Pattern formation in a surface chemical reaction with global delayed feedback

We consider effects of global delayed feedback on anharmonic oscillations in the reaction-diffusion model of the CO oxidation reaction on a Pt~110! single-crystal surface. Depending on the feedback intensity and the delay time, we find that various spatiotemporal patterns can be induced. These patterns are characterized using a transformation to phase and amplitude variables designed for anharmonic oscillations. Typical feedbackinduced patterns represent traveling phase flips, asynchronous oscillations, and dynamical clustering. Three different types of cluster patterns are identified: amplitude clusters, phase clusters, and cluster turbulence. For phase clusters, two different front instabilities are possible. A pitchfork bifurcation leads to propagation of cluster fronts. An instability of the state of phase balance results in spatial front oscillations.