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Bifurcations to bursting oscillations in memristor-based FitzHugh-Nagumo circuit

Author

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  • Bao, Bocheng
  • Chen, Liuhui
  • Bao, Han
  • Chen, Mo
  • Xu, Quan

Abstract

To characterize neuronal firing activities and elucidate its bifurcation mechanisms, a memristor-based FitzHugh-Nagumo (FHN) circuit is designed based on the FHN circuit architecture combined with a first-order memristive simulator, and its normalized system with periodic and quasi-periodic bursting oscillations is established. With the change of externally applied excitation, the memristor-based FHN system has the time-varying equilibrium point where the number, position and stability evolve slowly over time. In an evolution period of the time-domain waveform, different fold and/or Hopf bifurcations are triggered, resulting in periodic or quasi-periodic bursting oscillations. To explain the intrinsic bifurcation mechanisms, the fold and Hopf bifurcation sets are built and the transitions between the resting and spiking states are demonstrated, thus identifying the Hopf/fold and Hopf/Hopf bursting oscillations. Finally, based on the circuit simulation model, analog circuit simulations and hardware circuit measurements are developed for the memristor-based FHN circuit to confirm MATLAB numerical simulations. In addition, it is worth noting that the proposed circuit is a simple non-autonomous memristive neuron circuit that is particularly easy to physically implement.

Suggested Citation

  • Bao, Bocheng & Chen, Liuhui & Bao, Han & Chen, Mo & Xu, Quan, 2024. "Bifurcations to bursting oscillations in memristor-based FitzHugh-Nagumo circuit," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001590
    DOI: 10.1016/j.chaos.2024.114608
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    References listed on IDEAS

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    1. 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.
    2. Yu, Xihong & Bao, Han & Chen, Mo & Bao, Bocheng, 2023. "Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. 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).
    4. Wang, Zhixiang & Zhang, Chun & Bi, Qinsheng, 2022. "Bursting oscillations with bifurcations of chaotic attractors in a modified Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    5. Lai, Qiang & Lai, Cong & Zhang, Hui & Li, Chunbiao, 2022. "Hidden coexisting hyperchaos of new memristive neuron model and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    6. 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).
    7. Xu, Quan & Wang, Yiteng & Chen, Bei & Li, Ze & Wang, Ning, 2023. "Firing pattern in a memristive Hodgkin–Huxley circuit: Numerical simulation and analog circuit validation," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    8. 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).
    9. Minati, L. & Gambuzza, L.V. & Thio, W.J. & Sprott, J.C. & Frasca, M., 2020. "A chaotic circuit based on a physical memristor," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    10. Li, Yongxin & Li, Chunbiao & Zhong, Qing & Zhao, Yibo & Yang, Yong, 2024. "Coexisting hollow chaotic attractors within a steep parameter interval," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
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