Stability of n-Dimensional Patterns in a Generalized Turing System: Implications for Biological Pattern FormationNonlinearity (2004)
AbstractThe 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.
- Turing patterns,
- n-dimensional patterns,
- Biological pattern formation
Publication DateOctober, 2004
Citation InformationTilmann 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/