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