Abstract: Two magnetic flux neurons were coupled by magnetic flux coupling, and the coupled neuron model was established. Firstly, RouthHurwitz criterion was used to analyze the stability of the equilibrium point and calculate the unique equilibrium point of the model. Secondly, the analytic solution of bifurcation was obtained by Hopf theorem, and the bifurcation direction of the model and the stability of bifurcation periodic solution were studied. Finally, the dynamic behavior of the model was simulated by numerical simulation. The results show that, within a certain range of parameters, with the increase of the coupling strength, the model generates a subcritical Hopf bifurcation, and at the same time, the phenomenon of inverted doubling cycle, plus cycle bifurcation and more periodic windows appear, and increasing the external stimulation current can induce the spike discharge.

Key words: coupled neuron, Hopf bifurcation, discharge behavior, stability