Abstract
The minimal conditions for pattern formation are examined in reaction-diffusion systems and in the presence of cross-diffusion. It is found that for such systems self-organization properties appear even if the homogeneous reactions are very simple. A cell-cell contact mechanism, able to create cross-diffusion transport in biological systems is proposed. It turns out that a simple catalytic reaction, when associated with even very small cross-diffusion (as compared to normal self-diffusion), can lead to the formation of patterns. Experiments in this direction are possible. Finally, some further properties of the patterned new solutions are examined by means of bifurcation theory. Supercritical as well as subcritical solutions can emerge depending on the parameter values.
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