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Article
Stability of n-Dimensional Patterns in a Generalized Turing System: Implications for Biological Pattern Formation
Nonlinearity (2004)
  • Tilmann Glimm, Western Washington University
  • Mark S. Alber
  • H. George E. Hentschel
  • Bogdan Kazmierczak
  • Stuart A. Newman
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.
Keywords
  • Turing patterns,
  • n-dimensional patterns,
  • Biological pattern formation
Disciplines
Publication Date
October, 2004
Publisher Statement
2005 IOP Publishing Ltd and London Mathematical Society
Citation Information
Tilmann Glimm, Mark S. Alber, H. George E. Hentschel, Bogdan Kazmierczak, et al.. "Stability of n-Dimensional Patterns in a Generalized Turing System: Implications for Biological Pattern Formation" Nonlinearity Vol. 18 Iss. 1 (2004)
Available at: http://works.bepress.com/tilmann_glimm/15/