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Spatial Inhomogenity Due to Turing Instability in a Capital-Labour Model

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Author(s): Shaban Aly

Journal: Advances in Molecular Imaging
ISSN 2161-6728

Volume: 03;
Issue: 02;
Start page: 172;
Date: 2012;
Original page

Keywords: Cross-Diffusion | Diffusive Instability | Turing Bifurcation

ABSTRACT
A cross-diffusion system is set up modelling the distribution of capital and labour over the land of two identical patches (cites, markets or countries) in which the per capita migration rate of each species (investment capital or labour force) is influenced not only by its own but also by the other one’s density, i.e. there is cross-diffusion present. Numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation and the cross-mi- gration response is an important factor that should not be ignored when pattern emerges.

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