Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation. - Maini, P; Myerscough, MR; Winters, K; Murray, J (Kluwer Academic Publishers, 1991)
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.