UNSPECIFIED (2004) Some curious phenomena in coupled cell networks. JOURNAL OF NONLINEAR SCIENCE, 14 (2). pp. 207-236. doi:10.1007/s00332-003-0593-6

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery Q Science > QC Physics
Journal or Publication Title:	JOURNAL OF NONLINEAR SCIENCE
Publisher:	SPRINGER-VERLAG
ISSN:	0938-8974
Official Date:	March 2004
Dates:	Date Event March 2004 UNSPECIFIED
Volume:	14
Number:	2
Number of Pages:	30
Page Range:	pp. 207-236
DOI:	10.1007/s00332-003-0593-6
Publication Status:	Published

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