Coupled cells with internal symmetry: II. Direct products

Abstract

We continue the study of arrays of coupled identical cells that possess both global and internal symmetries, begun in part I. Here we concentrate on the `direct product' case, for which the symmetry group of the system decomposes as the direct product of the internal group and the global group . Again, the main aim is to find general existence conditions for symmetry-breaking steady-state and Hopf bifurcations by reducing the problem to known results for systems with symmetry or separately.