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Spatiotemporal Patterns in a Diffusive Predator-Prey Model with Prey Social Behavior

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Abstract

Our aim in this paper is to investigate the behavior of pattern formation for a predator-prey model with social behavior and spatial diffusion. Firstly, we give some solution behavior where the non-existence of a non-constant steady state solution has been proved for some values of the diffusion coefficients. On the other hand, by using the Leray-Schauder degree theory the existence of the non-constant steady-state solution has been proved under a suitable conditions on the diffusion coefficients.

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Authors and Affiliations

  1. Faculty of Exact and Computer Sciences, Mathematic Department, Hassiba Benbouali University, Chlef, Algeria

    Salih Djilali

  2. Department of Mathematics and Informatics, Center of Belhadj Bouchaib, Ain Temouchent, BP 284 RP, 46000, Algeria

    Soufiane Bentout

  3. Laboratoire d’Analyse Non Linéaire et Mathématiques Appliquées, Tlemcen University, Tlemcen, Algeria

    Salih Djilali & Soufiane Bentout

Authors
  1. Salih Djilali
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  2. Soufiane Bentout
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Correspondence to Salih Djilali.

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Djilali, S., Bentout, S. Spatiotemporal Patterns in a Diffusive Predator-Prey Model with Prey Social Behavior. Acta Appl Math 169, 125–143 (2020). https://doi.org/10.1007/s10440-019-00291-z

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  • DOI: https://doi.org/10.1007/s10440-019-00291-z

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