Before revision: The transient fluctuation of the population of species is investigated with a stochastic modelfor a catalytic network. The swinging changes in the fluctuation in the transient state from the initial growth to the final steady state is the consequence of a topology-dependent  competition between the catalysis and spontaneous decay.
After revision: The transient fluctuation of the population of species is investigated with an abstract stochastic model. The model describes the profit which firms make when they sell materials to a firm which produces a product and the fixed cost expense to the firms to produce those materials and product. The formulae for this model are parallel to those for population dynamics. The swinging changes in the fluctuation in the transient state from the initial growth to the final steady state is the consequence of a topology-dependent competition between the catalysis and spontaneous decay.