EN|RU Volume 21, No 4, 2014, P. 25-32 UDC 519.174 Ts. Ch.-D. Batueva Discrete dynamical systems with threshold functions at the vertices Abstract: We propose an algorithm for finding all fixed points of a discrete dynamical system of the ñirculant type with an arbitrary Boolean function at the vertices. We obtain the description of the origins and fixed points for the system with a Boolean function $f$ of $k$ variables with a single set $\widetilde v$, such that $f(\widetilde v)=1$, at the vertices. Ill. 1, tab. 2, bibliogr. 8. Keywords: discrete dynamical system, circulant, gene network, functional graph. Batueva Tsyndyma Chimit-Dorzhiyevna 1 1. S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia e-mail: batueva@math.nsc.ru © Sobolev Institute of Mathematics, 2015