Geodesic
The functional graph of a~linear discrete dynamical system with two dominating vertices
Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 4, pp. 81-96.

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

The change of the functional graph of a linear discrete dynamical system is described under transformation of the support graph of the system. Namely, the support graph is transformed by adding two dominating vertices. Bibliogr. 12.
Keywords: discrete dynamical system, linear discrete dynamical systems, functional graph, state diagram, support graph, linear sequential network. 
@article{DA_2018_25_4_a5,
     author = {A. S. Parfinenko and A. L. Perezhogin},
     title = {The functional graph of a~linear discrete dynamical system with two dominating vertices},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {81--96},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2018_25_4_a5/}
}
TY  - JOUR
AU  - A. S. Parfinenko
AU  - A. L. Perezhogin
TI  - The functional graph of a~linear discrete dynamical system with two dominating vertices
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2018
SP  - 81
EP  - 96
VL  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2018_25_4_a5/
LA  - ru
ID  - DA_2018_25_4_a5
ER  - 
%0 Journal Article
%A A. S. Parfinenko
%A A. L. Perezhogin
%T The functional graph of a~linear discrete dynamical system with two dominating vertices
%J Diskretnyj analiz i issledovanie operacij
%D 2018
%P 81-96
%V 25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2018_25_4_a5/
%G ru
%F DA_2018_25_4_a5
A. S. Parfinenko; A. L. Perezhogin. The functional graph of a~linear discrete dynamical system with two dominating vertices. Diskretnyj analiz i issledovanie operacij, Tome 25 (2018) no. 4, pp. 81-96. http://geodesic.mathdoc.fr/item/DA_2018_25_4_a5/

[1] Ts. Ch.-D. Batueva, “Discrete dynamical systems with threshold functions at the vertices”, Diskretn. Anal. Issled. Oper., 21:4 (2014), 25–32 | MR | Zbl

[2] I. S. Bykov, “Functioning of discrete dynamic circulant-type system with threshold functions”, Prikl. Diskretn. Mat., 2014, no. 4, 84–95

[3] A. I. Garber, “Graphs of linear operators”, Proc. Steklov Inst. Math., 263 (2008), 57–64 | DOI | MR | Zbl

[4] A. Gill, Linear Sequential Circuits: Analysis, Synthesis, and Applications, McGraw-Hill Book Co., New York, 1966 | MR | Zbl

[5] E. D. Grigorenko, A. A. Evdokimov, V. A. Likhoshvai, I. A. Lobareva, “The fixed points and cycles of automatic mapping modeling the functioning of genetic networks”, Vestn. TGU, 2005, no. 14, 206–212

[6] A. A. Evdokimov, A. L. Perezhogin, “Discrete dynamical systems of a circulant type with linear functions at vertices of network”, J. Appl. Ind. Math., 6:2 (2012), 160–166 | DOI | MR | Zbl

[7] A. M. Nazhmidenova, A. L. Perezhogin, “A discrete dynamical system on a double circulant”, Diskretn. Anal. Issled. Oper., 21:4 (2014), 80–88 | MR | Zbl

[8] Arnold V. I., “Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions”, Funct. Anal. Other Math., 1:1 (2006), 1–18 | DOI | MR

[9] Elspas B., “The theory of autonomous linear sequential networks”, IRE Trans. Circuit Theory, CT-6 (1959), 45–60 | DOI

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

[11] Hernández Toledo René A., “Linear finite dynamical systems”, Commun. Algebra, 33:9 (2005), 2977–2989 | DOI | MR | Zbl

[12] Lerner E. Yu., Multiplicative function instead of logarithm (an elementary approach, Cornell Univ. Libr. e-Print Archive, 2007, arXiv: 0710.2088