  We propose a class of diffusive lattice models where the internal states of
particles are subject to a periodic drive. The discrete symmetry of states
enforces an effective energy landscape which can counteract the drive to arrest
the dynamics. Such a mechanism is reminiscent of the arrest reported in dense
assemblies of pulsating deformable particles, in line with experiments in
confluent biological tissues. We show that the competition between arrest and
synchronisation promotes an instability which leads to spiral waves. Using
analytical coarse-graining, we rationalize the emergence of such spirals in
terms of a discrete gauge invariance at the hydrodynamic level.
