Chaotic phase space structure for two planets of mass ﹩{m}_{1}={m}_{2}=3\times {10}^{-5}{M}_{* }﹩ with different values of ﹩{ \mathcal W }﹩ (Equation (17)) integrated for 3000 orbits of the outer planet. The planets are initialized with ﹩{\lambda }_{1}={\lambda }_{2}=0﹩ and ﹩\mathrm{Im}{ \mathcal Z }=0﹩. Chaotic trajectories are shown in white while regular trajectories appear black. More precisely, the background consists of a gray-scale spanning a narrow range of MEGNO values ranging from MEGNO ﹩\leqslant \,2﹩ (black; ﹩{t}_{\mathrm{Ly}}\gtrsim 1500{P}_{2}﹩) to MEGNO ﹩\geqslant \,6﹩ (white; ﹩{t}_{\mathrm{Ly}}\lesssim 500{P}_{2}﹩). The narrow gray-scale range emphasizes the sharp transition from regular to chaotic orbits. Integrations that led to a close encounter within one Hill radius were stopped early and are also marked in white. The vertical axis shows the real component of the initial complex relative eccentricity ﹩{ \mathcal Z };﹩ the imaginary component is zero. The onset of chaos predicted by Equations (18) and (19) are shown as red solid and dashed lines, respectively. The predicted onset of chaos does not depend on ﹩{ \mathcal W }﹩ and is the same in all three panels.