The electrical potential difference across a nerve cell membrane can be recorded. The action potentials are really fast voltage oscillations caused by the movement of ions through the cell membrane.
More complex oscillations are possible.
For instance some cells produce bursts of fast action potentials riding on a much slower oscillation. Others produce bursts at one level of applied current and repetitive action potential at another. Cells in different brain regions produce many variants of these basic types of oscillation. The oscillation can be modelled by solving systems of differential equations on a computer. The trend in neuroscience is to make these models as accurate as possible by including detail, based on experimental measurement.