P.L. Buono, M. Golubitsky and A. Palacios

Heteroclinic cycles in systems with D_n symmetry

In: Bifurcation Theory and its Numerical Analysis. (Z. Chen, S-N Chow and K. Li, eds.) Springer-Verlag Singapore Pte. Ltd., 1999, 13-27.

• Abstract

In this paper we investigate numerically the existence of heteroclinic cycles connecting periodic solutions and equilibria in systems of differential equations with dihedral D_n symmetry. We study these cycles near steady-state/Hopf and Hopf/Hopf mode interaction points. The existence of these cycles depends on normal form symmetries and their construction is based on the lattice of isotropy subgroups. A variety of interesting forms of intermittency are found and illustrated.