Discrete dynamical systems with threshold functions of up to three variables
Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 1, pp. 17-34.

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

We propose a method for finding sources of discrete dynamical systems of the circulant type with a $q$-valued arbitrary function at the vertices. We find all the sources, all the fixed points and some cycles, as well as lengths of some maximal chains outside cycles for the systems with Boolean threshold functions of up to three variables at the vertices. Ill. 1, tab. 2, bibliogr. 15.
Keywords: discrete dynamical system, gene network, functional graph, threshold function
Mots-clés : circulant, source.
@article{DA_2016_23_1_a1,
     author = {Ts. Ch.-D. Batueva},
     title = {Discrete dynamical systems with threshold functions of up to three variables},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {17--34},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2016_23_1_a1/}
}
TY  - JOUR
AU  - Ts. Ch.-D. Batueva
TI  - Discrete dynamical systems with threshold functions of up to three variables
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2016
SP  - 17
EP  - 34
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2016_23_1_a1/
LA  - ru
ID  - DA_2016_23_1_a1
ER  - 
%0 Journal Article
%A Ts. Ch.-D. Batueva
%T Discrete dynamical systems with threshold functions of up to three variables
%J Diskretnyj analiz i issledovanie operacij
%D 2016
%P 17-34
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2016_23_1_a1/
%G ru
%F DA_2016_23_1_a1
Ts. Ch.-D. Batueva. Discrete dynamical systems with threshold functions of up to three variables. Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 1, pp. 17-34. http://geodesic.mathdoc.fr/item/DA_2016_23_1_a1/

[1] Ts. Ch.-D. Batueva, “Properties of gene networks with threshold functions”, Prikl. Diskretn. Mat., Suppl., 2013, no. 6, 72–73

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

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

[4] G. V. Demidenko, N. A. Kolchanov, V. A. Likhoshvai, Yu. G. Matushkin, S. I. Fadeev, “Mathematical modeling of regular contours of gene networks”, Comput. Math. Math. Phys., 44:12 (2004), 2166–2183 | MR | Zbl

[5] A. A. Evdokimov, “Discrete models of gene networks: Analysis and complexity of functioning,”, Vychisl. Technol., 13:3, Vestn. KazNU, Ser. Mat. Mekh. Inform., 2008, No 3, A joint issue based on Proc. Int. Conf. “Comput. Inf. Technol. Sci. Eng. Educ.” (Almaty, Kazakhstan, Sept. 10–14, 2008) Pt. II, Izd. KazNU, Almaty (2008), 31–37

[6] A. A. Evdokimov, E. O. Likhovidova, “A discrete model for a gene network of a circulant type with threshold functions”, Vestn. TGU, Upr. Vychisl. Tech. Inform., 2008, no. 2, 18–21

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

[8] E. O. Kutumova, A. A. Evdokimov, “Reversible states in functioning of regulatory loops in discrete models for gene networks”, Vestn. TGU, Upr. Vychisl. Tech. Inform., 2011, no. 1, 85–94

[9] V. A. Likhoshvai, V. P. Golubyatnikov, G. V. Demidenko, A. A. Evdokimov, I. I. Matveeva, S. I. Fadeev, “Theory of gene networks”, Computational Systems Biology, Izd. SO RAN, Novosibirsk, 2008, 397–482

[10] 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

[11] O. Ore, Theory of Graphs, AMS Colloq. Publ., 38, AMS, Providence, 1962 | MR | MR | Zbl

[12] Evdokimov A. A., Kutumova E. O., “The discrete model of the gene networks regulatory loops with the threshold functions”, Proc. 7th Int. Conf. Bioinformatics of genom regulation and structure (Novosibirsk, June 20–27, 2010), SB RAS Press, Novosibirsk, 2010, 155

[13] Kauffman S. A., At home in the universe: the search for the laws of self-organization and complexity, Oxford Univ. Press, New York, 1995, 336 pp.

[14] Kauffman S. A., Smith R. G., “Adaptive automata based on Darwinian selection”, Physica D, 22:1–3 (1986), 68–82 | DOI | MR

[15] Laubenbacher R., Mendes P., “A discrete approach to top-down modeling of biochemical networks”, Computational Systems Biology, eds. A. Kriete, R. Eils, Elsevier Acad. Press, Burlington, MA, USA, 2005, 229–247