Fig. 5: Stability of different cluster synchronization patterns.

a MLEs transverse to solution 1a. Solid and dotted lines refer to different transverse blocks. When a line crosses zero it identifies a symmetry-breaking bifurcation in one of the other invariant manifold (red: bifurcations on CS manifold 1b—yellow: bifurcations on CS manifold 2). Pattern 1a is stable when both the curves are negative. b MLEs transverse to stable solutions on the synchronized manifold 1b. Blue curves refer to the transverse MLE of solution of kind 1a, while the red curve refers to the transverse MLE of solution of kind 1b. Vertical lines indicate the bifurcations of the quotient system. c MLEs transverse to stable solutions on the synchronized manifold 2. Blue curves refer to the transverse MLE of solution of kind 1a, while the yellow curves refer to the transverse MLE of solution of kind 2. Vertical lines indicate the bifurcations of the quotient system. Colored lines represent symmetry breaking bifurcation (inferred from (a)), while black lines are other bifurcations.