Before revision:  We illustrate the validity, the efficiency and the universality of our results on several reaction networks arising in fields such as biochemistry, epidemiology and ecology  .
After revision:  We illustrate the validity, the efficiency and the universality of our results on several reaction networks arising in fields such as biochemistry, epidemiology and ecology . The biological implications of the results as well as an example of a non-ergodic biological network are also discussed .