Dynamical systems under constant organization I. Topological analysis of a family of non-linear differential equations--a model for catalytic hypercycles.

The paper presents a qualitative analysis of the following systems of n differential equations: ẋ i = x i x j − x i σ n r = 1 x r x s ( j = i − 1 + nδ il and s = r − 1 1 + n° r 1 ), which show cyclic symmetry. These dynamical systems are of particular interest in the theory of selforganization and biological evolution as well as for application to other fields.