The marvelous Wilson neuron model involves sodium and potassium ion currents, which offer great significance in generating firing activities. This paper firstly deduces that the sodium ion currents can be characterized by a locally active memristor (LAM) and the potassium ion current meets the definition of passive memristor. Thereafter, a memristive Wilson neuron circuit with memristive sodium and potassium ion channels is built and its equilibrium state stability is disclosed. Dynamical explorations display that the memristive Wilson neuron circuit can generate abundant periodic bursting activities with different periodicities under low-frequency stimulus and chaotic/periodic spiking activities under high-frequency stimulus. Particularly, the bifurcation mechanisms for generating the periodic bursting behaviors are uncovered, they are Hopf/fold and fold/fold bifurcations. Besides, the memristive Wilson neuron circuit can generate chaotic and periodic bubbles with Type-I. To physically confirm these periodic bursting and chaotic/spiking activities, a discrete circuit component-based hardware experiment is executed. The experimental results effectively addressed the validity of the numerical explorations and further exhibit the effectiveness of the memristive Wilson neuron circuit in reproducing neuron bursting and spiking activities.

中文翻译：

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具有忆阻钠和钾离子通道的威尔逊神经元回路中的爆发和尖峰活动

奇妙的威尔逊神经元模型涉及钠离子和钾离子电流，这对于产生放电活动具有重要意义。本文首先推论钠离子电流可以用局部有源忆阻器(LAM)来表征，钾离子电流满足无源忆阻器的定义。此后，建立了具有忆阻钠和钾离子通道的忆阻威尔逊神经元电路，并揭示了其平衡状态稳定性。动力学探索表明，忆阻威尔逊神经元电路在低频刺激下可以产生丰富的不同周期的周期性爆发活动，在高频刺激下可以产生混沌/周期性的尖峰活动。特别是，揭示了产生周期性爆发行为的分叉机制，它们是Hopf/fold和fold/fold分叉。此外，忆阻性威尔逊神经元电路可以通过Type-I产生混沌且周期性的气泡。为了从物理上确认这些周期性突发和混沌/尖峰活动，执行了基于分立电路组件的硬件实验。实验结果有效地解决了数值探索的有效性，并进一步展示了忆阻威尔逊神经元电路在再现神经元爆发和尖峰活动方面的有效性。