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<p>The Morris-Lecar model is a neuronal model designed to replicate the oscillatory activity of barnacle giant muscle fibers. This work presents a three-dimensional Morris-Lecar model with a novel fast-slow structure. The model introduces a current containing slow variables, thereby forming a new fast-slow structure with the membrane potential. Numerical results reveal the existence of two independent unstable foci and complex dynamical behaviors that include period-doubling bifurcations and spiking/bursting activities. Two types of bifurcation mechanisms for bursting activities are elucidated through theoretical analysis based on four typical bursting activities. Finally, a digital neuronal circuit was developed based on FPGA, and experimental results show good consistency with numerical results.</p>

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A Morris-Lecar model with novel fast-slow structure and its FPGA implementation

  • 期刊论文

  • 发表日期：

    2025年4月7日

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  • Xihong Yu,
  • Lilian Huang,
  • Han Bao,
  • Bocheng Bao

摘要

The Morris-Lecar model is a neuronal model designed to replicate the oscillatory activity of barnacle giant muscle fibers. This work presents a three-dimensional Morris-Lecar model with a novel fast-slow structure. The model introduces a current containing slow variables, thereby forming a new fast-slow structure with the membrane potential. Numerical results reveal the existence of two independent unstable foci and complex dynamical behaviors that include period-doubling bifurcations and spiking/bursting activities. Two types of bifurcation mechanisms for bursting activities are elucidated through theoretical analysis based on four typical bursting activities. Finally, a digital neuronal circuit was developed based on FPGA, and experimental results show good consistency with numerical results.