Selection in regulated autocatalytic systems

The paper deals with problems involved in the formation of stable structures in a system, in which processes typical of bimolecular autocatalytical reactions occur when the respective components are directly influenced from the outside. Such systems can arise in biochemical, biological and ecological sphere (see, e.g. Glansdorff and Prigogine 1971; Nicolis and Prigogine 1977; Haken 1977; 1980). It has been shown that a regions of so-called subcritical and supercritical regulation exist, manifested by the fact that the given system component would either persist or disappear. The selection of processes consists in the fact that generally only one solution can be realized from N alternatives as a stable state having the nature of a stable node, or a stable focus. When one of the components is supplied to the system from the exterior in a supercritical amount, the system can be "forced" to produce only that single substance. Thus, the system studied can be considered as a model of a biological filter. The results can also be applied in ecology and biotechnology.