In the language of mathematics, the method of cognition of the surrounding world in which the description of the object is carried out the name is mathematical modeling. The study of the model is carried out using certain mathematical methods. The systems of the ordinary differential equations modeling artificial neuronal networks and the systems modeling the gene regulatory networks are considered. The one system consists of a sigmoidal function which depends on linear combinations of the arguments minus the linear part. The other system consists of a sigmoidal function which depends on the hyperbolic tangent function. The linear combinations and hyperbolic tangent functions of the arguments are described by one regulatory matrix. For the three-dimensional cases, two types of matrices are considered and the behavior of the solutions of the system is analyzed. The attracting sets are constructed for several cases. Illustrative examples are provided. The list of references consists of 19 items.