Based on the e-HR neuron model, a magnetic flux e-HR neuron model is constructed under the influence of external electromagnetic fields with membrane potential changes. Firstly, the Shengjin formula is used to obtain the number of equilibrium points of the magnetic flux e-HR neuron model and the stability of the equilibrium points, and at the same time the bifurcation theory is further used to find out the conditions for the bifurcation of the system. Secondly, by changing the applied stimulation current and the magnetic flux feedback gain, it is found that the neurons present a variety of firing modes such as cluster firing and periodic firing. What's more, the unstable state of the equilibrium point corresponds to the neuronal firing mode; the steady state corresponds to the resting mode, that is, the non-discharge mode. Finally, an adaptive controller is designed based on the Lyapunov stability theory, and the effectiveness and feasibility of the controller is proved through theoretical analysis and numerical simulation.