IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v174y2023ics0960077923007695.html
   My bibliography  Save this article

From period-doubling bursting to chaotic–periodic bursting in a modified Chua’s circuit

Author

Listed:
  • Wang, Zhixiang
  • Zhang, Chun
  • Ding, Zuqin
  • Bi, Qinsheng

Abstract

The aim of this paper is to reveal the dynamical mechanism of bursting oscillations in non-smooth dynamical systems, and the interest is focused on the effects of period-doubling bifurcation and chaotic attractor on the bursting oscillations. By modifying a fourth-order Chua’s circuit, a dynamical system possessing non-smooth switching manifold and multiple scale variables, is established. By taking the slow-varying variable as a bifurcation parameter, Subcritical non-smooth Hopf bifurcation, C-bifurcation, and period-doubling bifurcation are obtained in the fast subsystem. Further more, chaotic attractors, which are generated from a series of period-doubling bifurcations, are also observed. Based on the numerical simulations and bifurcation analysis of the fast subsystem, eight typical bursting patterns are obtained, and their dynamical mechanism is revealed. Study shows that period-2 limit cycle in the fast subsystem may cause the slow–fast system to oscillates in alternating small and large amplitudes; A complex spiking attractors made up of limit cycles and chaotic attractors may lead to spiking states changing from chaotic oscillations to periodic ones, and the trajectory may jump directly from a chaotic attractor to other stable one without undergoing any bifurcation of the fast subsystem.

Suggested Citation

  • Wang, Zhixiang & Zhang, Chun & Ding, Zuqin & Bi, Qinsheng, 2023. "From period-doubling bursting to chaotic–periodic bursting in a modified Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007695
    DOI: 10.1016/j.chaos.2023.113868
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923007695
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113868?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. Kuetche Mbe, E.S. & Fotsin, H.B. & Kengne, J. & Woafo, P., 2014. "Parameters estimation based adaptive Generalized Projective Synchronization (GPS) of chaotic Chua’s circuit with application to chaos communication by parametric modulation," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 27-37.
    2. Singla, Tanu & Sinha, Tushar & Parmananda, P., 2015. "Antiperiodic oscillations in Chua’s circuits using conjugate coupling," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 212-217.
    3. Wang, Chunni & Liu, Zhilong & Hobiny, Aatef & Xu, Wenkang & Ma, Jun, 2020. "Capturing and shunting energy in chaotic Chua circuit," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Wang, Zhixiang & Zhang, Chun & Bi, Qinsheng, 2022. "Bursting oscillations with bifurcations of chaotic attractors in a modified Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    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. Rocha, Ronilson & Medrano-T, Rene Orlando, 2022. "Chua circuit based on the exponential characteristics of semiconductor devices," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Ghayyur Hussain & Muhammad Siddique & Muhammad Majid Hussain & Muhammad Tahir Hassan & Naeem Aslam, 2021. "Synchronization of N-Non-Linear Slave Systems with Master System Using Non-Adaptive and Adaptive Coupled Observers," Energies, MDPI, vol. 14(11), pages 1-16, May.
    3. Sharma, Vivek & Sharma, B.B. & Nath, R., 2017. "Nonlinear unknown input sliding mode observer based chaotic system synchronization and message recovery scheme with uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 51-58.
    4. Tutueva, Aleksandra V. & Moysis, Lazaros & Rybin, Vyacheslav G. & Kopets, Ekaterina E. & Volos, Christos & Butusov, Denis N., 2022. "Fast synchronization of symmetric Hénon maps using adaptive symmetry control," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    5. Aguirre-Hernández, B. & Campos-Cantón, E. & López-Renteria, J.A. & Díaz González, E.C., 2015. "A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 100-106.
    6. Chen, Chengjie & Min, Fuhong & Zhang, Yunzhen & Bao, Han, 2023. "ReLU-type Hopfield neural network with analog hardware implementation," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    7. Wang, Xuezhen & Zhang, Huasheng, 2023. "Intelligent control of convergence rate of impulsive dynamic systems affected by nonlinear disturbances under stabilizing impulses and its application in Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    8. Iqbal, Muhammad & Rehan, Muhammad & Hong, Keum-Shik & Khaliq, Abdul & Saeed-ur-Rehman,, 2015. "Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 158-169.

    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:174:y:2023:i:c:s0960077923007695. 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.