The dynamics of particles in a Penning-Malmberg-Surko trap with Rotating Wall (rotating quadrupole and/or dipole electric field) and a buffer gas is considered. Electromagnetic traps are widely used for the accumulation and confinement of charged particles during various experiments in nuclear and accelerator physics, mass spectroscopy, and other fields. Traps are the main element of sources of charged particles in accelerators. An especially important role is played by traps with efficient accumulation during operation (in a cyclic mode) of ion synchrotrons and colliders with short-lived isotopes. The purpose of this work was to develop algorithms for constructing regions of stability (according to Lyapunov) in the space of parameters describing additional rotating electric fields, and to determine the analytical conditions that must be satisfied by the trap parameters to achieve a given degree of stability. The influence of the space charge of a beam of accumulated particles on the stability of the system is also investigated. The calculation results and the proposed models can be used in the selection and adjustment of the main parameters of the designed traps of the considered type.