Libration centers of ZLK secondary 2:1 resonances determined by analyzing phase portraits (solid red circles) for different mass ratios at α_m = 1.1 (left panel) and α_m = 40 (right panel). For comparison, the characteristic curves of periodic families associated with ZLK resonance, the conventional ZLK centers and level curves of octupole-order Hamiltonian are presented (see the solid blue, red dashed, and gray lines). There is a good correspondence between the center of ZLK secondary resonance and the characteristic curves of periodic orbit families in the region near the bifurcation point.