Critical eccentricity as a function of planet period ratio for two equal mass planets using the ﹩{\tau }_{\mathrm{res}}=1﹩ criterion (see main text). Points show the transition to chaos computed from N-body simulations. Analytic predictions given by Equation (19) are plotted as dashed lines. Curves and points are colored according to planet mass. The value of Z corresponding to crossing orbits is indicated by the black dashed line.