On attractors in systems of ordinary differential equations arising in models of genetic networks

Kozlovska, O.; Sadyrbaev, Felix

doi:10.21595/vp.2023.23343

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D Gene Regulatory System1

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2023

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“…While various sigmoidal functions exist, the one mentioned above is particularly suitable for analysis and visualization [32]. Such systems were considered in [20,[33][34][35].…”

Section: D Gene Regulatory Systemmentioning

confidence: 99%

A New 3D Chaotic Attractor in Gene Regulatory Network

Kozlovska,

Sadyrbaev,

Samuilik

2023

Mathematics

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This paper introduces a new 3D chaotic attractor in a gene regulatory network. The proposed model has eighteen parameters. Formulas for characteristic numbers of critical points for three-dimensional systems were considered. We show that the three equilibrium points of the new chaotic 3D system are unstable and deduce that the three-dimensional system exhibits chaotic behavior. The possible outcomes of this 3D model were compared with the results of the Chua circuit. The bifurcation structures of the proposed 3D system are investigated numerically, showing periodic solutions and chaotic solutions. Lyapunov exponents and Kaplan-Yorke dimension are calculated. For calculations, the Wolfram Mathematica is used.

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“…While various sigmoidal functions exist, the one mentioned above is particularly suitable for analysis and visualization [32]. Such systems were considered in [20,[33][34][35].…”

Section: D Gene Regulatory Systemmentioning

confidence: 99%