Document Zbl 0716.92004

Spatial and spatio-temporal patterns in a cell-haptotaxis model. (English) Zbl 0716.92004

J. Math. Biol. 27, No. 5, 507-522 (1989).

Summary: We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyze the steady state problem for specific boundary conditions and show the existence of spatially heterogeneous 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 analyze the model in a parameter domain wherein it exhibits a singular dispersion relation.

Cited in 12 Documents

MSC:

92C15	Developmental biology, pattern formation
35Q92	PDEs in connection with biology, chemistry and other natural sciences
92C05	Biophysics

Keywords:

cell pattern formation; embryonic development; mechanochemical interaction of cells; periodic boundary conditions; morphogenesis; cell- haptotaxis model; steady state problem; existence of spatially heterogeneous steady states; Hopf bifurcation; nonlinear multi-time scale perturbation procedure; spatio-temporal patterns; singular dispersion relation

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