Elementary step dynamics of catalytic hypercycles.

Two model systems for hypercyclic organisation constructed from a series of uni- and bimolecular reaction steps were studied under the condition of unlimited growth by means of qualitative analysis and numerical integration of the corresponding differential equations. It is shown that both models lead, within wide ranges of parameter and initial conditions, to the same characteristic dynamical behaviour as the elementary hypercycles and hypercycles with translation introduced in 1978 by Eigen and Schuster.