Fig. 2: Cluster solutions and bifurcations for N = 16.

Each filled circle refers to the instantaneous position of a cluster or single oscillator, the line of the respective same colour to its trajectory. Sizes of filled circles mirror sizes of clusters. a 8 − 5 − 3 solution in the co-rotating frame of 〈W〉 for c₂ = − 0.715 and η = 0.64. b 4 − 4 − 5 − 3 solution for c₂ = −0.75 and η = 0.61. c Bifurcation diagram of 8 − 8-derived solutions with PD period-doubling, PF pitchfork. Dashed lines mark bifurcations of the 8 − 5 − 3 solution (a), solid lines those of the 8 − 4 − 4 (Fig. 1i-j) and the solutions emerging from it. Grey labels mark where each type of solution is stable. Labeled crosses mark the parameter values of the solutions depicted in Fig. 1e, f, i, j, a, b and d–f. The black line marks the c₂-incremented simulation in Fig. 3a, b. d 8 − 4 − 2 − 2 solution for c₂ = −0.72 and η = 0.62. e, f 8 − 4 − 1 − 1 − 1 − 1 solution for c₂ = −0.718 and η = 0.62, including time series of real part of each cluster and single oscillator.