Rigid transition to the stationary structure and imposed convective instability in a reaction-diffusion system with flow

Abstract Stationary flow and diffusion distributed structure (FDS) is known to appear in a reaction–diffusion system with open flow when the constant perturbation is applied at the inlet. Usually, the FDS is considered in the oscillatory Hopf domain when the instability of the Hopf mode is convective. This paper focuses on the formation of the FDS in presence of the absolute Hopf instability. In this case, both FDS and Hopf solutions tend to invade the space. The result of this competition depends on the amplitude of the inflow perturbation and on the flow rate. At large flow rate the Hopf solution dominates if the inflow perturbation is small. Increasing of the inflow perturbation gives rise the rigid transition to FDS and produces the imposed convective Hopf instability. Small flow rate always gives an advantage to the Hopf solution. The FDS solution, though still appears near the inlet at large inflow perturbation, does not expand, and the FDS-Hopf domain boundary stays in a fixed position.