IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v588y2022ics0378437121008359.html
   My bibliography  Save this article

Broken symmetry and dynamics of a memristive diodes bridge-based Shinriki oscillator

Author

Listed:
  • Ramadoss, Janarthanan
  • Kengne, Jacques
  • Kengnou Telem, Adélaïde Nicole
  • Rajagopal, Karthikeyan

Abstract

We investigate the impact of a broken symmetry on the dynamics of the well-known Shinriki oscillator. The broken symmetry is caused by the memristive diodes bridge with an asymmetric pinched hysteresis loop current–voltage characteristic designed by selecting two pairs of semiconductor diodes with different electrical properties. We examine how the broken symmetry affects the topology of attractors, the nature of fixed points, the bifurcation structures, the number and types of coexisting solutions, and the topology of the basins of attraction as well. These features are highlighted by utilizing plots of Lyapunov exponents, bifurcation diagrams, basins of attraction and phase portraits. As sample results, up to four coexisting asymmetric chaotic and periodic attractors are reported following changes in both initial conditions and parameters. Moreover, some sets of parameters are revealed where the system develops the striking feature of coexisting bubbles of bifurcation. Breadboard experiments are carried out to support the theoretical investigations. Although the breaking of symmetry may be seen as a common practice to discover new nonlinear events, the results obtained in this work may help for a better understanding of the impact of a real memristor on the global behavior of chaotic oscillators including a memristor as nonlinear device.

Suggested Citation

  • Ramadoss, Janarthanan & Kengne, Jacques & Kengnou Telem, Adélaïde Nicole & Rajagopal, Karthikeyan, 2022. "Broken symmetry and dynamics of a memristive diodes bridge-based Shinriki oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    • Handle: RePEc:eee:phsmap:v:588:y:2022:i:c:s0378437121008359
    DOI: 10.1016/j.physa.2021.126562
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121008359
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2021.126562?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. Cao, Hongjun & Seoane, Jesús M. & Sanjuán, Miguel A.F., 2007. "Symmetry-breaking analysis for the general Helmholtz–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 197-212.
    2. Min, Fuhong & Zhang, Wen & Ji, Ziyi & Zhang, Lei, 2021. "Switching dynamics of a non-autonomous FitzHugh-Nagumo circuit with piecewise-linear flux-controlled memristor," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Gómez-Aguilar, J.F., 2020. "Chaos and multiple attractors in a fractal–fractional Shinriki’s oscillator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    4. Kamdjeu Kengne, Léandre & Mboupda Pone, Justin Roger & Fotsin, Hilaire Bertrand, 2021. "On the dynamics of chaotic circuits based on memristive diode-bridge with variable symmetry: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Hanias, M.P. & Giannaris, G. & Spyridakis, A. & Rigas, A., 2006. "Time series analysis in chaotic diode resonator circuit," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 569-573.
    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. G. H. Kom & J. Kengne & J. R. Mboupda Pone & G. Kenne & A. B. Tiedeu, 2018. "Asymmetric Double Strange Attractors in a Simple Autonomous Jerk Circuit," Complexity, Hindawi, vol. 2018, pages 1-16, February.
    2. Leutcho, Gervais Dolvis & Kengne, Jacques, 2018. "A unique chaotic snap system with a smoothly adjustable symmetry and nonlinearity: Chaos, offset-boosting, antimonotonicity, and coexisting multiple attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 275-293.
    3. Wu, Huagan & Gu, Jinxiang & Guo, Yixuan & Chen, Mo & Xu, Quan, 2024. "Biphasic action potentials in an individual cellular neural network cell," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Njimah, Ouzerou Mouncherou & Ramadoss, Janarthanan & Telem, Adelaide Nicole Kengnou & Kengne, Jacques & Rajagopal, Karthikeyan, 2023. "Coexisting oscillations and four-scroll chaotic attractors in a pair of coupled memristor-based Duffing oscillators: Theoretical analysis and circuit simulation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Dong, Youheng & Zhao, Geng, 2021. "A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    6. Leutcho, G.D. & Kengne, J. & Kengne, L. Kamdjeu, 2018. "Dynamical analysis of a novel autonomous 4-D hyperjerk circuit with hyperbolic sine nonlinearity: Chaos, antimonotonicity and a plethora of coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 67-87.
    7. Ramadoss, Janarthanan & Kengne, Jacques & Tanekou, Sosthene Tsamene & Rajagopal, Karthikeyan & Kenmoe, Germaine Djuidje, 2022. "Reversal of period doubling, multistability and symmetry breaking aspects for a system composed of a van der pol oscillator coupled to a duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    8. Guo, Lei & Liu, Chengjun & Wu, Youxi & Xu, Guizhi, 2023. "fMRI-based spiking neural network verified by anti-damage capabilities under random attacks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    9. Wu, H. & Zhou, J. & Chen, M. & Xu, Q. & Bao, B., 2022. "DC-offset induced asymmetry in memristive diode-bridge-based Shinriki oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    10. Njitacke, Z.T. & kengne, J. & Kengne, L. Kamdjeu, 2017. "Antimonotonicity, chaos and multiple coexisting attractors in a simple hybrid diode-based jerk circuit," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 77-91.
    11. Ramamoorthy, Ramesh & Rajagopal, Karthikeyan & Leutcho, Gervais Dolvis & Krejcar, Ondrej & Namazi, Hamidreza & Hussain, Iqtadar, 2022. "Multistable dynamics and control of a new 4D memristive chaotic Sprott B system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    12. Liu, Yachong & Hu, Ankang & Han, Fenglei & Lu, Yu, 2015. "Stability analysis of nonlinear ship-roll dynamics under wind and wave," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 32-39.
    13. Peng, Yuexi & Liu, Jun & He, Shaobo & Sun, Kehui, 2023. "Discrete fracmemristor-based chaotic map by Grunwald–Letnikov difference and its circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    14. Zhang, Xu & Min, Fuhong & Dou, Yiping & Xu, Yeyin, 2023. "Bifurcation analysis of a modified FitzHugh-Nagumo neuron with electric field," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    15. Girault, Jean-Marc, 2015. "Recurrence and symmetry of time series: Application to transition detection," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 11-28.
    16. Kamdjeu Kengne, Léandre & Mboupda Pone, Justin Roger & Fotsin, Hilaire Bertrand, 2021. "On the dynamics of chaotic circuits based on memristive diode-bridge with variable symmetry: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    17. Kengne, Jacques & Mogue, Ruth Line Tagne & Fozin, Theophile Fonzin & Telem, Adelaide Nicole Kengnou, 2019. "Effects of symmetric and asymmetric nonlinearity on the dynamics of a novel chaotic jerk circuit: Coexisting multiple attractors, period doubling reversals, crisis, and offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 63-84.
    18. Siewe, M. Siewe & Cao, Hongjun & Sanjuán, Miguel A.F., 2009. "On the occurrence of chaos in a parametrically driven extended Rayleigh oscillator with three-well potential," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 772-782.
    19. Feng, Jingjing & Zhang, Qichang & Wang, Wei, 2012. "Chaos of several typical asymmetric systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 950-958.
    20. Siewe, M. Siewe & Cao, Hongjun & Sanjuán, Miguel A.F., 2009. "Effect of nonlinear dissipation on the basin boundaries of a driven two-well Rayleigh–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1092-1099.

    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:phsmap:v:588:y:2022:i:c:s0378437121008359. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.