Stability of n-dimensional patterns in a generalized Turing system: implications for biological pattern formation

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Published 1 October 2004 2005 IOP Publishing Ltd and London Mathematical Society
, , Citation Mark Alber et al 2005 Nonlinearity 18 125 DOI 10.1088/0951-7715/18/1/007

0951-7715/18/1/125

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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10.1088/0951-7715/18/1/007