The FitzHugh-Nagumo (FHN) neural model is widely used to study the dynamic characteristics of signal propagation, synchronization, stochastic resonance(SR), coherent resonance(CR), and bifurcation of neurons. Based on Helmholtz theorem and the FHN neuron model, the expression of Hamilton energy function of FHN neural model driven by high-low frequency(HLF) electromagnetic radiation is derived. The correctness and uniqueness of the analytical solution are verified by using the constraints, and the electrical activities and Hamilton energy function of neuron are discussed by numerical simulations. It is found that electrical activity mode of FHN neuron undergoes a succession transition of quiescent state, spiking state, bursting state, and mixed state by changing the parameters such as the intensity of the external forcing current, the amplitude and angular frequency of HLF signal. The electrical activities process of FHN neuron is accompanied by the storage and release of system energy, this result may provide an understanding of the coding and conversion of electrical activity from the perspective of the relevance and dependence of energy costs.

FitzHugh-Nagumo（FHN）神经模型被广泛用于研究信号传播，同步，随机共振（SR），相干共振（CR）和神经元分叉的动态特性。基于Helmholtz定理和FHN神经元模型，推导了由高低频电磁辐射驱动的FHN神经模型的汉密尔顿能量函数表达式。利用约束条件验证了解析解的正确性和唯一性，并通过数值模拟讨论了神经元的电活动和汉密尔顿能量函数。通过改变外部强迫电流强度等参数，发现FHN神经元的电活动模式经历了静态，尖峰状态，爆发状态和混合状态的连续转变，HLF信号的幅度和角频率。FHN神经元的电活动过程伴随着系统能量的存储和释放，该结果可以从能量成本的相关性和依赖性的角度提供对电活动的编码和转换的理解。