IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v109y2018icp146-153.html
   My bibliography  Save this article

Symmetric periodic bursting behavior and bifurcation mechanism in a third-order memristive diode bridge-based oscillator

Author

Listed:
  • Bao, B.C.
  • Wu, P.Y.
  • Bao, H.
  • Wu, H.G.
  • Zhang, X.
  • Chen, M.

Abstract

This paper presents a novel third-order autonomous memristive diode bridge-based oscillator with fast-slow effect. Based on the modeling of the presented memristive oscillator, stability of the equilibrium point is analyzed by using the eigenvalues of the characteristic polynomial, and then symmetric periodic bursting behavior is revealed through bifurcation diagrams, phase plane plots, time sequences, and 0–1 test. Furthermore, bifurcation mechanism of the symmetric periodic bursting behavior is explored by constructing the fold and Hopf bifurcation sets of the fast-scale subsystem with the variations of the system parameter and slow-scale variable. Consequently, the presented memristive oscillator is always unstable and exhibits complex dynamical behavior of symmetric periodic bursting oscillations with a symmetric fold/Hopf cycle-cycle burster. In addition, experimental measurements are performed by hardware circuit to confirm the numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:146-153
    DOI: 10.1016/j.chaos.2018.02.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918300912
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.02.031?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. 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.
    2. 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.
    3. Xu, Quan & Lin, Yi & Bao, Bocheng & Chen, Mo, 2016. "Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 186-200.
    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. Zhang, Xiufang & Yao, Zhao & Guo, Yeye & Wang, Chunni, 2021. "Target wave in the network coupled by thermistors," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. 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.
    3. Deng, Yue & Li, Yuxia, 2021. "Bifurcation and bursting oscillations in 2D non-autonomous discrete memristor-based hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Zhou, Chengyi & Xie, Fei & Li, Zhijun, 2020. "Complex bursting patterns and fast-slow analysis in a smallest chemical reaction system with two slow parametric excitations," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Zhao, Heqi & Ma, Xindong & Yang, Weijie & Zhang, Zhao & Bi, Qinsheng, 2023. "The mechanism of periodic and chaotic bursting patterns in an externally excited memcapacitive system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    6. Wu, H.G. & Ye, Y. & Bao, B.C. & Chen, M. & Xu, Q., 2019. "Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 178-185.
    7. Danjin Zhang & Youhua Qian, 2021. "Fast-Slow Coupling Dynamics Behavior of the van der Pol-Rayleigh System," Mathematics, MDPI, vol. 9(23), pages 1-13, November.
    8. 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).
    9. Bao, Bocheng & Zhang, Xi & Bao, Han & Wu, Pingye & Wu, Zhimin & Chen, Mo, 2019. "Dynamical effects of memristive load on peak current mode buck-boost switching converter," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 69-79.
    10. 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.
    11. Danjin Zhang & Youhua Qian, 2023. "Bursting Oscillations in General Coupled Systems: A Review," Mathematics, MDPI, vol. 11(7), pages 1-16, April.
    12. Wen, Zihao & Li, Zhijun & Li, Xiang, 2019. "Bursting oscillations and bifurcation mechanism in memristor-based Shimizu–Morioka system with two time scales," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 58-70.
    13. Lin, Yi & Liu, Wenbo & Hang, Cheng, 2023. "Revelation and experimental verification of quasi-periodic bursting, periodic bursting, periodic oscillation in third-order non-autonomous memristive FitzHugh-Nagumo neuron circuit," Chaos, Solitons & Fractals, Elsevier, vol. 167(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. 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).
    2. 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.
    3. 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.
    4. Lin, Yi & Liu, Wenbo & Hang, Cheng, 2023. "Revelation and experimental verification of quasi-periodic bursting, periodic bursting, periodic oscillation in third-order non-autonomous memristive FitzHugh-Nagumo neuron circuit," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    5. Yajuan Yu & Han Bao & Min Shi & Bocheng Bao & Yangquan Chen & Mo Chen, 2019. "Complex Dynamical Behaviors of a Fractional-Order System Based on a Locally Active Memristor," Complexity, Hindawi, vol. 2019, pages 1-13, November.
    6. Lai, Qiang & Xu, Guanghui & Pei, Huiqin, 2019. "Analysis and control of multiple attractors in Sprott B system," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 192-200.
    7. Yu, Hui & Du, Shengzhi & Dong, Enzeng & Tong, Jigang, 2022. "Transient behaviors and equilibria-analysis-based boundary crisis analysis in a smooth 4D dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    8. 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.
    9. 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.
    10. 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.
    11. Colin Sokol Kuka & Yihua Hu & Quan Xu & James Chandler & Mohammed Alkahtani, 2021. "A Novel True Random Number Generator in Near Field Communication as Memristive Wireless Power Transmission," J, MDPI, vol. 4(4), pages 1-20, November.
    12. 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.
    13. Wang, Mengjiao & Liao, Xiaohan & Deng, Yong & Li, Zhijun & Su, Yongxin & Zeng, Yicheng, 2020. "Dynamics, synchronization and circuit implementation of a simple fractional-order chaotic system with hidden attractors," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    14. 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).
    15. 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.
    16. 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).
    17. Li, Chunbiao & Sprott, Julien Clinton & Kapitaniak, Tomasz & Lu, Tianai, 2018. "Infinite lattice of hyperchaotic strange attractors," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 76-82.
    18. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
    19. Zhang, Chun & Ma, Xindong & Bi, Qinsheng, 2022. "Complex mixed-mode oscillations based on a modified Rayleigh-Duffing oscillator driven by low-frequency excitations," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    20. Qifeng Fu & Xuemei Xu & Chuwen Xiao, 2022. "LQR Chaos Synchronization for a Novel Memristor-Based Hyperchaotic Oscillator," Mathematics, MDPI, vol. 11(1), pages 1-16, December.

    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:109:y:2018:i:c:p:146-153. 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.