IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v587y2022ics0378437121007743.html
   My bibliography  Save this article

Multiple Hopf bifurcations, period-doubling reversals and coexisting attractors for a novel chaotic jerk system with Tchebytchev polynomials

Author

Listed:
  • Ramadoss, Janarthanan
  • Kengne, Jacques
  • Koinfo, Jean Baptiste
  • Rajagopal, Karthikeyan

Abstract

The study of complex nonlinear phenomena certainly represents a very hot ongoing research topic owing to recently published works. While a large number of contributions deal with systems with symmetry, very few works are concerned with those without any symmetry property. In this contribution, we introduce a novel asymmetric jerk system whose nonlinearity is in the form of a six-order Tchebytchev polynomial of the fundamental variable. The new system distinguishes by the presence of six equilibrium points symmetrically distributed along the x-axis. Three of these points are always unstable (regardless the values of parameter) while each of the three others undergoes Hopf type bifurcation at three different critical values of the control parameter resulting to self-excited coexisting behaviors such as: (i) a limit cycle and a pair of stable fixed points; (ii) a pair of limit cycles and a stable fixed point; (iii) a stable fixed point, a limit cycle and a chaotic attractor; just to cite a few. These features are studied by combining both analytical and numerical methods. More importantly, various parameter ranges are depicted where the new jerk system with Tchebytchev polynomials demonstrates extremely complex and striking nonlinear patterns such as antimonotonicity, hysteresis and coexisting bifurcation branches. These two latter properties give rise to multiple (i.e. two, three or four) coexisting (periodic and chaotic) attractors. Cross sections of the basins of attraction are provided to illustrate the magnetization of the state space caused by the various competing dynamics. The control of multistability in the new system is achieved via linear augmentation scheme. The practical feasibility of the new system is supported by a series of PSPICE simulations utilizing an electronic analogue of the proposed jerk system. The combination of features found in the new jerk system with Tchebytchev polynomials are rarely reported and thus merits dissemination.

Suggested Citation

  • Ramadoss, Janarthanan & Kengne, Jacques & Koinfo, Jean Baptiste & Rajagopal, Karthikeyan, 2022. "Multiple Hopf bifurcations, period-doubling reversals and coexisting attractors for a novel chaotic jerk system with Tchebytchev polynomials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
  • Handle: RePEc:eee:phsmap:v:587:y:2022:i:c:s0378437121007743
    DOI: 10.1016/j.physa.2021.126501
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121007743
    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.2021.126501?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. Zhang, Sen & Zeng, Yicheng, 2019. "A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 25-40.
    2. Njitacke, Z.T. & kengne, J. & Fotsin, H.B. & Negou, A. Nguomkam & Tchiotsop, D., 2016. "Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 180-197.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Fudong Li & Jingru Zeng, 2023. "Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System," Energies, MDPI, vol. 16(5), pages 1-12, March.

    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. Sun, Shuqi & Shi, Hang & Musha, Ji'e & Yan, Dengwei & Duan, Shukai & Wang, Lidan, 2022. "Design of heterogeneous time-lags system with multi-stability and its analog circuit," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Zhou, Ling & You, Zhenzhen & Tang, Yun, 2021. "A new chaotic system with nested coexisting multiple attractors and riddled basins," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Sundarapandian Vaidyanathan & Ahmad Taher Azar & Ibrahim A. Hameed & Khaled Benkouider & Esteban Tlelo-Cuautle & Brisbane Ovilla-Martinez & Chang-Hua Lien & Aceng Sambas, 2023. "Bifurcation Analysis, Synchronization and FPGA Implementation of a New 3-D Jerk System with a Stable Equilibrium," Mathematics, MDPI, vol. 11(12), pages 1-22, June.
    4. 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.
    5. Bodo, B. & Armand Eyebe Fouda, J.S. & Mvogo, A. & Tagne, S., 2018. "Experimental hysteresis in memristor based Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 190-195.
    6. 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).
    7. Zuolei Wang & Lizhou Zhuang & Jianjiang Yu & Haibo Jiang & Wanjiang Xu & Xuerong Shi, 2023. "Hidden Dynamics of a New Jerk-like System with a Smooth Memristor and Applications in Image Encryption," Mathematics, MDPI, vol. 11(22), pages 1-18, November.
    8. Chen, Mo & Wang, Ankai & Wang, Chao & Wu, Huagan & Bao, Bocheng, 2022. "DC-offset-induced hidden and asymmetric dynamics in Memristive Chua's circuit," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    9. Akgül, Akif & Rajagopal, Karthikeyan & Durdu, Ali & Pala, Muhammed Ali & Boyraz, Ömer Faruk & Yildiz, Mustafa Zahid, 2021. "A simple fractional-order chaotic system based on memristor and memcapacitor and its synchronization application," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Xu, Quan & Tan, Xiao & Zhu, Dong & Bao, Han & Hu, Yihua & Bao, Bocheng, 2020. "Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    11. 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.
    12. 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).
    13. Cai, Xinshan & Liu, Ling & Wang, Yaoyu & Liu, Chongxin, 2021. "A 3D chaotic system with piece-wise lines shape non-hyperbolic equilibria and its predefined-time control," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    14. Xu, Wanjiang & Shi, Xuerong & Jiang, Haibo & Yu, Jianjiang & Zhang, Liping & Zhuang, Lizhou & Wang, Zuolei, 2024. "A simple 4D no-equilibrium chaotic system with only one quadratic term and its application in pseudo-random number generator," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    15. Chen, M. & Feng, Y. & Bao, H. & Bao, B.C. & Yu, Y.J. & Wu, H.G. & Xu, Q., 2018. "State variable mapping method for studying initial-dependent dynamics in memristive hyper-jerk system with line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 313-324.
    16. Mahmoud, Emad E. & Trikha, Pushali & Jahanzaib, Lone Seth & Almaghrabi, Omar A., 2020. "Dynamical analysis and chaos control of the fractional chaotic ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    17. Cristian Lăzureanu & Jinyoung Cho, 2023. "On Hopf and Fold Bifurcations of Jerk Systems," Mathematics, MDPI, vol. 11(20), pages 1-15, October.
    18. Trikha, Pushali & Mahmoud, Emad E. & Jahanzaib, Lone Seth & Matoog, R.T. & Abdel-Aty, Mahmoud, 2021. "Fractional order biological snap oscillator: Analysis and control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    19. Jiri Petrzela, 2022. "Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example," Mathematics, MDPI, vol. 10(21), pages 1-28, November.
    20. 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).

    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:587:y:2022:i:c:s0378437121007743. 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.