Symmetry is used to investigate the existence and stability of heteroclinic
cycles involving steady-state and periodic solutions in coupled cell syste
ms with D-n-symmetry. Using the lattice of isotropy subgroups, we study the
normal form equations restricted to invariant fixed-point subspaces and pr
ove that it is possible fur the normal form equations to have robust, asymp
totically stable, heteroclinic cycles connecting periodic solutions with st
eady states and periodic solutions with periodic solutions. A center manifo
ld reduction from the ring of cells to the normal form equations is then pe
rformed. Using this reduction we find parameter values of the cell system w
here asymptotically stable cycles exist. Simulations of the cycles show tra
jectories visiting steady states and periodic solutions and reveal interest
ing spatio-temporal patterns in the dynamics of individual cells. We discus
s how these patterns are forced by normal form symmetries. (C) 2000 Elsevie
r Science B.V. All rights reserved.