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 \(\alpha=15\), \(B=0.76\), \(\beta=9\), \(\epsilon =0.003\), \(\kappa=0.5\) and \(\sigma^{2}=4\)