Abstract
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.
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Maini, P.K., Myerscough, M.R., Winter, K.H. et al. Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation. Bltn Mathcal Biology 53, 701–719 (1991). https://doi.org/10.1007/BF02461550
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DOI: https://doi.org/10.1007/BF02461550