Threshold bifurcation in tissue interaction models for spatial pattern generation
- 15 June 1994
- journal article
- Published by The Royal Society in Philosophical Transactions A
- Vol. 347 (1685) , 661-676
- https://doi.org/10.1098/rsta.1994.0073
Abstract
Experimental evidence indicates that tissue interaction plays an essential role during skin pattern formation. Here we focus on the mathematical aspects of two specific tissue interaction models. Introducing interaction mechanisms into the traditional pattern formation models is not only biologically consistent, but also leads to results agreeing more closer to those observed in embryogenesis. We specifically examine the bifurcations from spatially simple solutions to spatially complex patterns. In both models this increased complexity in solution is obtained by increasing the effect of the interaction mechanism through a certain threshold. The role of tissue interaction in sequential patterning is also considered.Keywords
This publication has 7 references indexed in Scilit:
- Pattern Formation in Tissue Interaction ModelsPublished by Springer Nature ,1994
- On a tissue interaction model for skin pattern formationJournal of Nonlinear Science, 1992
- Size-dependent pigmentation-pattern formation in embryos of Alligator mississippiensis : time of initiation of pattern generation mechanismProceedings of the Royal Society of London. B. Biological Sciences, 1990
- Mathematical BiologyPublished by Springer Nature ,1989
- Antibodies to liver cell adhesion molecule perturb inductive interactions and alter feather pattern and structure.Proceedings of the National Academy of Sciences, 1986
- Positional information and pattern formationPhilosophical Transactions of the Royal Society of London. B, Biological Sciences, 1981
- Role of cell shape in growth controlNature, 1978