  We investigate the pattern dynamics of the one-dimensional non-reciprocal
Swift-Hohenberg model. Characteristic spatiotemporal patterns, such as
disordered, aligned, swap, chiral-swap, and chiral phases, emerge depending on
the parameters. We classify the characteristic spatiotemporal patterns obtained
in the numerical simulations by focusing on the spatiotemporal Fourier spectrum
of the order parameters. We derive a reduced dynamical system by using the
spatial Fourier series expansion. We analyze the bifurcation structure around
the fixed points corresponding to the aligned and chiral phases and explain the
transitions between them. The disordered phase is destabilized either to the
aligned phase or to the chiral phase by the Turing bifurcation or the wave
bifurcation, and the aligned phase and the chiral phase are connected by the
pitchfork bifurcation.
