A dynamical model of the magnetization of a neutron star is given. The model shows three distinct behaviors, as characterized in the two-dimensional parameter space of the two relevant parameters. In one region of the parameter space, the magnetization, and correspondingly the magnetic field, behaves erratically, non-periodically, occasionally producing large pulses of directional electric and magnetic field. It is suggested that this field is associated with the mysterious "bursters," very energetic gamma-rich pulses of the order of 1 s duration, and believed to emanate from solo neutron stars. A second region of parameter space shows the magnetization precessing at a constant period around the spin or conserved angular momentum direction. This region is associated with the well-known pulsars. The third region is a "dead" region, where the magnetization is aligned with the spin axis, and the star is nonradiating. The model suggests a life history of a neutron star, in which the star typically evolves initially from a burster, later becoming a pulsar, and ending as a dead star; an alternative evolution is from burster directly to a dead star.