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

Author

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
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    Cited by:

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    3. 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.
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    5. 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).
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    10. 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).
    11. 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.
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    13. 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.

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