Pattern dynamics of the nonreciprocal Swift-Hohenberg model

TL;DR

This paper explores the complex pattern dynamics in a one-dimensional nonreciprocal Swift-Hohenberg model, identifying various phases and their bifurcations through numerical and analytical methods.

Contribution

It introduces a reduced dynamical system based on Fourier expansion and analyzes bifurcations, providing new insights into phase transitions in nonreciprocal pattern-forming systems.

Findings

Identification of disordered, aligned, swap, chiral-swap, and chiral phases.

Bifurcation analysis reveals transitions between phases.

Disordered phase destabilizes to ordered phases via bifurcations.

Abstract

We investigate the pattern dynamics of the one-dimensional nonreciprocal 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 numerical simulation 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 by the Turing bifurcation or to the chiral phase by the wave bifurcation, while the aligned phase and the chiral phase are connected by the pitchfork bifurcation.