Abstract
Within the framework of Von Neumann’s expanding model, we study the maximum growthrate achievable by an autocatalytic reaction network in which reactions involve a finite (fixed or fluctuating)number D of reagents. is calculated numerically using a variant of the Minover algorithm, and analytically viathe cavity method for disordered systems. As the ratio between the number of reactionsand that of reagents increases the system passes from a contracting () to an expanding regime (). These results extend the scenario derived in the fully connected model (D → ∞), with the important difference that, generically, larger growth rates are achievable in the expanding phasefor finite D and in more diluted networks. Moreover, the range of attainable values of shrinks as the connectivity increases.
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