title: Spatial and spatio-temporal patterns in a cell-haptotaxis model.
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.
authors: Department of Mathematics, University of Utah, Salt Lake City 84112.
authors: P K
authors: PK
authors: Maini
mesh_terms: D000818:Animals; D002468:Cell Physiological Phenomena; D002477:Cells / Q000166:cytology; D005314:Embryonic and Fetal Development; D008433:Mathematics; D008962:Models, Theoretical; D009024:Morphogenesis; D013997:Time Factors