Networks Describing Dynamical Systems

Eduard Brokan; Felix Sadyrbaev

doi:10.2478/tmmp-2018-0004

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Networks Describing Dynamical Systems

Tatra Mountains Mathematical Publications

Volume 71 (2018): Issue 1 (December 2018)

By: Eduard Brokan and Felix Sadyrbaev

Open Access

|Jan 2019

Abstract

We consider systems of ordinary differential equations that arise in the theory of gene regulatory networks. These systems can be of arbitrary size but of definite structure that depends on the choice of regulatory matrices. Attractors play the decisive role in behaviour of elements of such systems. We study the structure of simple attractors that consist of a number of critical points for several choices of regulatory matrices.

References

[1] CROMBACH, A.—HOGEWEG, P.: Evolution of evolvability in gene regulatory networks, PLoS Comput. Biol. 4 (7/2008): e1000112.10.1371/journal.pcbi.1000112243203218617989
Search in Google Scholar Back to article
[2] VOHRADSKÝ, J.: Neural network model of gene expression, FASEB J. 15 (3/2001), 846–854.10.1096/fj.00-0361com11259403
Open DOI Search in Google Scholar Back to article
[3] WUENSCHE, A.: Genomic regulation modeled as a network with basins of attraction, Pac. Symp. Biocomput. 1998: 89–102.
Search in Google Scholar Back to article
[4] TUŠEK, A.—KURTANJEK, Ž.: Mathematical modelling of gene regulatory networks, in: Applied Biological Engineering – Principles and Practice (Ganesh R. Naik, ed.), InTech, pp. 113–132.
Search in Google Scholar Back to article
[5] ALAKWAA, F. M.: Modeling of gene regulatory networks: a literature review, J. Comput. Systems Biology 1 (2014), 1–8.10.15744/2455-7625.1.102
Search in Google Scholar Back to article
[6] JONG, H. D.: Modeling and simulation of genetic regulatory systems: a literature review, J. Comput. Biol. 9 (2002), 67–103.10.1089/1066527025283320811911796
Open DOI Search in Google Scholar Back to article
[7] VIJESH, N.—CHAKRABARTI, S. K.—SREEKUMAR, J.: Modeling of gene regulatory networks: A review, J. Biomedical Science and Engineering 6 (2013), 223–231.10.4236/jbise.2013.62A027
Search in Google Scholar Back to article
[8] KOIZUMI, Y.—MIYAMURA, T.—ARAKAWA, S.—OKI, E.—SHIOMOTO, K.––MURATA, M. : Adaptive virtual network topology control based on attractor selection, J. Lightwave Technology 28 (2010), 1720–1731.10.1109/JLT.2010.2048412
Search in Google Scholar Back to article
[9] KOIZUMI, Y.—MIYAMURA, T.—ARAKAWA, S.—OKI, E.—SHIOMOTO, K.––MURATA, M.: Application of attractor selection to adaptive virtual network topology control, in: BIONETICS ‘08, Proc. of the 3rd Internat. Conf. on Bio-Inspired Models of Network, Information and Computing Sytems, Vol. 9, Hyogo, Japan, 2008, ICST, Brussels, Belgium, 2008.10.4108/ICST.BIONETICS2008.4714
Search in Google Scholar Back to article
[10] ACARY, V.—DE JONG, H.—BROGLIATO, B.: Numerical simulation of piecewise-linear models of gene regulatory networks using complementarity systems, [Research Report] RR-8207, INRIA, 2013, pp. 42.
Search in Google Scholar Back to article
[11] BROKAN, E.—SADYRBAEV, F.: On a differential system arising in the network control theory, Nonlinear Anal. Model. Control 21(2016), 687–701.10.15388/NA.2016.5.8
Search in Google Scholar Back to article
[12] ARROWSMITH, D. K.—PLACE, C. M.: Dynamical Systems. Differential equations, maps and chaotic behavior. Chapman and Hall, London, 1992.10.1007/978-94-011-2388-4
Search in Google Scholar Back to article
[13] PERKO, L.: Differential Equations and Dynamical Systems (3rd ed.), Springer, New York, 2001.10.1007/978-1-4613-0003-8
Open DOI Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2018-0004 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 39 - 52

Submitted on: Dec 11, 2017

Published on: Jan 25, 2019

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

nonlinear systems of ordinary differential equations,

Related subjects:

© 2019 Eduard Brokan, Felix Sadyrbaev, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 71 (2018): Issue 1 (December 2018)