Reaction-diffusion dynamics in an oscillatory medium of finite size: Pseudoreflection of waves

Wave propagation in an oscillatory reaction-diffusion, one-dimensional domain of finite size with Dirichlet boundary conditions is analyzed. For sizes below a certain threshold length, the medium cannot sustain wave motion. Above this threshold we find that for a relatively small domain extent, a strong correlation exists between the dynamics of the system and its size. This correlation gradually disappears with increasing domain size. For still larger sizes, we observe an effect of wave pseudo reflection near the boundary. It is shown both numerically and analytically that pseudoreflected waves are periodically generated inside the medium by a fast, self-generated “source” near the boundary.