  We numerically investigate the phase separation dynamics of the
non-reciprocal Allen-Cahn model in which two non-conserved order parameters are
coupled. The system exhibits several dynamical patterns such as the randomly
oscillating phase and the spiral phase as well as the homogeneously oscillating
phase. Topological defects in the spirals are either bound or unbound depending
on the non-reciprocality. The traveling stripe pattern is also found when the
diffusion constants are highly asymmetric and the non-reciprocality is small.
