The topology and dynamics of stripe-like magnetic domains obtained in a ferrimagnetic garnet subjected to a time-dependent external magnetic field is studied experimentally and theoretically. Experiments are performed on a commercially available magnetic bubble apparatus, allowing the observation of the time-evolution of the magnetic domain structure. The system is modeled by a meso-scale Ising-type lattice model. Exchange and dipolar interactions between the spins, and interaction of the spins with the external magnetic field are considered. The model is investigated by kinetic Monte Carlo simulations with time-varying transition rates. In the limit of low temperatures the elaborated model leads to a magnetic domain topology and dynamics that is similar to the ones observed in the experiments. In the highly non-equilibrium limit with a high driving frequency the model reproduces the experimentally recorded hysteresis loops as well.