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dc.contributor.authorSmith-Roberge, Julien
dc.date.accessioned2017-04-07T18:54:58Z
dc.date.available2017-04-07T18:54:58Z
dc.date.issued2017-04-07T18:54:58Z
dc.identifier.urihttp://hdl.handle.net/10222/72825
dc.description.abstractRecent experiments have shown that patterns can emerge in bacterial colonies programmed to have a drop in diffusion when population densities (detected via a quorum sensing mechanism) are sufficiently large. We examine one partial differential equation model of this system, and construct its non-constant stationary solutions. We demonstrate analytically that these solutions are stable when the diffusion rate of bacteria is large and the diffusion rate of signalling molecules, D_h, is small. We further demonstrate that increasing D_h induces a Hopf bifurcation, resulting in a loss of stability. These results are confirmed by numerical simulations.en_US
dc.language.isoenen_US
dc.subjectpattern formationen_US
dc.subjectpartial differential equationsen_US
dc.subjectmathematical biologyen_US
dc.titlePattern Formation in Bacterial Colonies with Density-Dependent Diffusionen_US
dc.typeThesisen_US
dc.date.defence2017-04-06
dc.contributor.departmentDepartment of Mathematics & Statistics - Math Divisionen_US
dc.contributor.degreeMaster of Scienceen_US
dc.contributor.external-examinern/aen_US
dc.contributor.graduate-coordinatorDavid Ironen_US
dc.contributor.thesis-readerAndrew Rutenbergen_US
dc.contributor.thesis-readerAlan Coleyen_US
dc.contributor.thesis-supervisorDavid Ironen_US
dc.contributor.thesis-supervisorTheodore Kolokolnikoven_US
dc.contributor.ethics-approvalNot Applicableen_US
dc.contributor.manuscriptsNot Applicableen_US
dc.contributor.copyright-releaseNot Applicableen_US
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