Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation.
We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989, J. exp. Zool. 251, 186-202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.
Maini
P K
PK
Department of Mathematics, University of Utah, Salt Lake City 84112.
Myerscough
M R
MR
Winters
K H
KH
Murray
J D
JD
D000818:Animals; D002465:Cell Movement; D002633:Chemotaxis; D005314:Embryonic and Fetal Development; D008954:Models, Biological; D012880:Skin Pigmentation