Pattern dynamics of the non-reciprocal Swift-Hohenberg model

Abstract

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.