Symmetry and Pattern Formation in Coupled Cell Networks

  • Martin Golubitsky
  • Ian Stewart
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 115)


We describe some basic concepts and techniques from symmetric bifurcation theory in the context of coupled systems of cells (‘oscillator networks’). These include criteria for the existence of symmetry-breaking branches of steady and periodic states. We emphasize the role of symmetry as a general framework for such analyses. As well as overt symmetries of the network we discuss internal symmetries of the cells, ‘hidden’ symmetries related to Neumann boundary conditions, and spatio-temporal symmetries of periodic states. The methods are applied to a model central pattern generator for legged animal locomotion.


Hopf Bifurcation Central Pattern Generator Wreath Product Isotropy Subgroup Internal Symmetry 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Martin Golubitsky
    • 1
  • Ian Stewart
    • 2
  1. 1.Mathematics DepartmentUniversity of HoustonHoustonUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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