Fig. 1: Two-cluster solutions and their bifurcations.
From: Between synchrony and turbulence: intricate hierarchies of coexistence patterns
Each filled circle refers to the instantaneous position of a cluster, the line of the respective same colour to its trajectory. a Trajectory of an N/2 − N/2 modulated-amplitude cluster solution for c2 = −0.71 and η = 0.65. b Time series of the real part of each oscillator in a. c, d Like a, b for an unbalanced 3N/4 − N/4 solution at c2 = −1.0 and η = 0.65. e–h The solutions in a, b and c, d, respectively, when viewed in a frame co-rotating with the ensemble average 〈W〉 = η e−iνt. For the N/2 − N/2 solution, the two clusters follow the same trajectory. i, j N/2 − N/4 − N/4 three-cluster solution at c2 = −0.69, emerging from the solution in a, b in a period-doubling bifurcation. k Bifurcations destabilizing the two-cluster solution as a function of c2 and the relative size of the larger cluster N1/N for η = 0.67. The blue line denotes a period-doubling (PD) that splits the smaller cluster, and the green line a subcritical pitchfork (PF) that blows it up. The vertical black line marks the c2-incremented simulation in Fig. 6.
