The dynamical system in Turing space emerges further to get influenced by prey refuge while it unveils diffusion controlled spatiotemporal pattern formation namely, growth of spots, stripe-spot mixtures, stripes, labyrinthine, stripe-hole mixtures and holes reproduction. The quantitative analysis reveals that the interaction of both self- and cross-diffusion plays a significant role on the pattern formation of the present system in a way to enrich the pattern at a greater height.

Suggested Citation

  • Guin, Lakshmi Narayan & Djilali, Salih & Chakravarty, Santabrata, 2021. "Cross-diffusion-driven instability in an interacting species model with prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921008559
    DOI: 10.1016/j.chaos.2021.111501
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    References listed on IDEAS

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    1. Gui-Quan Sun & Zhen Jin & Yi-Guo Zhao & Quan-Xing Liu & Li Li, 2009. "Spatial Pattern In A Predator-Prey System With Both Self- And Cross-Diffusion," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 71-84.
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    Cited by:

    1. Zhu, Linhe & Zheng, Wenxin & Shen, Shuling, 2023. "Dynamical analysis of a SI epidemic-like propagation model with non-smooth control," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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