Pattern formation in prey-taxis systems

• Author(s) / Creator(s)

  • Hillen, T.
  • Lewis, M.A.
  • Lee, J.M.

• 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

  • Stability
  • Predator-prey models
  • Pattern formation
  • Biological control
  • Prey-taxis

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/R3Z199

• License

  © 2009 Taylor & Francis