IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v121y2019icp63-84.html
   My bibliography  Save this article

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

Author

Listed:
  • Kengne, Jacques
  • Mogue, Ruth Line Tagne
  • Fozin, Theophile Fonzin
  • Telem, Adelaide Nicole Kengnou

Abstract

A novel self-driven RC chaotic jerk circuit with the singular feature of having a smoothly adjustable nonlinearity and symmetry is proposed and investigated. The novel chaotic circuit is mathematically modeled by a third order system with a single nonlinear term in the form ϕk(x)=0.5(exp(kx)−exp(−x)) where parameter k maps a smoothly adjustable control resistor. Obviously for k=1, the system is point symmetric with respect to the origin of the system coordinates since the nonlinear term reduces to the hyperbolic sine function. The case k ≠ 1 corresponds to a non-symmetric system. The numerical experiment reveals a plethora of events including period doubling route to chaos, hysteresis, periodic windows, asymmetric double scroll chaos, symmetric double scroll chaos, and coexisting bifurcations branches as well. This latter phenomenon induces multiple coexisting attractors consisting of two, three, four, five, or six disconnected symmetric or asymmetric attractors for the same set of parameter values when monitoring solely the initial conditions. Laboratory experimental measurements are carried out to confirm the theoretical predictions.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:chsofr:v:121:y:2019:i:c:p:63-84
    DOI: 10.1016/j.chaos.2019.01.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919300451
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2019.01.033?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. Kingni, S.T. & Nana, B. & Mbouna Ngueuteu, G.S. & Woafo, P. & Danckaert, J., 2015. "Bursting oscillations in a 3D system with asymmetrically distributed equilibria: Mechanism, electronic implementation and fractional derivation effect," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 29-40.
    2. Manimehan, I. & Philominathan, P., 2012. "Composite dynamical behaviors in a simple series–parallel LC circuit," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1501-1509.
    3. 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.
    4. 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.
    5. Kengne, J. & Njikam, S.M. & Signing, V.R. Folifack, 2018. "A plethora of coexisting strange attractors in a simple jerk system with hyperbolic tangent nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 201-213.
    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. Gu, Shuangquan & He, Shaobo & Wang, Huihai & Du, Baoxiang, 2021. "Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. 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).
    3. Kuate, Paul Didier Kamdem & Tchendjeu, Achille Ecladore Tchahou & Fotsin, Hilaire, 2020. "A modified Rössler prototype-4 system based on Chua’s diode nonlinearity : Dynamics, multistability, multiscroll generation and FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Zhang, Xiaohong & Xu, Jingjing & Moshayedi, Ata Jahangir, 2024. "Design and FPGA implementation of a hyperchaotic conservative circuit with initial offset-boosting and transient transition behavior based on memcapacitor," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    5. Zhang, Jianlin & Bao, Han & Yu, Xihong & Chen, Bei, 2024. "Heterogeneous coexistence of extremely many attractors in adaptive synapse neuron considering memristive EMI," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    6. Njitacke, Zeric Tabekoueng & Doubla, Isaac Sami & Mabekou, Sandrine & Kengne, Jacques, 2020. "Hidden electrical activity of two neurons connected with an asymmetric electric coupling subject to electromagnetic induction: Coexistence of patterns and its analog implementation," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    7. Chen, Mo & Ren, Xue & Wu, Huagan & Xu, Quan & Bao, Bocheng, 2020. "Interpreting initial offset boosting via reconstitution in integral domain," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    8. Sun, Xi & Yan, Shaohui & Zhang, Yuyan & Wang, Ertong & Wang, Qiyu & Gu, Binxian, 2022. "Bursting dynamics and the zero-Hopf bifurcation of simple jerk system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

    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. Kengne, J. & Njikam, S.M. & Signing, V.R. Folifack, 2018. "A plethora of coexisting strange attractors in a simple jerk system with hyperbolic tangent nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 201-213.
    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. 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).
    4. 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.
    5. 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.
    6. 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).
    7. Lin, Y. & Liu, W.B. & Bao, H. & Shen, Q., 2020. "Bifurcation mechanism of periodic bursting in a simple three-element-based memristive circuit with fast-slow effect," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    8. 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.
    9. Kingni, Sifeu Takougang & Jafari, Sajad & Pham, Viet-Thanh & Woafo, Paul, 2017. "Constructing and analyzing of a unique three-dimensional chaotic autonomous system exhibiting three families of hidden attractors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 172-182.
    10. Ngamsa Tegnitsap, J.V. & Fotsin, H.B. & Megam Ngouonkadi, E.B., 2021. "Magnetic coupling based control of a chaotic circuit: Case of the van der Pol oscillator coupled to a linear circuit," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. Bao, B.C. & Wu, P.Y. & Bao, H. & Xu, Q. & Chen, M., 2018. "Numerical and experimental confirmations of quasi-periodic behavior and chaotic bursting in third-order autonomous memristive oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 161-170.
    12. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.
    13. 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.
    14. Kingni, Sifeu Takougang & Pham, Viet-Thanh & Jafari, Sajad & Woafo, Paul, 2017. "A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order form," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 209-218.
    15. Yan, Minxiu & Jie, Jingfeng, 2022. "Fractional-order multiwing switchable chaotic system with a wide range of parameters," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    16. Cheng, Guanghui & Gui, Rong, 2022. "Bistable chaotic family and its chaotic mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    17. Bao, B.C. & Wu, P.Y. & Bao, H. & Wu, H.G. & Zhang, X. & Chen, M., 2018. "Symmetric periodic bursting behavior and bifurcation mechanism in a third-order memristive diode bridge-based oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 146-153.
    18. 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).
    19. 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).
    20. 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).

    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:121:y:2019:i:c:p:63-84. 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.