Formation of stable patterns when uniform state is unstable

Formation of stable patterns when uniform state is unstable 

In the previous section we have taken care to keep well away from parameter values /i and k for which the uniform stationary state is unstable to Hopf bifurcations. Thus, instabilities have been induced solely by the inequality of the diffusivities. We now wish to look at a different problem and ask whether diffusion processes can have a stabilizing effect. We will be interested in conditions where the uniform state shows time-dependent periodic oscillations, i.e. for which /i and k lie inside the Hopf locus. We wish to see whether, as an alternative to uniform oscillations, the system can move on to a time-independent, stable, but spatially non-uniform, pattern. In fact the 

---