Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction-Diffusion Systems
نویسنده
چکیده
David Iron; Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada, John Rumsey; Faculty of Management, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada, Michael Ward; Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada, Juncheng Wei, Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada and Department of Mathematics, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong.
منابع مشابه
On Accurately Estimating Stability Thresholds for Periodic Spot Patterns of Reaction-Diffusion Systems in R
In the limit of an asymptotically large diffusivity ratio of order O(ε) ≫ 1, steady-state spatially periodic patterns of localized spots, where the spots are centred at lattice points of a Bravais lattice, are well-known to exist for certain twocomponent reaction-diffusion systems (RD) in R. For the Schnakenberg RD model, such a localized periodic spot pattern is linearly unstable when the diff...
متن کاملLogarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction-Diffusion Systems in R2
David Iron; Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada, John Rumsey; Faculty of Management, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada, Michael Ward; Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2, Canada, Juncheng Wei, Department of Mathematics, University of British Columbia, Vancouve...
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In the first part of this thesis, we study the existence and stability of multi-spot patterns on the surface of a sphere for a singularly perturbed Brusselator and Schnakenburg reaction-diffusion model. The method of matched asymptotic expansions, tailored to problems with logarithmic gauge functions, is used to construct both symmetric and asymmetric spot patterns. There are three distinct typ...
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In this thesis, we asymptotically construct steady-state localized spot solutions to the Brusselator reaction-diffusion system in the semi-strong interaction regime characterized by an asymptotically large diffusivity ratio. We consider two distinct settings: a periodic pattern of localized spots in R2 concentrating at lattice points of a Bravais lattice, and multi-spot solutions that concentra...
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In this thesis, we asymptotically construct steady-state localized spot solutions to the Brusselator reaction-diffusion system in the semi-strong interaction regime characterized by an asymptotically large diffusivity ratio. We consider two distinct settings: a periodic pattern of localized spots in R2 concentrating at lattice points of a Bravais lattice, and multi-spot solutions that concentra...
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