ABSTRACT
A network of processes is considered an autocatalytic reaction network if elements are produced by a copying mechanism. The introduction of mutation into error-free nonlinear autocatalytic networks commonly simplifies their dynamics. Autocatalytic reaction networks are properly subdivided into two classes: quasi-linear and essentially nonlinear networks. In addition to the network of autocatalytic processes, the details of the experimental setup or the environmental conditions have to be known in order to formulate the kinetic differential equations. In order to be able to make full use of normalized concentrations and to derive a classification of nonlinear autocatalytic reaction networks from the kinetic differential equations, it is advisable to consider exclusively second-order reactions. Direct qualitative analysis of catalytic networks with mutation was carried out for special cases of low-dimensional systems also based on different model assumptions. Quasi-linear replicator networks do not form spatial patterns under homogeneous Neumann or no-flux boundary conditions.
