title: Pattern formation in prey-taxis systems.
abstract: 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.
authors.affiliation: Centre for Mathematical Biology, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1. jungmin@bio-math10.biology.kyushu-u.ac.jp
authors.forename: J M
authors.initials: JM
authors.lastname: Lee
authors.forename: T
authors.initials: T
authors.lastname: Hillen
authors.forename: M A
authors.initials: MA
authors.lastname: Lewis
mesh_terms: D000818:Animals; D004058:Diffusion; D017753:Ecosystem; D008954:Models, Biological; D011235:Predatory Behavior / Q000502:physiology*