Fig. 8

Bump widths and profiles for a spatially heterogeneous threshold. Top: solutions of (32)–(33), where \(\Delta =x_{2}-x_{1}\), for \(h(x)=0.05+0.01\cos{x}\). Only the red solution is stable. Bottom: bump profiles for the solutions in the upper panel, and threshold \(h(x)\) (dash-dotted). The solid bump is stable, all others (dashed) are unstable. Parameter values are \(\alpha=5\), \(B=0.76\) and \(\beta=3\)