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Journal of Mathematical Biology

, Volume 27, Issue 5, pp 507–522 | Cite as

Spatial and spatio-temporal patterns in a cell-haptotaxis model

  • P. K. Maini
Article

Abstract

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation.

Key words

Morphogenesis Spatio-temporal pattern Mechanochemical Haptotaxis Singular dispersion relation 

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • P. K. Maini
    • 1
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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