Dynamic phase transition in the Ginzburg-Landau model of the anisotropic XY spin system in a rotating external field is studied. We observe several types of oscillations, limit cycles, quasiperiodic oscillations and chaotic motions. It is found that limit cycle oscillations can have the periodicity of multiple times of the period of the applied field and that the system shows two kinds of scenarios leading to the onset of quasiperiodic oscillations, i.e., the saddle-node and Hopf bifurcations. Furthermore, this paper reports the findings of chaotic behaviors in the context of dynamic phase transition and that there exist two types of chaos with and without a certain kind of symmetry.