Dynamical spike solutions in a nonlocal model of pattern formation

Coupling a reaction-diffusion equation with ordinary differential equa- tions (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant solutions and Turing patterns. Using a shadow-type limit of a rea...

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Bibliographic Details
Published inNonlinearity Vol. 31; no. 5; pp. 1757 - 1781
Main Authors Marciniak-Czochra, Anna, Härting, Steffen, Karch, Grzegorz, Suzuki, Kanako
Format Journal Article
LanguageEnglish
Published IOP Publishing 27.03.2018
Subjects
diffusion-driven instability
reaction-diffusion-ODE equations
shadow system
unbounded spike patterns
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ISSN0951-7715
1361-6544
DOI10.1088/1361-6544/aaa5dc

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Summary:Coupling a reaction-diffusion equation with ordinary differential equa- tions (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant solutions and Turing patterns. Using a shadow-type limit of a reaction-diffusion-ODE model, we show that in such cases the instability driven by nonlocal terms (a counterpart of DDI) may lead to formation of unbounded spike patterns.
Bibliography:NON-102142.R2
London Mathematical Society
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aaa5dc