Journal of Mathematical Biology

, Volume 11, Issue 3, pp 295–310 | Cite as

Positional differentiation as pattern formation in reaction-diffusion systems with permeable boundaries. Bifurcation analysis

  • M. A. Livshits
  • G. T. Gurija
  • B. N. Belintsev
  • M. V. Volkenstein


Pattern formation in a unicomponent reaction-diffusion system with trigger type dynamics and combined boundary conditions is considered. The boundary permeabilities and reservoir concentrations as well as the dimension of the system are the control parameters. The whole assemblage of steady states, their bifurcations and changes under the variation of these parameters is described. Among all steady distributions possible for given values of the parameters, only the simplest ones prove to be asymptotically stable. The relation to catastrophe theory is discussed.

Key words

Morphogenesis Pattern formation Bifurcation 


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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • M. A. Livshits
    • 1
  • G. T. Gurija
    • 1
  • B. N. Belintsev
    • 1
  • M. V. Volkenstein
    • 1
  1. 1.Institute of Molecular BiologyUSSR Academy of SciencesMoscowUSSR

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