On modelling of artificial networks arising in applications

On a Planar Dynamical System Arising in the Network Control Theory

We study the structure of attractors in the two-dimensional dynamical system that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.

Multiple period annuli in Liénard type equations

Abstract We consider the equation x ″ x 1 − x 2 x ′ 2 + g ( x ) = 0 , where g ( x ) is a polynomial. We provide the conditions for existence of multiple period annuli enclosing several critical points.

Dynamical Models of Interrelation in a Class of Artificial Networks

The system of ordinary differential equations that models a type of artificial networks is considered. The system consists of a sigmoidal function that depends on linear combinations of the arguments minus the linear part. The linear combinations of the arguments are described by the regulatory matrix W. For the three-dimensional cases, several types of matrices W are considered and the behavior of solutions of the system is analyzed. The attractive sets are constructed for most cases. The illustrative examples are provided. The list of references consists of 12 items.