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<p>In this paper, a novel flux-controlled memristor is constructed and validated by numerical simulation and circuit simulation, and a three-dimensional Hindmarsh-Rose (HR) neuron model based on the memristor is proposed. The complex dynamical behavior of the system is described by phase portrait, time-domain waveform diagram, bifurcation diagram, basin of attraction, Lyapunov exponents spectrum, average Hamiltonian energy, complexity and offset boosting. The proposed model has a significant demarcation point, shows obvious bifurcation phenomenon under different parameters, and can produce coexisting multiple firing patterns under different initial values. Finally, the analog circuit is simulated by Multisim, and the hardware design is completed by using the digital circuit of field programmable gate array (FPGA), and the results are all consistent with the numerical simulation. These findings provide important theoretical support and experimental verification for understanding the parameter-dependent multimodal firing mechanism of biological neurons and realizing high-precision bionic circuits.</p>

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Dynamics analysis and bionic circuit implementation of a memristor coupled Hindmarsh-Rose neuron model with demarcation point

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Shaohui Yan,
  • Yali Wang,
  • Jiawei Jiang,
  • Jiandong Zhang,
  • Hanbing Zhang,
  • Fangya Zhu

摘要

In this paper, a novel flux-controlled memristor is constructed and validated by numerical simulation and circuit simulation, and a three-dimensional Hindmarsh-Rose (HR) neuron model based on the memristor is proposed. The complex dynamical behavior of the system is described by phase portrait, time-domain waveform diagram, bifurcation diagram, basin of attraction, Lyapunov exponents spectrum, average Hamiltonian energy, complexity and offset boosting. The proposed model has a significant demarcation point, shows obvious bifurcation phenomenon under different parameters, and can produce coexisting multiple firing patterns under different initial values. Finally, the analog circuit is simulated by Multisim, and the hardware design is completed by using the digital circuit of field programmable gate array (FPGA), and the results are all consistent with the numerical simulation. These findings provide important theoretical support and experimental verification for understanding the parameter-dependent multimodal firing mechanism of biological neurons and realizing high-precision bionic circuits.