On attractors in dynamical systems modeling genetic networks-Reference-Cited by-同舟云学术

On attractors in dynamical systems modeling genetic networks

Published:2023-07-23 Issue:2 Volume:7 Page:486-498
ISSN:2587-2648
Container-title:Advances in the Theory of Nonlinear Analysis and its Application
language:
Short-container-title:

Author:

OGORELOVA Diana¹,SADYRBAEV Felix²^ORCID,SAMUILIK Inna³

Affiliation:

1. Daugavpils Universit

2. Institute of Mathematics and Computer Science

3. Riga Technical University

Abstract

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.

Publisher

Erdal Karapinar

Subject

Applied Mathematics,Analysis

Reference13 articles.

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.