Before revision:  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. Species in a sparse random network may be more likely to become extinct than expected from the value of the limit of the fluctuation in the steady state, and there is a risk of failing to reach by far the less fluctuating steady state.
After revision:  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 profitable interactions and expense. The firm in a sparse random network may be more likely to become extinct than expected from the value of the limit of the fluctuation in the steady state, and there is a risk of failing to reach by far the less fluctuating steady state.