Abstract
The stability of Turing patterns in an n-dimensional cube (0, π)n is studied, where n ≥ 2. It is shown by using a generalization of a classical result of Ermentrout concerning spots and stripes in two dimensions that under appropriate assumptions only sheet-like or nodule-like structures can be stable in an n-dimensional cube. Other patterns can also be stable in regions comprising products of lower-dimensional cubes and intervals of appropriate length. Stability results are applied to a new model of skeletal pattern formation in the vertebrate limb.
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Recommended by J A Glazier
Corrections were made to this article on 28 October 2004. These changes occurred in equation (2.7). The corrected electronic version is identical to the print version.