Geodesic
Functioning of discrete dynamic circulant-type system with threshold functions
Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 84-95.

Voir la notice de l'article provenant de la source Math-Net.Ru

The functioning of discrete dynamic circulant-type systems with threshold functions is studied. The general properties of the functional graph of a system are described. In binary case, all states of the system are classified according to the length of $0$-series and $1$-series. As a result, some properties of cycles in the functional graph and a lower estimate for the number of connected components are given. For an arbitrary value $p$, a criterion for the existence of stable states in the system is given, the forms and the number of these states are determined.
Keywords: discrete dynamic systems, functional graph, threshold functions, cycles of functional graph, stable states.
Mots-clés : circulant graph 
@article{PDM_2014_4_a9,
     author = {I. S. Bykov},
     title = {Functioning of discrete dynamic circulant-type system with threshold functions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {84--95},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_4_a9/}
}
TY  - JOUR
AU  - I. S. Bykov
TI  - Functioning of discrete dynamic circulant-type system with threshold functions
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2014
SP  - 84
EP  - 95
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2014_4_a9/
LA  - ru
ID  - PDM_2014_4_a9
ER  - 
%0 Journal Article
%A I. S. Bykov
%T Functioning of discrete dynamic circulant-type system with threshold functions
%J Prikladnaâ diskretnaâ matematika
%D 2014
%P 84-95
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2014_4_a9/
%G ru
%F PDM_2014_4_a9
I. S. Bykov. Functioning of discrete dynamic circulant-type system with threshold functions. Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 84-95. http://geodesic.mathdoc.fr/item/PDM_2014_4_a9/

[1] Harary F., “The number of functional digraphs”, Math. Ann., 139 (1959), 203–210 | DOI | MR

[2] Evdokimov A. A., Likhovidova E. O., “Diskretnaya model gennoi seti s porogovymi funktsiyami”, Vestnik TGU. Prilozhenie, 2008, no. 2, 18–21

[3] Kutumova E. O., “Tsikly funktsionirovaniya diskretnoi modeli regulyatornogo kontura gennoi seti s porogovymi funktsiyami”, Diskretnyi analiz i issledovanie operatsii, 38:3 (2011), 65–75 | MR | Zbl

[4] Grigorenko E. D., Evdokimov A. A., Likhoshvai V. A., Lobareva I. A., “Nepodvizhnye tochki i tsikly avtomatnykh otobrazhenii, modeliruyuschikh funktsionirovanie gennykh setei”, Vestnik Tomskogo gosudarstvennogo universiteta. Prilozhenie, 2005, no. 14, 206–212