We will consider a family of dynamical systems modeling Josephson effect in superconductivity. Following the series of works our main goal is to describe the properties of the rotation number (which in physics is the average voltage over a long time interval up to a constant factor) and find the borders of its phase-locked domains. We suggest a new approach that uses the theory of isomonodromic deformations and leads to the Bessel solutions of the Painlev\'e III equations. Speaker(s): Yulia Bibilo (IITP RAS)