Non-turing stationary patterns in flow-distributed oscillators with general diffusion and flow rates

An analytical prediction [P. Andresen et al., Phys. Rev. E 60, 297 (1999)] and its experimental confirmation [M. Kaern et al., Phys. Rev. E 60, 3471 (1999)] establish a mechanism for forming stationary, space-periodic structures in a reactive flow (reaction-diffusion-convection system) with equal diffusion and flow rates. In this paper we generalize the analysis to systems with unequal diffusion and flow rates. Interestingly, stationary waves also exist outside the oscillatory Hopf domain of the batch system-hence the parameter space in which these structures exist is bigger than that initially predicted [P. Andresen et al., Phys. Rev. E. 60, 297 (1999)] (for equal diffusion and flow rates). On the other hand, we find that these stationary waves exist only for parameter values outside of and up to the Turing regime. We clarify the nature of the instability in terms of a boundary-forcing problem, whereby a time-periodic pattern is carried over the whole domain by the flow while the phase is fixed at the inflow boundary.