Universal dynamics of spatiotemporal entrainment with phase symmetry

We study the entrainment of a localized pattern by an external signal via its coupling to zero modes associated with broken symmetries. We show that when internal symmetries are broken, entrainment is governed by a multi-degree of freedom locking dynamical system that has a universal structure defined by the internal symmetry group and its breaking. We derive explicitly the universal locking dynamics for entrainment of patterns breaking internal phase symmetry, and calculate the locking domains and the entrainment structure for the example of complex-Ginzburg-Landau solitons.