Figure 8.

The effect of α on the range of wavelengths in the travelling wave family for equations (3.2a) and (3.2b), and on the wavelength picked out by zero Dirichlet boundary conditions in numerical simulations. The values of the kinetic parameters are σ=0.15, μ=0.05 and κ=0.2. Light shaded areas denote the region of unstable travelling waves and dark shaded areas denote the region of stable travelling waves; in unshaded areas there are no travelling waves. The solid line corresponds to the position of the Hopf bifurcation of the wave family. Circles correspond to the values predicted by numerical simulations. Filled circles denote waves that showed no evidence of instability. Open circles denote waves that existed transiently before developing into irregular spatio-temporal behaviour. Spatio-temporal dynamics for two cases, α=1 and 100, are shown in figures 3b and 7a, respectively. Values reported for apparently unstable periodic travelling waves were measured from the region of waves that form directly behind the Dirichlet boundary, as is visible in figure 7a. Note the log axis for α.