Circulant discrete dynamical systems with threshold functions of at most three variables

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• 作者：Ts. Ch. -D. Batueva
• 关键词：discrete dynamical system ; circulant ; gene network ; functional graph ; threshold function ; source
• 刊名：Journal of Applied and Industrial Mathematics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：10
• 期：1
• 页码：51-60
• 全文大小：694 KB
• 参考文献：1.Ts. Ch.-D. Batueva, “Properties of Gene Networks with Threshold Functions,” Prikl. Diskret. Mat. Suppl. No. 6, 72–73 (2013).
  2.Ts. Ch.-D. Batueva, “Discrete Dynamical Systems with Threshold Functions at the Vertices,” Diskret. Anal. Issled. Oper. 21 (4), 25–32 (2014).MathSciNet MATH
  3.E. D. Grigorenko, A. A. Evdokimov, V. A. Likhoshvai, and I. A. Lobareva, “Fixed Points and Cycles of Automaton MappingsWhichModel the Functioning of Gene Networks,” Vestnik Tomsk. Gos. Univ. 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 (12), 2276–2295 (2004) [Comput. Math. Math. Phys. 44 (12), 2166–2183 2004].MathSciNet MATH
  5.A. A. Evdokimov, “Discrete Models of Gene Networks: Analysis and Complexity of Functioning,” Vychisl. Technol. 13 (2008) and Vestnik Al-Farabi KazNU Ser. Mat. Mekh. Inform. No. 3 (2008) (A joint issue based on Proceedings of International Conference “Comput. Inform. Technol. Science, Engineering, and Education”, Almaty, Kazakhstan, September 10–14, 2008), Part II (Izd. KazNU, Almaty, 2008), pp. 31–37.
  6.A. A. Evdokimov and E. O. Likhovidova, “A Discrete Model of a Gene Network of a Circulant Type with Threshold Functions,” Vestnik Tomsk. Gos. Univ. Upravl. Vychisl. Tekhn. 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,” Diskret. Anal. Issled. Oper. 18 (3), 39–48 (2011) [J. Appl. Indust. Math. 6 (2), 160–166 2012].MathSciNet MATH
  8.E. O. Kutumova and A. A. Evdokimov, “Reversible States in Functioning of Regulatory Loops in Discrete Models ofGene Networks,” Vestnik Tomsk. Gos. Univ. Upravl. Vychisl. Tekhn. 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 Computational Systems Biology (Sibirsk. Otdel. Ross. Akad. Nauk, Novosibirsk, 2008), pp. 397–482.
  10.A. M. Nazhmidenova and A. L. Perezhogin, “A Discrete Dynamical System on a Double Circulant,” Diskret. Anal. Issled. Oper. 21 (4), 80–88 (2014).MathSciNet MATH
  11.O. Ore, Theory of Graphs (AMS, Providence, 1962; Nauka, Moscow, 1980).MATH
  12.A. A. Evdokimov and E. O. Kutumova, “The Discrete Model of the Gene Net works Regulatory Loops with the Threshold Functions,” in Abstracts of the 7th International Conference on Bioinformatics of Genome Regulation and Structure. Systems Biology. Novosibirsk, Russia, June 20–27, 2010 (Sibirsk. Otdel. Ross. Akad. Nauk, Novosibirsk, 2010), p.155.
  13.S. A. Kauffman, At Home in the Universe: The Search for the Laws of Self-Organization 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 (1–3), 68–82 (1986).MathSciNet CrossRef
  15.R. Laubenbacher and P. Mendes, “A Discrete Approach to Top-Down Modeling of Biochemical Networks,” in Computational Systems Biology, Ed. by A. Kriete and R. Eils (Elsevier Acad. Press, Burlington, MA, 2005), pp. 229–247.
  
• 作者单位：Ts. Ch. -D. Batueva (1)
  
  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1990-4797

文摘

We propose a method for finding sources of discrete dynamical systems of the circulant type with a q-valued arbitrary function at vertices. We find all sources, all fixed points, and some cycles, as well as lengths of some maximal chains outside cycles for the systems with Boolean threshold functions of at most three variables at the vertices.