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

Affiliation(s)

Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia.

Department of Mathematics, Faculty of Science, King Khalid University, Abha, Saudi Arabia.

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-migration response is an important factor that should not be ignored when pattern emerges.

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-migration response is an important factor that should not be ignored when pattern emerges.

Cite this paper

S. Aly, "Spatial Inhomogenity Due to Turing Instability in a Capital-Labour Model,"*Applied Mathematics*, Vol. 3 No. 2, 2012, pp. 172-176. doi: 10.4236/am.2012.32027.

S. Aly, "Spatial Inhomogenity Due to Turing Instability in a Capital-Labour Model,"

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