  Perturbations around autonomous one-dimensional single-species
reaction-diffusion systems are investigated. It is shown that the parameter
space corresponding to the autonomous systems is divided into two parts: In one
part, the system is stable against the perturbations, in the sense that largest
relaxation time of the one-point functions changes continuously with
perturbations. In the other part, however, the system is unstable against
perturbations, so that any small perturbation drastically modifies the
large-time behavior of the one-point functions.
