Based on the study of the synchronization of two electric synapse-coupled Sherman neuron systems, this paper analyzes the rich discharge behavior of Sherman neurons through the peak-to-peak interval bifurcation diagram, which determines the parameter values for the study of the electrical synapse coupling Sherman neuron system synchronization. By using the synchronization difference and the correlation coefficient value, this paper analyzes the synchronous transition process of the two electrical synapse-coupled Sherman neuron systems with the change of coupling intensity and studies the bifurcation behavior of neurons in the two electrical synapse-coupled Sherman neuron systems. The experimental results show the transition process of two electrical synapse-coupled Sherman neurons from nonsynchronized, peak-independent cluster synchronization to fully synchronized. In addition, we study the synchronization process of the ring-connected electrical synapse-coupled Sherman neuron system. The experimental results show that the two electrical synapse-coupled Sherman neuron systems show a similar synchronous transition process.

Noise exists widely in the nervous system, and plays a crucial role in the nervous system information processing. Noise can not only enhance but also weaken the ability of the nervous system to process information. Neurons are in a complex and variable electromagnetic field. Electromagnetic induction plays an important role in regulating the changes of neuronal membrane potential. Therefore, this paper simulates the electromagnetic field environment of the nervous system with a memristor and analyses the rich coherence resonance behavior of FitzHugh-Nagumo (FHN) neuron system under the drive of phase noise. By taking the amplitude, period and noise intensity of phase noise as the main parameters and the parameters of memristor as auxiliary parameters, the two-parameter changes are made from the angle of the amplitude and period of phase noise, the amplitude and intensity of phase noise, and the noise intensity and period of phase noise, respectively. The dynamic behaviors of coherent resonance of FHN neuron system are analyzed from the amplitude and period, amplitude and intensity as well as intensity and period of phase noise, respectively. When the amplitude and period of the phase noise and the intensity and period of the phase noise are used as independent variables for the two-parameter analysis, the FHN neuron system shows rich dynamic behaviors such as coherence mono-resonance, coherence bi-resonance and coherence multi-resonance. Especially when the amplitude and period of phase noise change as two-parameter, the system presents a coherence resonance of discharge pattern with period-adding cluster discharge at the valley. When the amplitude and intensity of phase noise are taken as independent variables for two-parameter analysis, FHN neuronal system presents single or dual coherence resonance at any value of noise intensity with the change of phase noise amplitude. The simulated results show that the FHN neuron system demonstrates rich coherence resonance behaviors under the drive of phase noise when the effect of electromagnetic induction in the nervous system is simulated by memristor.