Bulletin of Mathematical Biology

, Volume 53, Issue 5, pp 701–719 | Cite as

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

  • P. K. Maini
  • M. R. Myerscough
  • K. H. Winter
  • J. D. Murray


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.


Pattern Formation Pigment Cell Flux Boundary Condition Chemotaxis Model Spatial Pattern Formation 
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Copyright information

© Society for Mathematical Biology 1991

Authors and Affiliations

  • P. K. Maini
    • 1
  • M. R. Myerscough
    • 2
  • K. H. Winter
    • 3
  • J. D. Murray
    • 4
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  3. 3.Theoretical Studies DepartmentHarwell LaboratoryDidcotUK
  4. 4.Applied MathematicsUniversity of WashingtonSeattleUSA

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