Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation.

@article{Maini1991BifurcatingSH,
  title={Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation.},
  author={Philip K. Maini and Mary R. Myerscough and K. H. Winters and James D. Murray},
  journal={Bulletin of mathematical biology},
  year={1991},
  volume={53 5},
  pages={701-19}
}
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… CONTINUE READING