We study pattern dynamics in a one-dimensional anisotropic XY model driven by a rotating external field. We find that the dynamical properties change qualitatively through a dynamic phase transition, which is a bifurcation of the spatially uniform states under a periodic external field. When two stable uniform limit cycles coexist, we observe a domain wall structure. Furthermore, there is a domain wall connecting domains of different phases of one limit cycle attractor. We find a periodic structure which is caused by the collapse of the domain wall. We derive approximate equations that describe the long time behavior of the domain walls and find that some results based on this approximation are qualitatively in agreement with those of numerical simulations. The properties of the interaction between the two domain walls depend on the symmetry of the wall. We observe a propagation of the phase wave in the quasi-periodic phase. This result implies the possibility of a phase description in non-autonomous systems. We find two chaotic patterns with different statistical properties in the symmetry-broken chaos region.
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