IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v146y2021ics0960077921002010.html
   My bibliography  Save this article

Voltages responses and synchronization of an array of Grudzinski and Zebrowski oscillators coupled to an electrical load

Author

Listed:
  • Fouego, Dorota Youmbi
  • Dongmo, Eric Donald
  • Woafo, Paul

Abstract

In this work, we consider a system consisting of an array of Grudzinski and Zebrowski oscillators coupled to an electrical load and analyze the variation of voltages amplitudes and power versus the number of oscillators, the coupling coefficient and the values of the loads. An equivalent electrical circuit of the Grudzinski and Zebrowski oscillator is first proposed. It is then demonstrated that the power in electrical loads (RLC, RL, RC and R) coupled to an array of such oscillator's increases with the number of oscillators till a constant value depending on the types of loads and values of the load parameters. Considering both direct and indirect coupling of an array, synchronization is observed. The synchronization domain is seen to depend on the values of the direct coupling, the value of the indirect coupling and on the number of oscillators in the array.

Suggested Citation

  • Fouego, Dorota Youmbi & Dongmo, Eric Donald & Woafo, Paul, 2021. "Voltages responses and synchronization of an array of Grudzinski and Zebrowski oscillators coupled to an electrical load," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
  • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002010
    DOI: 10.1016/j.chaos.2021.110848
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921002010
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2021.110848?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.
    2. Nana, B. & Woafo, P., 2008. "Power delivered by an array of Van der Pol oscillators coupled to a resonant cavity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3305-3313.
    3. Youmbi Fouego, D. & Dongmo, E.D. & Woafo, P., 2017. "Powering RLC load by an array of self-sustained oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 222-227.
    4. Grudziński, Krzysztof & Żebrowski, Jan J, 2004. "Modeling cardiac pacemakers with relaxation oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 153-162.
    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. Asher Yahalom & Natalia Puzanov, 2024. "Feedback Stabilization Applied to Heart Rhythm Dynamics Using an Integro-Differential Method," Mathematics, MDPI, vol. 12(1), pages 1-14, January.
    2. Lounis, Fatima & Boukabou, Abdelkrim & Soukkou, Ammar, 2020. "Implementing high-order chaos control scheme for cardiac conduction model with pathological rhythms," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Jiang, Wei & Chen, Zhong & Hu, Ning & Song, Haiyang & Yang, Zhaohong, 2020. "Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    4. Gois, Sandra R.F.S.M. & Savi, Marcelo A., 2009. "An analysis of heart rhythm dynamics using a three-coupled oscillator model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2553-2565.
    5. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Isao Shoji & Masahiro Nozawa, 2020. "A geometric analysis of nonlinear dynamics and its application to financial time series," Papers 2012.11825, arXiv.org.
    7. Acosta, A. & Gallo, R. & García, P. & Peluffo-Ordóñez, D., 2023. "Positive invariant regions for a modified Van Der Pol equation modeling heart action," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    8. Semenov, Vladimir V. & Bukh, Andrei V. & Semenova, Nadezhda, 2023. "Delay-induced self-oscillation excitation in the Fitzhugh–Nagumo model: Regular and chaotic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    9. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.
    10. Chagas, T.P. & Toledo, B.A. & Rempel, E.L. & Chian, A.C.-L. & Valdivia, J.A., 2012. "Optimal feedback control of the forced van der Pol system," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1147-1156.
    11. Templos-Hernández, Diana J. & Quezada-Téllez, Luis A. & González-Hernández, Brian M. & Rojas-Vite, Gerardo & Pineda-Sánchez, José E. & Fernández-Anaya, Guillermo & Rodriguez-Torres, Erika E., 2021. "A fractional-order approach to cardiac rhythm analysis," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    12. Lahmiri, Salim, 2017. "A study on chaos in crude oil markets before and after 2008 international financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 389-395.
    13. Nana, B. & Yamgoué, S.B. & Kemajou, I. & Tchitnga, R. & Woafo, P., 2018. "Dynamics of a RLC series circuit with hysteretic iron-core inductor," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 184-192.
    14. Lahmiri, Salim, 2017. "On fractality and chaos in Moroccan family business stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 29-39.
    15. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    16. Eshaghi, Shiva & Khoshsiar Ghaziani, Reza & Ansari, Alireza, 2020. "Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 321-340.
    17. Lahmiri, Salim, 2017. "Investigating existence of chaos in short and long term dynamics of Moroccan exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 655-661.

    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:eee:chsofr:v:146:y:2021:i:c:s0960077921002010. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.