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<p>The negative differential resistance characteristic of locally active memristors enhances the neuronal capability to describe firing pattern transitions and complex oscillations, offering a novel approach for constructing neurodynamic models that more closely resemble biological systems. This paper first proposes a discrete locally active memristor, subsequently, this memristor is introduced as a synaptic coupling term into a discrete Chialvo neuron, constructing a non-autonomous memristive Chialvo neuron model (NMCN). Numerical simulations are employed to analyze the rich dynamical behaviors exhibited by the model as the memristor coupling strength k and the external sinusoidal stimulus amplitude <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{I}_{m}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>I</mi> <mi>m</mi> </msub> </math></EquationSource> </InlineEquation> vary, including periodic spiking, periodic bursting, chaotic spiking, chaotic bursting, period-doubling bifurcations, and attractor coexistence phenomena. Furthermore, the study extends to electrically coupling two NMCN models, delving into the complex regulatory mechanisms of initial states and coupling strength on neuronal synchronization behaviors, revealing multiple transitions between synchronous and asynchronous states. Finally, the architecture developed in this study is successfully realized on an FPGA-based hardware platform. The experimentally observed time-domain waveforms and phase-space attractors show high consistency with numerical simulations, physically verifying the correctness and realizability of the theoretical model and demonstrating its application potential.</p>

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Firing transition, synchronization and circuit implementation in discrete neurons coupled with locally active memristors

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Lilian Huang,
  • Lu Han,
  • Xihong Yu

摘要

The negative differential resistance characteristic of locally active memristors enhances the neuronal capability to describe firing pattern transitions and complex oscillations, offering a novel approach for constructing neurodynamic models that more closely resemble biological systems. This paper first proposes a discrete locally active memristor, subsequently, this memristor is introduced as a synaptic coupling term into a discrete Chialvo neuron, constructing a non-autonomous memristive Chialvo neuron model (NMCN). Numerical simulations are employed to analyze the rich dynamical behaviors exhibited by the model as the memristor coupling strength k and the external sinusoidal stimulus amplitude \({{I}_{m}}\) I m vary, including periodic spiking, periodic bursting, chaotic spiking, chaotic bursting, period-doubling bifurcations, and attractor coexistence phenomena. Furthermore, the study extends to electrically coupling two NMCN models, delving into the complex regulatory mechanisms of initial states and coupling strength on neuronal synchronization behaviors, revealing multiple transitions between synchronous and asynchronous states. Finally, the architecture developed in this study is successfully realized on an FPGA-based hardware platform. The experimentally observed time-domain waveforms and phase-space attractors show high consistency with numerical simulations, physically verifying the correctness and realizability of the theoretical model and demonstrating its application potential.