An AutocatalyticSet is a chain of catalyzed reactions that folds back on itself.
Suppose that A catalyzes a reaction that increases the concentration of B, which I will denote as
A -> B
Then an AutocatalyticSet is a reaction such that:
A -> B -> ... -> N -> A
Or
A ->* A
Yes, I just wanted to beat the reader over the head with its sequential nature. Specifically, suppose there are two AutocatalyticSets AC1 and AC2, so that:
AC1 = A->B->A
AC2 = A->C->A
These are different AutocatalyticSets. I'm not sure that the more terse notation sufficiently reveals their difference.
See http://en.wikipedia.org/wiki/Autocatalytic_set