Journal of Nonlinear Science

, Volume 14, Issue 2, pp 207–236

Some Curious Phenomena in Coupled Cell Networks


DOI: 10.1007/s00332-003-0593-6

Cite this article as:
Golubitsky, M., Nicol, M. & Stewart, I. J Nonlinear Sci (2004) 14: 207. doi:10.1007/s00332-003-0593-6


We discuss several examples of synchronous dynamical phenomena in coupled cell networks that are unexpected from symmetry considerations, but are natural using a theory developed by Stewart, Golubitsky, and Pivato. In particular we demonstrate patterns of synchrony in networks with small numbers of cells and in lattices (and periodic arrays) of cells that cannot readily be explained by conventional symmetry considerations. We also show that different types of dynamics can coexist robustly in single solutions of systems of coupled identical cells. The examples include a three-cell system exhibiting equilibria, periodic, and quasiperiodic states in different cells; periodic 2n × 2n arrays of cells that generate 2n different patterns of synchrony from one symmetry-generated solution; and systems exhibiting multirhythms (periodic solutions with rationally related periods in different cells). Our theoretical results include the observation that reduced equations on a center manifold of a skew product system inherit a skew product form.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Mathematics, University of Houston, Houston, TX 77204-3008USA
  2. 2.Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XHUnited Kingdom
  3. 3.Mathematics Institute, University of Warwick, Coventry CV4 7ALUnited Kingdom

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