IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921006731.html
   My bibliography  Save this article

Magnetic coupling based control of a chaotic circuit: Case of the van der Pol oscillator coupled to a linear circuit

Author

Listed:
  • Ngamsa Tegnitsap, J.V.
  • Fotsin, H.B.
  • Megam Ngouonkadi, E.B.

Abstract

This paper investigates the control of the dynamics of the van der Pol oscillator coupled to Linear circuit (VDPCL oscillator). The method consists of carrying out a magnetic coupling (wireless interaction) of a VDPCL oscillator to a magnetic core coil supplied by a sinusoidal voltage. One of the most important outlets of the proposed control scheme is the ability to control the dynamic of the oscillator by varying three external parameters as well as to generate very rich and complicated behaviors including attractors not yet reported in the non-controlled model. In this impetus, the frequency and the amplitude of the excitation source of the RL circuit as well as the magnetic coupling coefficient are thus used to adjust the VDPCL oscillator dynamics in a desired state. The basic properties of the model are discussed, such as fixed point stability, symmetry and dissipation. Using the control parameters mentioned above, the dynamic behaviors of the model are studied using the classical tools of nonlinear dynamics such as the two-parameters and one parameter Lyapunov exponents, the one-parameter bifurcation diagrams, phase portraits and time series. Numerical simulation reveals a rich repertoire of dynamic behaviors in the system, including periodicity, period doubling, quasi-periodicity, 2-torus, 3-torus and chaos. In particular, complex and striking phenomena such as antimonotonicity, intermittency, coexistence of attractors and amplitude modulation are reported in the model when monitoring the frequency of the sinusoidal excitation. Sample coexisting bifurcation diagrams are drawn and the coexistence of attractors is illustrated using the phase portraits and the cross section of the basin of attraction. Pspice based simulations and laboratory experimental measurements are included to confirm the theoretical results and the feasibility of the proposed control scheme.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006731
    DOI: 10.1016/j.chaos.2021.111319
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921006731
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111319?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. 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.
    2. Jiangbin Wang & Ling Liu & Chongxin Liu & Xiaoteng Li, 2020. "Adaptive Sliding Mode Control Based on Equivalence Principle and Its Application to Chaos Control in a Seven-Dimensional Power System," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, February.
    3. Fu, Shihui & Liu, Yuan & Ma, Huizhen & Du, Ying, 2020. "Control chaos to different stable states for a piecewise linear circuit system by a simple linear control," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Fotsin, H.B. & Woafo, P., 2005. "Adaptive synchronization of a modified and uncertain chaotic Van der Pol-Duffing oscillator based on parameter identification," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1363-1371.
    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. Fotsin, Hilaire & Bowong, Samuel, 2006. "Adaptive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 822-835.
    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. Liqin Liu & Chunrui Zhang, 2023. "Multiple Hopf Bifurcations of Four Coupled van der Pol Oscillators with Delay," Mathematics, MDPI, vol. 11(23), pages 1-16, November.
    2. Ngamsa Tegnitsap, J.V. & Fotsin, H.B., 2022. "Multistability, transient chaos and hyperchaos, synchronization, and chimera states in wireless magnetically coupled VDPCL oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 158(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. 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.
    2. Sun, Fengyun & Zhao, Yi & Zhou, Tianshou, 2007. "Identify fully uncertain parameters and design controllers based on synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1677-1682.
    3. Fotsin, Hilaire & Bowong, Samuel, 2006. "Adaptive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 822-835.
    4. Signing, V.R. Folifack & Kengne, J. & Pone, J.R. Mboupda, 2019. "Antimonotonicity, chaos, quasi-periodicity and coexistence of hidden attractors in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 187-198.
    5. Dlamini, A. & Doungmo Goufo, E.F., 2023. "Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    6. Hu, Yongbing & Li, Qian & Ding, Dawei & Jiang, Li & Yang, Zongli & Zhang, Hongwei & Zhang, Zhixin, 2021. "Multiple coexisting analysis of a fractional-order coupled memristive system and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Ningning Yang & Shucan Cheng & Chaojun Wu & Rong Jia & Chongxin Liu, 2019. "Dynamic Behaviors Analysis of a Chaotic Circuit Based on a Novel Fractional-Order Generalized Memristor," Complexity, Hindawi, vol. 2019, pages 1-15, May.
    8. 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).
    9. Elabbasy, E.M. & El-Dessoky, M.M., 2008. "Synchronization of van der Pol oscillator and Chen chaotic dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1425-1435.
    10. Junhai Ma & Lijian Sun & Xueli Zhan, 2017. "Study on Triopoly Dynamic Game Model Based on Different Demand Forecast Methods in the Market," Complexity, Hindawi, vol. 2017, pages 1-12, July.
    11. Chang, Wei-Der, 2006. "Parameter identification of Rossler’s chaotic system by an evolutionary algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1047-1053.
    12. Shen, Liqun & Wang, Mao, 2008. "Robust synchronization and parameter identification on a class of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 106-111.
    13. Fu, Shihui & Liu, Yuan, 2020. "Complex dynamical behavior of modified MLC circuit," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    14. Guerra, Fábio A. & Coelho, Leandro dos S., 2008. "Multi-step ahead nonlinear identification of Lorenz’s chaotic system using radial basis neural network with learning by clustering and particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 967-979.
    15. Hao Jia & Chen Guo, 2020. "The Application of Accurate Exponential Solution of a Differential Equation in Optimizing Stability Control of One Class of Chaotic System," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    16. Zhang, Ting & Wang, Jiang & Fei, Xiangyang & Deng, Bin, 2007. "Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 194-202.
    17. Huang, Guodong & Zhou, Shu & Zhu, Rui & Wang, Yunhai & Chai, Yuan, 2024. "Stability and complexity evaluation of attractors in a controllable piezoelectric Fitzhugh-Nagumo circuit," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    18. Zhou, Jin & Cheng, Xuhua & Xiang, Lan & Zhang, Yecui, 2007. "Impulsive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 607-616.
    19. Peng, Bo & Liu, Bo & Zhang, Fu-Yi & Wang, Ling, 2009. "Differential evolution algorithm-based parameter estimation for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2110-2118.
    20. 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).

    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:152:y:2021:i:c:s0960077921006731. 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.