It has been extensively studied to employ memristors to model the relationship between the electromagnetic field and the membrane potential, especially for the research of modeling and dynamical analyses of electrical activity using HR neurons with memristors. This paper proposes a novel 4D HR model with a threshold flux-controlled memristor (MHR), which describes the electromagnetic induction effect. The proposed 4D HR model retains the original HR properties and can describe the complex dynamics of neurons' electrical activities with fewer parameters than the existing models. Due to the particularity of the no equilibrium point of the MHR model, the hidden dynamics are found in the proposed MHR model. The generalized Hamiltonian function is fully derived for the MHR neuron model using Helmholtz's theorem. The simplest form of the Hamiltonian form is given by assigning special values. The average Hamiltonian energy and its bifurcation are employed to find the connection between energy and firing patterns. The band-limited white noise is also studied, and it is found that it positively influences the electrical activities in the proposed MHR system.

使用忆阻器对电磁场和膜电位之间的关系进行建模已得到广泛研究，特别是使用带有忆阻器的 HR 神经元对电活动进行建模和动力学分析的研究。本文提出了一种具有阈值磁通控制忆阻器 (MHR) 的新型 4D HR 模型，该模型描述了电磁感应效应。所提出的 4D HR 模型保留了原始 HR 属性，并且可以用比现有模型更少的参数来描述神经元电活动的复杂动态。由于 MHR 模型无平衡点的特殊性，在所提出的 MHR 模型中发现了隐藏的动力学。广义哈密顿函数是使用亥姆霍兹定理为 MHR 神经元模型完全推导出来的。哈密​​顿形式的最简单形式是通过分配特殊值给出的。平均哈密顿能量及其分岔被用来寻找能量和点火模式之间的联系。还研究了带限白噪声，发现它对提议的 MHR 系统中的电活动产生积极影响。