Skip to main content
Article thumbnail
Location of Repository

Reaction and diffusion on growing domains: Scenarios for robust pattern formation

By E. J. Crampin, E. A. Gaffney and P. K. Maini


We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-similarity argument to predict a frequency-doubling sequence of patterns for exponential domain growth and we find numerically that frequency-doubling is realized for a finite range of exponential growth rate. We consider pattern formation under different forms for the growth and show that in one dimension domain growth may be a mechanism for increased robustness of pattern formation

Topics: Biology and other natural sciences
Year: 1999
DOI identifier: 10.1006/bulm.1999.0131
OAI identifier:
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles


    1. (1980). A model for the formation of ocular dominance stripes. doi
    2. (1992). A perturbation analysis of a mechanical model for stable spatial patterning in embryology.
    3. (1981). A pre-pattern formation mechanism for animal coat markings.
    4. (1995). A reaction–diffusion wave on the skin of the marine angelfish pomacanthus.
    5. (1972). A theory of biological pattern formation.
    6. (1999). and accepted 21 doi
    7. (1997). Confined Turing patterns in growing systems.
    8. (1990). Experimental evidence of a sustained Turing-type nonequilibrium chemical pattern.
    9. (1974). How well does Turing’s theory of morphogenesis work?
    10. (1993). Is morphogenesis an intrinsically robust process?
    11. (1993). Mathematical Biology,
    12. (1996). On a model mechanism for the spatial pattering of teeth primordia in the alligator.
    13. (1982). Parameter space for Turing instability in reaction diffusion mechanisms: a comparison of models.
    14. (1980). Pattern formation by reaction– diffusion instabilities: applications to morphogenesis in Drosophila.
    15. (1994). Pattern formation in generalized Turing systems I: steady-state patterns in systems with mixed boundary conditions.
    16. (1989). Pattern formation models and developmental constraints.
    17. (1986). Pattern sensitivity to boundary and initial conditions in reaction–diffusion models.
    18. (1991). Reaction–diffusion patterns on growing domains: asymmetric growth.
    19. (1995). Reliable segmentation by successive bifurcation. doi
    20. (1980). Scale-invariance in reaction–diffusion models of spatial pattern formation.
    21. (1979). Simple chemical reaction systems with limit cycle behaviour. doi
    22. (1988). Size adaptation in Turing prepatterns.
    23. (1997). Spatial pattern formation in chemical and biological systems.
    24. (1991). Spots or stripes? Nonlinear effects in bifurcation of reaction– diffusion equations on the square.
    25. (1999). Stripe formation in Juvenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis. doi
    26. (1952). The chemical basis of morphogenesis. doi
    27. (1988). Theoretical aspects of stripe formation in relation to Drosophila segmentation.

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.