One-Dimensional Brusselator Model

In the paper, it is proven that the Q-process corresponding to one-dimensional Brusselator model is not strongly ergodic by two different methods. Meanwhile, for a one-dimensional modified Brusselator model, the strong ergodicity of the corresponding Q-process is deduced. Applying the ideas for an extended class of continuous-time branching processes, one necessary condition is obtained for the strong ergodicity of the processes.