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. 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.
The transient fluctuation of the prosperity of firms in a network economy 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 are the consequence of a topology-dependent time trial competition between the profitable interactions and expense. The firm in a sparse random network economy is more likely to go bankrupt 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.
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population of species
prosperity of firms in a network economy
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a stochastic modelfor a catalytic network. The
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
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is
are
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time trial
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catalysis and spontaneous decay. Species
profitable interactions and expense. The firm
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may be
economy is
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become extinct
go bankrupt