Geodesic
A~discrete dynamical system on a~double circulant
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 4, pp. 80-88.

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A discrete dynamical system on a double circulant with additive and multiplicative functions at the vertices is studied. We describe all the cycles and fixed points of the functional graph of the system. Bibliogr. 9.
Keywords: discrete dynamical system, gene network, regulator circuit, functional graph.
Mots-clés : circulant 
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A. M. Nazhmidenova; A. L. Perezhogin. A~discrete dynamical system on a~double circulant. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 4, pp. 80-88. http://geodesic.mathdoc.fr/item/DA_2014_21_4_a7/

[1] Grigorenko E. D., Evdokimov A. A., Likhoshvai V. A., Lobareva I. A., “Nepodvizhnye tochki i tsikly avtomatnykh otobrazhenii, modeliruyuschikh funktsionirovanie gennykh setei”, Vestn. TGU, 2005, no. 14, 206–212

[2] Demidenko G. V., Kolchanov N. A., Likhoshvai V. A., Matushkin Yu. G., Fadeev S. I., “Matematicheskoe modelirovanie regulyarnykh konturov gennykh setei”, Zhurn. vychisl. matematiki i mat. fiziki, 44:12 (2004), 2276–2295 | MR | Zbl

[3] Evdokimov A. A., Likhovidova E. O., “Diskretnaya model gennoi seti tsirkulyantnogo tipa s porogovymi funktsiyami”, Vestn. TGU. Upravlenie, vychislitelnaya tekhnika i informatika, 3:2 (2008), 18–21

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

[5] Likhoshvai V. A., Golubyatnikov V. P., Demidenko G. V., Evdokimov A. A., Matveeva I. I., Fadeev S. I., “Teoriya gennykh setei”, Sistemnaya kompyuternaya biologiya, Izd-vo SO RAN, Novosibirsk, 2008, 397–480

[6] Ore O., Teoriya grafov, Nauka, M., 1980, 336 pp. | MR

[7] Evdokimov A. A., Kutumova E. O., “Reversible states of functioning the regulatory circuits discrete models the gene nets”, Vestn. TGU. Upravlenie, vychislitelnaya tekhnika i informatika, 14:1 (2011), 85–94

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

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