Brushless motors are characterized by extreme power density, thermal management and steady dynamic performance which are commonly utilized in aerospace, high-end robotics and precision medical equipment. The nonlinear solutions and the corresponding stabilities in the brushless DC motor system reveal the inherent current-speed properties. In this study, the semi-analytical solutions and the corresponding stabilities in the brushless DC motor system are obtained via a discretized mapping method. The governing equations are discretized into nonlinear polynomials through an implicit mid-point scheme. The semi-analytical solution trees from period-1 to period-2 and period-1 to period-4 are obtained. Some independent periodic solutions are observed. The stability and bifurcations are obtained quantitatively where the period-doubling bifurcations trigger the bifurcation trees and saddle-node bifurcations bound the independent solutions. Interestingly, unstable bifurcation trees are also observed. For verification, numerical simulation is conducted. The stable and unstable properties of current–velocity coupling dynamics are discussed finally.
Wang et al. (2026) studied this question.