Abstract: In this paper, based on the modified Hindmarsh-Rose neuron model, we construct a four-dimensional model by considering the effect of magnetic flux and electromagnetic induction across cell membranes. According to the interspike intervals analysis, we find complex dynamic phenomena that inverse period-adding bifurcation, inverse period-doubling bifurcation and period-doubling bifurcation leading to chaos. We observe four kinds of bursting patterns by using fast-slow dynamics method. Then, we analyze the transition mechanisms between different bursting patterns through two-parameter bifurcation of the fast subsystem. Finally, codimension-two bifurcation analysis shows more details of bifurcation.