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
Article

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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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
  5. 5.Centre for Mathematical BiologyMathematical InstituteOxfordUK

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