Different single computational neuron models have been proposed in the literature. Most of them belong to the Hodgkin–Huxley (H-H) type, in which they can produce complex behavior of the neuron and have efficient computational cost. In this paper, a modified FitzHugh-Rinzel (FH-R) model considering the effect of magnetic induction is proposed. Different features of the model are explored from a complex and nonlinear perspective. For instance, the impact of the magnetic field on the stability of the equilibrium points is studied by stability analysis. Bifurcation analysis reveals that the proposed neuron model has multi-stability. Furthermore, the spatiotemporal behavior of the proposed model is investigated in the complex network consisting of FH-R oscillators, and the effect of external stimuli is explored on wave propagation of the network.