Figure 6.

Illustration of periodic travelling waves generated by the invasion of (a) a prey population by (b) predators in one space dimension. We plot population densities as a function of distance from the centre of the obstacle, with the vertical separation of the solutions proportional to the time intervals. There is a receding wavefront of prey, and a corresponding advancing wavefront of predators, behind which there is a periodic travelling wave. We solved equations (3.2a) and (3.2b) numerically for parameter values μ=0.083, σ=0.25, κ=0.33 and α=1, using the method of lines and Gear's method. The initial conditions corresponded to a prey-only state everywhere, except at x=0, where we introduced a small non-zero predator density.