IDEAS home Printed from https://ideas.repec.org/a/hin/complx/4624792.html
   My bibliography  Save this article

Riddled Attraction Basin and Multistability in Three-Element-Based Memristive Circuit

Author

Listed:
  • Quan Xu
  • Xiao Tan
  • Yunzhen Zhang
  • Han Bao
  • Yihua Hu
  • Bocheng Bao
  • Mo Chen

Abstract

By coupling a diode bridge-based second-order memristor and an active voltage-controlled memristor with a capacitor, a three-element-based memristive circuit is synthesized and its system model is then built. The boundedness of the three-element-based memristive circuit is theoretically proved by employing the contraction mapping principle. Besides, the stability distributions of equilibrium points are theoretically and numerically expounded in a 2D parameter plane. The results imply the memristive circuit has a zero unstable saddle focus and a pair of nonzero stable node-foci or unstable saddle-foci depending on the considered parameters. The dynamical behaviors include point attractor, period, chaos, coexisting bifurcation mode, period-doubling bifurcation route, and crisis scenarios, which are explored using some common dynamical methods. Of particular concern, riddled attraction basins and multistability are uncovered under two sets of specified model parameters nearing the tiny neighborhood of crisis scenarios by local attraction basins and phase plane plots. The riddled attraction basins with island-like structure demonstrate that their dynamical behaviors are extremely sensitive to the initial conditions, resulting in the coexistence of limit cycles with period-2 and period-6, as well as the coexistence of period-1 limit cycles and single-scroll chaotic attractors. Moreover, a feasible on-breadboard hardware circuit is manually made and the experimental measurements are executed, upon which phase plane trajectories for some discrete model parameters are captured to further confirm the numerically simulated ones.

Suggested Citation

  • Quan Xu & Xiao Tan & Yunzhen Zhang & Han Bao & Yihua Hu & Bocheng Bao & Mo Chen, 2020. "Riddled Attraction Basin and Multistability in Three-Element-Based Memristive Circuit," Complexity, Hindawi, vol. 2020, pages 1-13, August.
  • Handle: RePEc:hin:complx:4624792
    DOI: 10.1155/2020/4624792
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2020/4624792.pdf
    Download Restriction: no

    File URL: http://downloads.hindawi.com/journals/8503/2020/4624792.xml
    Download Restriction: no

    File URL: https://libkey.io/10.1155/2020/4624792?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lin, Hairong & Wang, Chunhua & Du, Sichun & Yao, Wei & Sun, Yichuang, 2023. "A family of memristive multibutterfly chaotic systems with multidirectional initial-based offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Echenausía-Monroy, J.L. & Gilardi-Velázquez, H.E. & Wang, Ning & Jaimes-Reátegui, R. & García-López, J.H. & Huerta-Cuellar, G., 2022. "Multistability route in a PWL multi-scroll system through fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

    More about this item

    Statistics

    Access and download statistics

    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:hin:complx:4624792. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.