AUTHORS: Eduard Brokan, Felix Sadyrbaev

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ABSTRACT: We provide the scheme for driving a network modelled by dynamical system from one state (“undesired”) to another one. This can be done by changing in time adjustable parameters and require knowledge of the structure of attractors of a system. The process is explained and illustrated by analyzing the two-element network.

KEYWORDS: network control, attracting sets, dynamical system, phase portrait, gene regulatory networks

REFERENCES:

[1] F.M. Alakwaa, Modeling of Gene Regulatory Networks: A Literature Review, Journal of Computational Systems Biology 1, (2014), issue 1, 1-8.

[2] S. Atslega, D. Finaskins, F. Sadyrbaev, On a Planar Dynamical System Arising in the Network Control Theory, Mathematical Modelling and Analysis 21, (2016), 385 – 398.

[3] E. Brokan, F. Zh. Sadyrbaev, On Attractors in Gene Regulatory Systems, AIP Conference Proceedings 1809,(020010), 2017 doi: 10.1063/1.4975425.

[4] E. Brokan and F. Sadyrbaev, Attracting Sets in Gene Regulatory Systems, Proceedings of Intern. Conf. on Simulation, Modelling and Math. Statistics (SMMS 2015), November 22-23, 2015 Chiang Mai, Thailand, pp. 135-138. DEStech Publication, Inc., Lancaster, U.S.A.

[5] E. Brokan and F. Sadyrbaev, Attraction in ndimensional differential systems from network regulation theory, em Mathematical Methods in the Applied Sciences 41, (2018), Issue 17, 7498- 7509 https://doi.org/10.1002/mma.5086

[6] Le-Zhi Wang, Ri-Qi Su, Zi-Gang Huang, Xiao Wang, Wen-Xu Wang, Celso Grebogi and Ying-Cheng Lai, A geometrical approach to control and controllability of nonlinear dynamical networks, Nature Communications 7, Article number: 11323 (2016), DOI: 10.1038/ncomms11323

[7] Y. Koizumi et al., Adaptive Virtual Network Topology Control Based on Attractor Selection, Journal of Lightwave Technology 28 (06/2010), Issue 11, pp. 1720 - 1731 DOI:10.1109/JLT.2010.2048412