Symmetry and pattern formation in coupled cell networks

M. Golubitsky and I. Stewart
Symmetry and pattern formation in coupled cell networks
In: Pattern Formation in Continuous and Coupled Systems. (M. Golubitsky, D. Luss and S.H. Strogatz, eds.) IMA Volumes in Mathematics and its Applications 115 Springer, New York, 1999, 65-82.

Abstract

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.

M. Golubitsky and I. Stewart Symmetry and pattern formation in coupled cell networks In: Pattern Formation in Continuous and Coupled Systems. (M. Golubitsky, D. Luss and S.H. Strogatz, eds.) IMA Volumes in Mathematics and its Applications 115 Springer, New York, 1999, 65-82.

Abstract

M. Golubitsky and I. Stewart
Symmetry and pattern formation in coupled cell networks
In: Pattern Formation in Continuous and Coupled Systems. (M. Golubitsky, D. Luss and S.H. Strogatz, eds.) IMA Volumes in Mathematics and its Applications 115 Springer, New York, 1999, 65-82.