A multi-parameter system of ordinary differential equations, modelling genetic networks, is considered. Attractors of this system correspond to future states of a network. Sufficient conditions for the non-existence of stable critical points are given. Due to the special structure of the system, attractors must exist. Therefore the existence of more complicated attractors was expected. Several examples are considered, confirming this conclusion.

Two three-dimensional systems are considered, which have solutions with irregular behavior, tending to attractors. The comparison and comparative analysis are made