Figure 2.

Plots of u₁ from simulations of the Schnakenberg system using α = 1, d = 1/40 = 0.025, and β = 3/5 + [1 − cos (πx)]/25 with varying ε. The blue solid curve is from the numerical simulation whereas the black dashed curve is the stationary state $u_1^{\ast }(x)=\beta (x)$ (note that the blue region is due to the highly oscillatory nature of the solution). The red dash-dotted curve is the boundary of ${\mathcal{T}}_0$ at x ≈ 0.7774 (i.e. the singular point $x_{\ast }$). The insets show a zoomed-in region near the boundary of ${\mathcal{T}}_0$; these insets are over different regions in (a) and (b), though (c) and (d) share the same x-axis for their insets. (a) ε = 10⁻², (b) ε = 10⁻³, (c) ε = 10⁻⁴, (d) ε = 10⁻⁵. (Online version in colour.)