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Pattern Dynamics in a Spatial Predator‐Prey System with Allee Effect

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  • Gui-Quan Sun
  • Li Li
  • Zhen Jin
  • Zi-Ke Zhang
  • Tao Zhou

Abstract

We investigate the spatial dynamics of a predator‐prey system with Allee effect. By using bifurcation analysis, the exact Turing domain is found in the parameters space. Furthermore, we obtain the amplitude equations and determine the stability of different patterns. In Turing space, it is found that predator‐prey systems with Allee effect have rich dynamics. Our results indicate that predator mortality plays an important role in the pattern formation of populations. More specifically, as predator mortality rate increases, coexistence of spotted and stripe patterns, stripe patterns, spotted patterns, and spiral wave emerge successively. The results enrich the finding in the spatial predator‐prey systems well.

Suggested Citation

  • Gui-Quan Sun & Li Li & Zhen Jin & Zi-Ke Zhang & Tao Zhou, 2013. "Pattern Dynamics in a Spatial Predator‐Prey System with Allee Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:921879
    DOI: 10.1155/2013/921879
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    References listed on IDEAS

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    1. Verdy, Ariane, 2010. "Modulation of predator–prey interactions by the Allee effect," Ecological Modelling, Elsevier, vol. 221(8), pages 1098-1107.
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    Cited by:

    1. Pal, Pallav Jyoti & Biswas, Debabrata & Saha, Tapan, 2025. "Spatial dynamics and pattern formation in fragmented habitats: A study using a diffusive Bazykin model with Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).

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