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On attractors in dynamical systems modeling genetic networks

Cilt: 7 Sayı: 2 23 Temmuz 2023
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On attractors in dynamical systems modeling genetic networks

Öz

The system of ordinary differential equations that arises in the theory of genetic networks is studied. Attracting sets of a special kind is the focus of the study. These attractors appear as combinations of attractors of lower dimensions, which are stable limit cycles. The properties of attractors are studied. Visualizations and examples are provided.

Anahtar Kelimeler

Kaynakça

  1. [1] R. Edwards and L. Ironi. Periodic solutions of gene networks with steep sigmoidal regulatory functions. Physica D, 282 (2014), 1 - 15. https://doi.org/10.1016/j.physd.2014.04.013
  2. [2] C. Furusawa, K. Kaneko. A generic mechanism for adaptive growth rate regulation. PLoS Comput Biol 4(1), 2008: e3. doi:10.1371/journal.pcbi.0040003
  3. [3] G. van der Heijden. Hopf bifurcation. www.ucl.ac.uk/~ucesgvd/hopf.pdf
  4. [4] Le-Zhi Wang, Ri-Qi Su, Zi-Gang Huang, Xiao Wang, Wen-Xu Wang, Grebogi Celso and Ying-Cheng Lai: A geometrical approach to control and controllability of nonlinear dynamical networks. Nature Communications, Volume 7, Article number: 11323 (2016), DOI: 10.1038/ncomms11323
  5. [5] S.P. Cornelius, W.L. Kath, A.E. Motter. Realistic control of network dynamic. Nature Communications, Volume 4, Article number: 1942 (2013), 1–9.
  6. [6] H.D. Jong. Modeling and Simulation of Genetic Regulatory Systems: A Literature Review, J. Comput Biol. 2002;9(1):67-103, DOI:10.1089/10665270252833208
  7. [7] V.W. Noonburg Differential Equations: From Calculus to Dynamical Systems, Providence, Rhode Island: MAA Press, 2019, 2nd edition. [8] L. Perko. Differential Equations and Dynamical Systems, 3rd Edition. [9] F. Sadyrbaev, S. Atslega, E. Brokan. (2020) Dynamical Models of Interrelation in a Class of Artificial Networks. In: Pinelas S., Graef J.R., Hilger S., Kloeden P., Schinas C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham.
  8. [10] F. Sadyrbaev, V. Sengileyev, A. Silvans. On Coexistence of Inhibition and Activation in Genetic Regulatory Networks. 19 Intern. Confer. Numer. Analys and Appl. Mathematics, Rhodes, Greece, 20-26 September 2021, To appear in AIP Conference Proceedings.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Erken Görünüm Tarihi

7 Ağustos 2023

Yayımlanma Tarihi

23 Temmuz 2023

Gönderilme Tarihi

7 Şubat 2023

Kabul Tarihi

3 Temmuz 2023

Yayımlandığı Sayı

Yıl 2023 Cilt: 7 Sayı: 2

Kaynak Göster

APA
Ogorelova, D., Sadyrbaev, F., & Samuılık, I. (2023). On attractors in dynamical systems modeling genetic networks. Advances in the Theory of Nonlinear Analysis and its Application, 7(2), 486-498. https://doi.org/10.31197/atnaa.1248853
AMA
1.Ogorelova D, Sadyrbaev F, Samuılık I. On attractors in dynamical systems modeling genetic networks. ATNAA. 2023;7(2):486-498. doi:10.31197/atnaa.1248853
Chicago
Ogorelova, Diana, Felix Sadyrbaev, ve Inna Samuılık. 2023. “On attractors in dynamical systems modeling genetic networks”. Advances in the Theory of Nonlinear Analysis and its Application 7 (2): 486-98. https://doi.org/10.31197/atnaa.1248853.
EndNote
Ogorelova D, Sadyrbaev F, Samuılık I (01 Temmuz 2023) On attractors in dynamical systems modeling genetic networks. Advances in the Theory of Nonlinear Analysis and its Application 7 2 486–498.
IEEE
[1]D. Ogorelova, F. Sadyrbaev, ve I. Samuılık, “On attractors in dynamical systems modeling genetic networks”, ATNAA, c. 7, sy 2, ss. 486–498, Tem. 2023, doi: 10.31197/atnaa.1248853.
ISNAD
Ogorelova, Diana - Sadyrbaev, Felix - Samuılık, Inna. “On attractors in dynamical systems modeling genetic networks”. Advances in the Theory of Nonlinear Analysis and its Application 7/2 (01 Temmuz 2023): 486-498. https://doi.org/10.31197/atnaa.1248853.
JAMA
1.Ogorelova D, Sadyrbaev F, Samuılık I. On attractors in dynamical systems modeling genetic networks. ATNAA. 2023;7:486–498.
MLA
Ogorelova, Diana, vd. “On attractors in dynamical systems modeling genetic networks”. Advances in the Theory of Nonlinear Analysis and its Application, c. 7, sy 2, Temmuz 2023, ss. 486-98, doi:10.31197/atnaa.1248853.
Vancouver
1.Diana Ogorelova, Felix Sadyrbaev, Inna Samuılık. On attractors in dynamical systems modeling genetic networks. ATNAA. 01 Temmuz 2023;7(2):486-98. doi:10.31197/atnaa.1248853