Figure 1.

(A) The blue-shaded wedge in the parameter plane $\left({\gamma }_1,\kappa \right)$ for $\delta =0.01$ shows the region of bistability in which both pure states are stable and may transiently coexist in space; however, the fronts separating them would generally move in either direction when diffusion is not zero. (B–D) demonstrate how one-dimensional fronts reverse direction when κ is increased from 0.06 (B) to 0.087 (C) to 0.12 (D) for ${\gamma }_1=6$ (direct numerical integration of Eqs. 1 and 2). Only the dynamics of $n_1$ are shown here. In the region where $n_1$ is high, $n_2$ is low and vice versa. The red solid line in (A), which is plotted according to formula (4), corresponds to the stationary front solution. It separates the parameter regions in which either $n_1$ or $n_2$ win the competition. The symbols show the parameter values for which the fronts were indeed found to be stationary in direct simulations. To see this figure in color, go online.