Article thumbnail
Location of Repository

Some curious phenomena in coupled cell networks

By 

Abstract

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 x 2n arrays of cells that generate 2(n) 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

Topics: QA, TJ, QC
Publisher: SPRINGER-VERLAG
OAI identifier: oai:wrap.warwick.ac.uk:8608
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://dx.doi.org/10.1007/s003... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.