WIAS Preprint No. 173, (1995)

Heteroclinic cycles for reaction diffusion systems by forced symmetry-breaking


  • Lauterbach, Reiner
    ORCID: 0000-0002-9310-3177
  • Maier-Paape, Stanislaus

2010 Mathematics Subject Classification

  • 37G40 35B32 34C14 37G25


  • axisymmetric equilibrium, group orbit, invariant manifold, higher codimension, bifurcation




We consider solutions of the semilinear parabolic equation (1.1) on the 2-Sphere. Assuming (1.1) has an axisymmetric equilibrium uα, the group orbit of uα gives a whole (invariant) manifold M of equilibria for (1.1). Under generic conditions we have that, after perturbing (1.1) by a (small) L ⊂ O(3)-equivariant perturbation, M persists as an invariant manifold ͠M slightly changed. However, the flow on ͠M is in general no longer trivial. Indeed, we find heteroclinic orbits on ͠M and, in case L = 𝕋 (the tetrahedral subgroup of O(3)), even heteroclinic cycles.

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