Fig. 18.

Multibumps. Top: $L^2$ norm of stable steady states of (3) for a Gaussian threshold distribution, with many different initial conditions, different realisations of $h(x)$, and various $h_0$. Solutions indicated by blue stars are shown in the bottom panel. Bottom: typical stable steady states solutions of (3) with 1, 2 and 3 bumps, for $h_0=0.03$. Their $L^2$ norms increase as the number of bumps increases (blue dots in the top panel). These three solutions correspond to three different realisations of $h(x)$. Parameter values are $\alpha =15$, $B=0.76$, $\beta =9$, $ϵ=0.003$, $\kappa =0.5$ and ${\sigma }^2=4$