Comparative analysis of models of genetic and neuronal networks
Abstract
The comparative analysis of systems of ordinary differential equations, modeling gene regulatory networks and neuronal networks, is provided. In focus of the study are asymptotical behavior of solutions, types of attractors. Emphasis is made on the chaotic behavior of solutions.
Keyword : dynamical systems, gene regulatory network, artificial neural network, periodic solution, Lyapunov exponents
How to Cite
Ogorelova, D., & Sadyrbaev, F. (2024). Comparative analysis of models of genetic and neuronal networks. Mathematical Modelling and Analysis, 29(2), 277–287. https://doi.org/10.3846/mma.2024.19714
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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E. Brokan and F. Sadyrbaev. On attractors in gene regulatory systems. AIP Conference Proceedings, 1809:2–10, 2017. https://doi.org/10.1063/1.4975425
E. Brokan and F. Sadyrbaev. Attraction in n-dimensional differential systems from network regulation theory. Mathematical Methods in the Applied Sciences, 41(17):7498–7509, 2018. https://doi.org/10.1002/mma.5086
A. Das, A.B. Roy and P. Das. Chaos in a three dimensional neural network. Applied Mathematical Modelling, 24(7):511–522, 2000. https://doi.org/10.1016/S0307-904X(99)00046-3
R. Edwards and L. Ironi. Periodic solutions of gene networks with steep sigmoidal regulatory functions. Physica D: Nonlinear Phenomena, 282:1–15, 2014. https://doi.org/10.1016/j.physd.2014.04.013
K. Funahashi and Y. Nakamura. Approximation of dynamical systems by continuous time recurrent neural networks. Neural Networks, 6(6):801–806, 1993. https://doi.org/10.1016/S0893-6080(05)80125-X
C. Furusawa and K. Kaneko. A generic mechanism for adaptive growth rate regulation. PLoS Computational Biology, 1(4):35–42, 2008. https://doi.org/10.1371/journal.pcbi.0040003
S. Haykin. Neural networks. A comprehensive foundation. Prentice Hall, Singapore, 1998.
Y. Koizumi and et al. Adaptive virtual network topology control based on attractor selection. Journal of Lightwave Technology, 28(11):1720–1731, 2010. https://ieeexplore.ieee.org/document/5452985
Y. Koizumi, T. Miyamura, S. Arakawa, E. Oki, K. Shiomoto and M. Murata. Application of attractor selection to adaptive virtual network topology control. Proceedings of BIONETICS, pp. 1–8, 2008. https://doi.org/10.5555/1512504.1512516
O. Kozlovska and F. Sadyrbaev. Models of genetic networks with given properties. WSEAS Transactions on Computer Research, 10:43–49, 2022. https://doi.org/10.37394/232018.2022.10.6
V.W. Noonburg. Differential Equations: From Calculus to Dynamical Systems, 2nd edition. Providence, Rhode Island: MAA Press, 2019.
D. Ogorelova, F. Sadyrbaev and V. Sengileyev. Control in inhibitory genetic regulatory network models. Contemporary Mathematics, 1(5):421–428, 2020. https://doi.org/10.37256/cm.152020538
F. Sadyrbaev, D. Ogorelova and I. Samuilik. A nullclines approach to the study of 2d artificial network. Contemporary Mathematics, 1(1):1–11, 2019. https://doi.org/10.37256/cm.11201976.1-11
F. Sadyrbaev, I. Samuilik and V. Sengileyev. On modelling of genetic regulatory networks. WSEAS Transactions in Electronics, 12:73–80, 2021. https://doi.org/10.37394/232017.2021.12.10
I. Samuilik, F. Sadyrbaev and D. Ogorelova. Comparative analysis of models of gene and neural networks. Contemporary Mathematics, 4(2):217–22, 2023. https://doi.org/10.37256/cm.4220232404
J.C. Sprott. Elegant Chaos. World Scientific, Singapore, 2010.
L.-Z. Wang, R.-Q. Su, Z.-G. Huang, X. Wang, W.-X. Wang, C. Grebogi and Y.-C. Lai. A geometrical approach to control and controllability of nonlinear dynamical networks. Nature Communications, 7(11323):1–11, 2016. https://doi.org/10.1038/ncomms11323
H.R. Wilson and J.D. Cowan. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J., 12(1):1–24, 1972. https://doi.org/10.1016/S0006-3495(72)86068-5
W. Ye, X. Huang, X. Huang, P. Li, Q. Xia and G. Hu. Self-sustained oscillations of complex genomic regulatory networks. Physics Letters A, 374:2521–2526, 2010. https://doi.org/10.1016/j.physleta.2010.04.015