Permanence of Sparse Autocatalytic Networks

Peter F. Stadler and Peter Schuster

Some global dynamical properties of catalytic networks, in particular permanence, are closely related with a directed graph representing the differential equation. It can be shown that for every directed graph with a Hamiltonian circuit there is a choice of rate constants such that the system is permanent. On the other hand one can find properties of the graphs, e.g. reducibility or the presence of end points, which are incompatiable with permanence.

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