Small autocatalytic reaction networks—III. Monotone growth functions

Abstract

The classification of the dynamical behaviour of first order replicator equations is extended to models with monotonical growth rates. It is shown that for two species there is a general classification independent of the particular form of the growth function. For three species a common dynamical behaviour for all power laws can be found and the existence of limit cycles is disproved. For more general growth functions, however, limit cycles may occur.