Figure 6

Normal, anomalous, and hybrid branches for attractive second coupling. The global order parameter of traveling wave states as functions of λ. The parameters are \({{\rm{\Theta }}}_{2}=0\) and \({\rm{\Delta }}=0.5\), and the values of \({{\rm{\Theta }}}_{1}\) are (a): \({{\rm{\Theta }}}_{1}=0.2\pi \); (b): \({{\rm{\Theta }}}_{1}=0.6\pi \); (c): \({{\rm{\Theta }}}_{1}=0.75\pi \); (d): \({{\rm{\Theta }}}_{1}=0.85\pi \). Bold lines: states with all \({P}_{l}=1\) (all oscillators locked); dashed lines: states that are partially locked \(0 < {P}_{l} < 1\); dotted lines: all oscillators are unlocked \({P}_{l}=0\). Stable traveling wave and incoherent solutions are highlighted with bold green line in background.