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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.

Type

Journal article

Journal

J Math Biol

Publication Date

1989

Volume

27

Pages

507 - 522

Keywords

Animals, Cell Physiological Phenomena, Cells, Embryonic and Fetal Development, Mathematics, Models, Theoretical, Morphogenesis, Time Factors