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

Shaban Aly

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

DOI: 10.4236/am.2012.32027                

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.

Keywords

Cross-Diffusion; Diffusive Instability; Turing Bifurcation

Conflicts of Interest

The authors declare no conflicts of interest.

References

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