Fig. 3: Cluster-splitting cascades for different N.
From: Between synchrony and turbulence: intricate hierarchies of coexistence patterns
a Maxima of \({{{{{{{\rm{Re}}}}}}}}({w}_{k})\) in an N = 16 c2-incremented simulation at η = 0.63. Labels on the figure mark the clusters reaching the different maxima as the solution changes from 8 − 4 − 4 via 8 − 4 − 2 − 2 to 8 − 4 − (4 × 1). Labels on the abscissa mark occurring bifurcations. The additional smallest yellow maximum appearing at c2 ≈ −0.712 is caused by the continuous deformation of the oscillator trajectories and not by a bifurcation. At c2 ≈ −0.7115, the torus bifurcation to three-frequency dynamics manifests itself in a distinct broadening of the formerly discrete maxima. b Schematic portrayal of the period-doubling cluster splittings in the simulation in a. c, d Like b for c2-incremented simulations at η = 0.63 with N = 32 and N = 256, respectively, based on quantitative results shown in Supplementary Figs. 1–3 and described in Supplementary Note 1.
