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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:4, 706–715

Volume 25, No 4, 2018, P. 81-96

UDC 519.174
A. S. Parfinenko and A. L. Perezhogin
The functional graph of a linear discrete dynamical system with two dominating vertices

Abstract:
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.

DOI: 10.17377/daio.2018.25.604

Anastasia S. Parfinenko 1
Aleksey L. Perezhogin 1,2

1. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
2. Sobolev Institute of Mathematics,
4 Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: anastasia.s.parfinenko@gmail.com, pereal@math.nsc.ru

Received 19 December 2017
Revised 6 April 2018

References

[1] Ts. Ch.-D. Batueva, Discrete dynamical systems with threshold functions at the vertices, Diskretn. Anal. Issled. Oper., 21, No. 4, 25–32, 2014.

[2] I. S. Bykov, Functioning of discrete dynamic circulant-type system withthreshold functions, Prikl. Diskretn. Mat., No. 4, 84–95, 2014.

[3] A. I. Garber, Graphs of linear operators, Tr. Mat. Inst. Steklova, 263, 64–71, 2008. Translated in Proc. Steklov Inst. Math., 263, 57–64, 2008.

[4] A. Gill, Linear Sequential Circuits: Analysis, Synthesis, and Applications, McGraw-Hill Book Co., New York, 1966. Translated under the title Lineinye posledovatel’nostnye mashiny: Analiz, sintez i primenenie, Nauka, Moscow, 1974.

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

[6] A. A. Evdokimov and A. L. Perezhogin, Discrete dynamical systems of a circulant type with linear functions at vertices of network, Diskretn. Anal. Issled. Oper., 18, No. 3, 39–48, 2011. Translated in J. Appl. Ind. Math., 6, No. 2, 160–166, 2012.

[7] A. M. Nazhmidenova and A. L. Perezhogin, A discrete dynamical system on a double circulant, Diskretn. Anal. Issled. Oper., 21, No. 4, 80–88, 2014.

[8] V. I. Arnold, Complexity of finite sequences of zeros and ones and geometry of finite spaces of functions, Funct. Anal. Other Math., 1, No. 1, 1–18, 2006.

[9] B. Elspas The theory of autonomous linear sequential networks, IRE Trans. Circuit Theory, 6, No. 1, 45–60, 1959.

[10] F. Harary, The number of functional digraphs, Math. Ann., 139, 203–210, 1959.

[11] René A. Hernández Toledo, Linear finite dynamical systems, Commun. Algebra, 33, No. 9, 2977–2989, 2005.

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