Pattern formation in prey-taxis systems

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dc.contributor.authorHillen, T.
dc.contributor.authorLewis, M.A.
dc.contributor.authorLee, J.M.
dc.date.accessioned2025-05-01T12:02:32Z
dc.date.available2025-05-01T12:02:32Z
dc.date.issued2009
dc.descriptionIn 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.
dc.identifier.doihttps://doi.org/10.7939/R3Z199
dc.language.isoen
dc.relation.isversionofJ. 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
dc.rights© 2009 Taylor & Francis
dc.subjectStability
dc.subjectPredator-prey models
dc.subjectPattern formation
dc.subjectBiological control
dc.subjectPrey-taxis
dc.titlePattern formation in prey-taxis systems
dc.typehttp://purl.org/coar/resource_type/c_6501 http://purl.org/coar/version/c_970fb48d4fbd8a85
ual.jupiterAccesshttp://terms.library.ualberta.ca/public

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