Mode transition and energy dependence of FitzHugh-Nagumo neural model driven by high-low frequency electromagnetic radiation

Abstract

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.