Next, it was confirmed by experiments that a steady state of an ORN is stable against fluctuation though it is in non-equilibrium (Figure ). To our knowledge, there is no general theory to explain this fact. Prigogine's theorem about the stability of a steady state on the basis of minimum entropy production only applies to the near-equilibrium linear region. In fact, the aforementioned fact that the results similar to that in Figure are often observed indicates that Prigogine's theorem cannot be used for judging the stability of a steady state of an ORN against fluctuation. A number of studies have been reported on dynamics of non-equilibrium reaction networks but the behavior of such systems is in general very complex. For an ORN, the time courses of concentrations Ci of chemical substances Ri can be described by a set of differential equations: