Example of Chaotic Behavior in Systems of Ordinary Differential Equations Arising in Modeling of Gene Regulatory Networks

20th International Scientific Conference on Dynamical System Modeling and Stability Investigation (DSMSI 2023). CEUR Workshop Proceedings. Vol.3746 2023
Felix Sadyrbaev, Olga Kozlovska

The three-dimensional system of ordinary differential equations arising in mathematical models of genetic networks is considered. The systems under consideration first appeared in the study of neural networks. They were later applied by several authors to the treatment of genetic regulatory networks and telecommunication networks. In this article, we will focus on genetic networks. The proposed equation models the evolution of the genetic regulatory network. The system has attractors in the phase space that strongly influence the behavior of the trajectories and other important properties of the network. Attractors are built in systems with dimensions greater than three. These attractors are not solutions themselves, but they attract periodic solutions of the system. A system of equations can exhibit chaotic behavior that is not easy to detect. An information is provided about possible attracting sets in the phase space. The role of attracting sets is discussed. An example of the system possessing the attractor of chaotic nature is constructed.

Keywords
attractors; chaotic behavior; Dynamical systems; gene regulatory networks;
Hyperlink
https://ceur-ws.org/Vol-3746/Short_1.pdf

Sadyrbaev, F., Kozlovska, O. Example of Chaotic Behavior in Systems of Ordinary Differential Equations Arising in Modeling of Gene Regulatory Networks. In: 20th International Scientific Conference on Dynamical System Modeling and Stability Investigation (DSMSI 2023). CEUR Workshop Proceedings. Vol.3746, Ukraine, Kyiv, 20-21 December, 2023. Aachen: RWTH, 2023, pp.85-89. ISSN 1613-0073.

Publication language
English (en)