INVARIANT SYNCHRONY SUBSPACES OF SETS OF MATRICES

by John M. Neuberger, Nándor Sieben, James W. Swift

Companion web site

Code in Sage cells

Sage cell implementation of the split and cir algorithm for finding invariant subspaces.

Sage cell implementation of the split and cir algorithm for finding tactical decompositions.

Examples

Balanced partitions of the Petersen graph

Balanced partitions of the 3x3 square grid graph

Balanced partitions of the 4x4 square grid graph

Exo-balanced partitions of the 4x4 square grid graph

Balanced partitions of the 16x16 square grid graph

Balanced partitions of the Sierpinski pre-gasket with 81 vertices

Exo-balanced partitions of the Sierpinski pre-gasket with 27 vertices

Exo-balanced partitions of the path with 28 vertices

Exo-balanced partitions of the McKay graph

Balanced partitions of the cell network in Figure 2 of [1]

Exo-balanced partitions of the cell network in Figure 2 of [1]

Balanced partitions of the cell network in Figure 11 of [3]

References

[1] Manuela A. D. Aguiar and Ana Paula S. Dias. The lattice of synchrony subspaces of a coupled cell network: characterization and computation algorithm. J. Nonlinear Sci., 24(6):949–996, 2014.

[2] Hiroko Kamei and Peter J. A. Cock. Computation of balanced equivalence relations and their lattice for a coupled cell network. SIAM J. Appl. Dyn. Syst., 12(1):352382, 2013.

[3] Ian Stewart, Martin Golubitsky, and Marcus Pivato. Symmetry groupoids and patterns of synchrony in coupled cell networks. SIAM J. Appl. Dyn. Syst. 2 (2003), no. 4, 609–646