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Self-organized spatial structures in a ratio-dependent predator–prey model

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  • Bartumeus, Fede
  • Alonso, David
  • Catalan, Jordi

Abstract

Using linear stability analysis we demonstrate that a simple reaction-diffusion predator–prey model with a ratio-dependent functional response for the predator, can develop diffusion driven instabilities, also known as Turing structures. The ratio-dependent predator functional response assumes that predator density has a negative effect, due to mutual interference between predators, on the rate of prey consumption by an average predator. We suggest that this mechanism is the most convincing hypothesis for the spontaneous generation of patchiness through diffusion and trophic interaction in a homogeneous environment and add a new feature in the controversial issue of ratio and prey dependent predator–prey models in ecology.

Suggested Citation

  • Bartumeus, Fede & Alonso, David & Catalan, Jordi, 2001. "Self-organized spatial structures in a ratio-dependent predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 53-57.
    • Handle: RePEc:eee:phsmap:v:295:y:2001:i:1:p:53-57
    DOI: 10.1016/S0378-4371(01)00051-6
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    Cited by:

    1. Huang, Tousheng & Yang, Hongju & Zhang, Huayong & Cong, Xuebing & Pan, Ge, 2018. "Diverse self-organized patterns and complex pattern transitions in a discrete ratio-dependent predator–prey system," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 141-158.
    2. Della Rossa, Fabio & Fasani, Stefano & Rinaldi, Sergio, 2013. "Conditions for patchiness in plankton models," Theoretical Population Biology, Elsevier, vol. 83(C), pages 95-100.
    3. Arancibia-Ibarra, Claudio & Aguirre, Pablo & Flores, José & van Heijster, Peter, 2021. "Bifurcation analysis of a predator-prey model with predator intraspecific interactions and ratio-dependent functional response," Applied Mathematics and Computation, Elsevier, vol. 402(C).

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