IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i22p4208-d969283.html
   My bibliography  Save this article

Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms

Author

Listed:
  • Roman Ivanovich Parovik

    (Laboratory of Physical Process Modeling, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 7, Mirnaya St., Yelizovsky District, Paratunka 684034, Russia)

Abstract

A non-linear fractional Selkov dynamic system for mathematical modeling of microseismic phenomena is proposed. This system is a generalization of the previously known Selkov system, which has self-oscillatory modes and is used in biology to describe glycolytic vibrations of the substrate and product. The Selkov fractional dynamical system takes into account the influence of heredity and is described using derivative fractional orders. The article investigates the Selkov fractional dynamic model using the Adams–Bashforth–Moulton numerical method, constructs oscillograms and phase trajectories, and studies the equilibrium points. Based on the spectra of the maximum Lyapunov exponents, it is shown that in the fractional dynamic model there can be relaxation and damped oscillations.

Suggested Citation

  • Roman Ivanovich Parovik, 2022. "Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms," Mathematics, MDPI, vol. 10(22), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4208-:d:969283
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/22/4208/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/22/4208/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Roberto Garrappa, 2018. "Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial," Mathematics, MDPI, vol. 6(2), pages 1-23, January.
    2. Khennaoui, Amina-Aicha & Ouannas, Adel & Bendoukha, Samir & Grassi, Giuseppe & Lozi, René Pierre & Pham, Viet-Thanh, 2019. "On fractional–order discrete–time systems: Chaos, stabilization and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 150-162.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mayada Abualhomos & Abderrahmane Abbes & Gharib Mousa Gharib & Abdallah Shihadeh & Maha S. Al Soudi & Ahmed Atallah Alsaraireh & Adel Ouannas, 2023. "Bifurcation, Hidden Chaos, Entropy and Control in Hénon-Based Fractional Memristor Map with Commensurate and Incommensurate Orders," Mathematics, MDPI, vol. 11(19), pages 1-19, October.
    2. Dutta, Maitreyee & Roy, Binoy Krishna, 2020. "A new fractional-order system displaying coexisting multiwing attractors; its synchronisation and circuit simulation," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Faïçal Ndaïrou & Delfim F. M. Torres, 2023. "Pontryagin Maximum Principle for Incommensurate Fractional-Orders Optimal Control Problems," Mathematics, MDPI, vol. 11(19), pages 1-12, October.
    4. Dmytro Sytnyk & Barbara Wohlmuth, 2023. "Exponentially Convergent Numerical Method for Abstract Cauchy Problem with Fractional Derivative of Caputo Type," Mathematics, MDPI, vol. 11(10), pages 1-35, May.
    5. Hansin Bilgili & Chwen Sheu, 2022. "A Bibliometric Review of the Mathematics Journal," Mathematics, MDPI, vol. 10(15), pages 1-17, July.
    6. Pakhare, Sumit S. & Bhalekar, Sachin & Gade, Prashant M., 2022. "Synchronization in coupled integer and fractional-order maps," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    7. Ran, Jie & Li, Yu-Qin & Xiong, Yi-Bin, 2022. "On the dynamics of fractional q-deformation chaotic map," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    8. Wang, Lingyu & Sun, Kehui & Peng, Yuexi & He, Shaobo, 2020. "Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    9. Fiaz, Muhammad & Aqeel, Muhammad & Marwan, Muhammad & Sabir, Muhammad, 2022. "Integer and fractional order analysis of a 3D system and generalization of synchronization for a class of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. Wu, Jianjun & Xia, Lu, 2024. "Double well stochastic resonance for a class of three-dimensional financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    11. Liu, Xianggang & Ma, Li, 2020. "Chaotic vibration, bifurcation, stabilization and synchronization control for fractional discrete-time systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    12. Kai Diethelm, 2022. "A New Diffusive Representation for Fractional Derivatives, Part II: Convergence Analysis of the Numerical Scheme," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
    13. Özköse, Fatma & Yavuz, Mehmet & Şenel, M. Tamer & Habbireeh, Rafla, 2022. "Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    14. Mangal, Shiv & Misra, O.P. & Dhar, Joydip, 2023. "Fractional-order deterministic epidemic model for the spread and control of HIV/AIDS with special reference to Mexico and India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 82-102.
    15. Cao, Dewei & Chen, Hu, 2023. "Error analysis of a finite difference method for the distributed order sub-diffusion equation using discrete comparison principle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 109-117.
    16. J. Alberto Conejero & Jonathan Franceschi & Enric Picó-Marco, 2022. "Fractional vs. Ordinary Control Systems: What Does the Fractional Derivative Provide?," Mathematics, MDPI, vol. 10(15), pages 1-18, August.
    17. Huang, Yuanyuan & Huang, Huijun & Huang, Yunchang & Wang, Yinhe & Yu, Fei & Yu, Beier & Liu, Chenghao, 2024. "Asymptotic shape synchronization in three-dimensional chaotic systems and its application in color image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    18. Li, Hang & Shen, Yongjun & Han, Yanjun & Dong, Jinlu & Li, Jian, 2023. "Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    19. Danca, Marius-F., 2022. "Fractional order logistic map: Numerical approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    20. Xin, Baogui & Peng, Wei & Kwon, Yekyung, 2020. "A discrete fractional-order Cournot duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4208-:d:969283. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.