Catalysts are chemical substances that modify reaction rates without themselves being changed in the process. Their kinetics are characterized by threshold and amplification phenomena. Enzymes are the major class of biological catalysts.

The molecules of an autocatalytic system speed up the very reactions by which they are formed. Autocatalytic loops are like feedback loops in that the presence of a substance stimulates production of the same element and that the kinetic equations describing them are non-linear . (Eg. the rate of variation of the concentration of X is proportional to the square of its concentration) 

Cross-Catalysis is a similar loop involving several elements. The first element triggers the production of the second, which in turn produces the first. A hypercycle is a system of autocatalytic reactions arranged in a circle so each reaction's product catalyzes production of its clockwise neighbor. 

The gene was described by H.J. Muller in 1926 as possessing the property of "specific autocatalysis," meaning self-replication. "Still more remarkable," he wrote, the gene can mutate without losing its specific autocatalytic power. 

Stuart Kauffman studied auto-catalytic sets as a possible explanation of the origin of life, for they tend to grow as long as the materials for their synthesis are available. For Kaufman, at its heart, a living organism is a system of chemicals that has the capacity to catalyze its own reproduction. (See At Home in the Universe, p. 49) Different auto-catalytic sets might compete for the same raw materials and life could indeed have bootstraped itself into existence through this process rather than have waited for some ridiculously improbable random events. But is the occurence of auto-catalysis a simply fortuitous event? Kauffman studied systems to find out when auto-catalysis might occur and found that this tended to happen "at the edge of chaos" This state corresponded to the " phase transition" behaviour studied by Chris Langton and the students of Artificial life. For Langton, Life is eternally trying to keep its balance on the edge of chaos, always in danger of falling off into too much order on the one side, and too much chaos on the other. 

For Kauffman, life, instead of being improbable, is an expected, emergent, collective property of complex systems of polymer catalysts when a system acheives catalytic closure. "As the complexity of a collection of polymer catalysts increases, a critical complexity threshold is reached. Beyond this threshold, the probability that a subsystem of polymers exists in which formation of each member is catalyzed by other members of the subsystem becomes very high" (p.289)

(See Prigogine Order Out of Chaos, pp. 133-135, Waldrop Complexity pp 124 - 125)