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Volume 23, No 1, 2016, P. 1734 UDC 519.174
Keywords: discrete dynamical system, circulant, gene network, functional graph, threshold function, source. DOI: 10.17377/daio.2016.23.473 Tsyndyma Ch.D. Batueva ^{1} Received 7 February 2015 References[1] Ts. Ch.D. Batueva, Properties of gene networks with threshold functions, Prikl. Diskretn. Mat., Suppl., No. 6, 72–73, 2013.[2] Ts. Ch.D. Batueva, Discrete dynamical systems with threshold functions at the vertices, Diskretn. Anal. Issled. Oper., 21, No. 4, 25–32, 2014. [3] E. D. Grigorenko, A. A. Evdokimov, V. A. Likhoshvai, and A. I. Lobareva, The fixed points and cycles of automaton mappings modeling functioning of genetic networks, Vestn. TGU, Suppl., No. 14, 206–212, 2005. [4] G. V. Demidenko, N. A. Kolchanov, V. A. Likhoshvai, Yu. G. Matushkin, and S. I. Fadeev, Mathematical modeling of regular contours of gene networks, Zh. Vychisl. Mat. Mat. Fiz., 44, No. 12, 2276–2295, 2004. Translated in Comput. Math. Math. Phys., 44, No. 12, 2166–2183, 2004. [5] A. A. Evdokimov, Discrete models of gene networks: Analysis and complexity of functioning, Vychisl. Technol., 13, 2008 and Vestn. KazNU, Ser. Mat. Mekh. Inform., No. 3, 2008 (A joint issue based on Proc. Int. Conf. “Comput. Inf. Technol. Sci. Eng. Educ.”, Almaty, Kazakhstan, Sept. 10–14, 2008) Pt. II, pp. 31–37, Izd. KazNU, Almaty, 2008. [6] A. A. Evdokimov and E. O. Likhovidova, A discrete model for a gene network of a circulant type with threshold functions, Vestn. TGU, Upr. Vychisl. Tech. Inform. No. 2, 18–21, 2008. [7] A. A. Evdokimov and A. L. Perezhogin, Discrete dynamical systems of a circulant type with linear functions at the vertices of a network, Diskretn. Anal. Issled. Oper., 18, No. 3, 39–48, 2011. Translated in J. Appl. Ind. Math., 6, No. 2, 160–166, 2012. [8] E. O. Kutumova and A. A. Evdokimov, Reversible states in functioning of regulatory loops in discrete models for gene networks, Vestn. TGU, Upr. Vychisl. Tech. Inform., No. 1, 85–94, 2011. [9] V. A. Likhoshvai, V. P. Golubyatnikov, G. V. Demidenko, A. A. Evdokimov, I. I. Matveeva, and S. I. Fadeev, Theory of gene networks, in Sistemnaya komp’yuternaya biologiya (Computational Systems Biology), pp. 397–482, Izd. SO RAN, Novosibirsk, 2008. [10] 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. [11] O. Ore, Theory of Graphs, AMS, Providence, 1962 (AMS Colloq. Publ., Vol. 38). Translated under the title Teoriya grafov, Nauka, Moscow, 1980. [12] A. A. Evdokimov and E. O. Kutumova, The discrete model of the gene networks regulatory loops with the threshold functions, in Abstr. 7th Int. Conf. Bioinform. Genome Regul. Struct.\Syst. Biol., Novosibirsk, Russia, June 20–27, 2010, p. 155, SB RAS Press, Novosibirsk, 2010. [13] S. A. Kauffman, At Home in the Universe: The Search for the Laws of SelfOrganization and Complexity, Oxford Univ. Press, New York, 1995. [14] S. A. Kauffman and R. G. Smith, Adaptive automata based on Darwinian selection, Physica D, 22, No. 1–3, 68–82, 1986. [15] R. Laubenbacher and P. Mendes, A discrete approach to topdown modeling of biochemical networks, in A. Kriete and R. Eils, eds., Computational Systems Biology, pp. 229–247, Elsevier Acad. Press, Burlington, MA, USA, 2005. 

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