Figure 5.

The sets Θ_g(H) for different H partition the canonical invariant region $\mathcal{C}$ for the fully symmetric system of N = 3 oscillators. The CIR is sketched in (a): its boundary is given by the sets θ₁ − θ₂ = 0, θ₂ − θ₃ = 0 and θ₃ − θ₁ = 0 (black lines) which intersect in Θ^sync (black dot, •). The splay phase Θ^splay is the centroid (hollow dot, °) and is the fixed point of the residual ${\mathbb{Z}}_3=⟨\tau ⟩$ symmetry which rotates the CIR (indicated by grey lines). Dashed lines indicate phase configurations where one phase difference is equal to π. For a dead zone symmetric coupling function $\mathrm{g}\in \mathcal{F}(1)$ only the undirected subgraphs of K₃ can be realized; these correspond to the ones shown in figure 4 excluding the cycles. (b) The partition of the CIR for DZ(g) = (π/3, 5π/3). (c) The partition for a dead zone symmetric coupling function with DZ(g) = (5π/6, 7π/6). (Online version in colour.)