Surface-induced chemical oscillations and their influence on space- and time-periodic patterns

Within the framework of a reaction-diffusion model we study the influence of active or passive surfaces (e.g., membranes) on extended chemical systems. The surface is described by boundary conditions. Using linear stability analysis we find time-independent boundary conditions which induce oscillatory instabilities of the homogeneous state leading to boundary oscillations. Two cases are of special interest:(i) autocatalysis takes place only in the bulk, whereas coupling occurs only at the surface (or vice versa); (ii) all reactions take place at the surface but bulk diffusion is still essential for the oscillations. Phase diffusion theory and numerical simulation show that for oscillating and excitable (or bistable) bulk systems these boundary conditions can act as a pacemaker leading to phase-locked and quasiperiodic oscillations. The stability of the arising phase waves is discussed. For systems with stationary spatial bulk patterns boundary oscillations can constitute an efficient wavelength selection mechanism.