A genetic network exists in any cell of any living organism. This network is responsible for most vital functions, including reactions to changes in the environment and adaptation to poor conditions. The evolution of a genetic network in time can be modeled by a specially constructed system of differential equations. This system contains many equations and a lot of parameters. Each gene is identified with the variable xi(t), and the entire network is represented by the vector X(t)=(x1(t), …, xn(t)), where n is the number of elements in a network and, consequently, the number of equations in the dynamical model. Each gene is connected with others and interrelation between elements in a network is described by the regulatory matrix W. Due to the specific structure of the system, modeling the network, there are one or many attractors. Attractors are subsets of the phase space X=(x1, …, xn) and they attract the trajectories X(t). Future states X(t) therefore are heavily dependent on the structure and properties of attractors. Some authors interpret serious diseases as tending the genetic network to a “wrong” attractor. Redirecting of trajectories to a normal attractor requires an understanding of the structure of the phase space and the location of attractors there. We consider a 3-element network, modeling by a system of three differential equations. For some choices of matrices W the attractors are considered, their properties explained, and conclusions about the evolution of a network are made. Examples and illustrations are provided.