Abstract: The pre-B?tzinger complex is essential for the generation of the respiratory rhythm of newborn mammals and it is the center for the generation of the respiratory rhythm. The function of the memristor is similar to the plasticity of neuronal synapses, which can be used to simulate magnetic flux. In this paper, by adding stimulation current and magnetic flux-controlled memristor to the Butera dynamics model, we mainly investigate the influences of these two factors on the mixed bursting firing pattern of a single pre-B?tzinger neuron. Timescale analysis of variables is carried out by dimensionless methods. The results indicate that the model contains three different time scales. The dynamic mechanism of mixed bursting is studied through fast-slow decomposition and bifurcation analysis. Both the stimulation current and the magnetic flux can affect the number of somatic part of mixed bursting. Decrease the values of stimulation currentand magnetic flux, the number of somatic bursts will also decrease accordingly, and the stimulation current and magnetic flux can make the firing patterns of the somatic bursts transit from "fold/homoclinic" bursting to "Hopf/Hopf" bursting via "fold/homoclinic" hysteresis loop. Two-parameter bifurcation analysis in (h, Ca) plane shows that with the gradual increase of calcium ion, the trajectory of the full system crosses back and forth between the fold bifurcation and homoclinic bifurcation curve, which implies the dynamic mechanism of mixed bursting mainly rely on these two bifurcations. The number of transitions between the fold bifurcation and homoclinic bifurcation curve of the full system trajectory corresponds to the amount of somatic bursts in the mixed bursting.