Maximum eccentricity reached by the trajectories is shown as a function of the Hamiltonian ℋ for the cases of α_m = 1.1 (left panel) and α_m = 40 (right panel). The solid lines represent the curves determined under the octupole-order model, while the dashed lines represent the curves determined under the quadrupole-order model. The initial eccentricities are assumed at 0.45 for α_m = 1.1 and 0.6 for α_m = 40. Under the octupole-order model, the peak of e_1,max happens near the bifurcation point. It is observed that, in the region near the bifurcation point (see the shaded region), the maximum eccentricities reached under the quadrupole- and octupole-order Hamiltonian models have significant differences, while in the region far away from the bifurcation point they have no differences. This means that the octupole-order terms contribute significantly to the excitation of eccentricity in those regions near the bifurcation point.