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arXiv · 1307.6236

Dynamical spike solutions in a nonlocal model of pattern formation

Anna Marciniak-Czochra·Steffen Härting·Grzegorz Karch·Kanako Suzuki
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Abstract

Coupling a reaction-diffusion equation with ordinary differential equations (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.

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Anna Marciniak-Czochra, Steffen Härting, Grzegorz Karch, Kanako Suzuki. 2013-07-23. Dynamical spike solutions in a nonlocal model of pattern formation. https://arxiv.org/abs/1307.6236

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