and current depend only on α . For larger values ( α > 0 . 8 and β > 0 . 6), the system is in the maximum-current phase, in which density and current are independent of both α and β , and the current takes its maximum value. Thus the continuous-space model exhibits the same three phases observed in lattice model. As in the lattice model, the transition between the low- and high-density phases is discontinuous, whereas transitions between the maximum-current phase and the other phases are continuous. (While the density is discontinuous in the former case, the current is always continuous at the transition.) We adopted the following procedure (“polynomial method”) to determine the values of ( α, β ) along the discontinuous transition line. Consider the case of fixed α . For small β , the stationary current depends only on β (see Fig. 7(c)). We therefore fit a polynomial P ( β ) to the current in this regime, using data for a large, fixed α (in practice, α ≥ 1 . 4). For larger values of β , the current depends only on α ; in Fig. 7(c) this regime corresponds to one of the plateaux, J = J $^{∗}$( α ). The transition point β$_{c}$ ( α ) is taken as the value at which the plateau intersects the polynomial fit to the small- β data, i.e., P ( β$_{c}$ ) = J $^{∗}$( α ). Determination of α$_{c}$ ( β ) follows an analogous procedure, in which we fit a polynomial to the current data for small α . We find that a quadratic polynomial is sufficient to fit (to within uncertainty) the current j ( β ) at fixed α , while a good fit of j ( α ) (at fixed β ) requires a quartic polynomial. In both cases the constant term in the polynomial is zero, since the current vanishes for α and/or β zero. The above method is quite effective in locating points along the discontinuous transition line. Although it can in principle be used to locate continuous transitions as well, we found that in this case the estimates for α$_{c}$ and β$_{c}$ are rather sensitive to one’s choice of the range of values fit using the polynomial. We found the following approach (“derivative method”) to be more useful for continuous transition points. For fixed α , we estimate the derivative dJ/dβ using a spline fit (see Fig. 8). The 15