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Pattern formation in prey-taxis systems

  • Author(s) / Creator(s)
  • In this paper, we consider spatial predator–prey models with diffusion and prey-taxis. We investigate necessary conditions for pattern formation using a variety of non-linear functional responses, linear and non-linear predator death terms, linear and non-linear prey-taxis sensitivities, and logistic growth or growth with an Allee effect for the prey.We identify combinations of the above non-linearities that lead to spatial pattern formation and we give numerical examples. It turns out that prey-taxis stabilizes the system and for large prey-taxis sensitivity we do not observe pattern formation. We also study and find necessary conditions for global stability for a type I functional response, logistic growth for the prey, non-linear predator death terms, and non-linear prey-taxis sensitivity.

  • Date created
    2009
  • Subjects / Keywords
  • Type of Item
    Article (Published)
  • DOI
    https://doi.org/10.7939/R3Z199
  • License
    © 2009 Taylor & Francis
  • Language
  • Citation for previous publication
    • J. M. Lee, T. Hillen & M. A. Lewis (2009): Pattern formation in prey-taxis systems, Journal of Biological Dynamics, 3:6, 551-573. doi: 10.1080/17513750802716112