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A New 3D Chaotic Attractor in Gene Regulatory Network

Author

Listed:
  • Olga Kozlovska

    (Institute of Applied Mathematics, Riga Technical University, Zunda Embankment 10, LV-1048 Riga, Latvia
    These authors contributed equally to this work.)

  • Felix Sadyrbaev

    (Institute of Mathematics and Computer Science, University of Latvia, Rainis Boulevard 29, LV-1459 Riga, Latvia
    These authors contributed equally to this work.)

  • Inna Samuilik

    (Institute of Applied Mathematics, Riga Technical University, Zunda Embankment 10, LV-1048 Riga, Latvia
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Olga Kozlovska & Felix Sadyrbaev & Inna Samuilik, 2023. "A New 3D Chaotic Attractor in Gene Regulatory Network," Mathematics, MDPI, vol. 12(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:100-:d:1308734
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    References listed on IDEAS

    as
    1. Nikolai A. Magnitskii, 2023. "Universal Bifurcation Chaos Theory and Its New Applications," Mathematics, MDPI, vol. 11(11), pages 1-20, May.
    2. Diana Ogorelova & Felix Sadyrbaev & Inna Samuilik, 2023. "On Targeted Control over Trajectories of Dynamical Systems Arising in Models of Complex Networks," Mathematics, MDPI, vol. 11(9), pages 1-14, May.
    Full references (including those not matched with items on IDEAS)

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