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Pattern dynamics of the nonreciprocal Swift-Hohenberg model.

Yuta Tateyama1, Hiroaki Ito1, Shigeyuki Komura2,3,4

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This study explores pattern dynamics in the one-dimensional nonreciprocal Swift-Hohenberg model, identifying distinct disordered, aligned, and chiral phases. Transitions between these phases are explained through bifurcation analysis.

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Area of Science:

  • Nonlinear dynamics
  • Pattern formation
  • Mathematical physics

Background:

  • The Swift-Hohenberg equation is a fundamental model for pattern formation.
  • Nonreciprocity introduces complex dynamics not seen in conservative systems.
  • Understanding pattern transitions is crucial for various scientific fields.

Purpose of the Study:

  • To investigate pattern dynamics in the one-dimensional nonreciprocal Swift-Hohenberg model.
  • To classify emergent spatiotemporal patterns.
  • To analyze phase transitions and bifurcations.

Main Methods:

  • Numerical simulations of the nonreciprocal Swift-Hohenberg model.
  • Analysis of spatiotemporal Fourier spectra for pattern classification.
  • Derivation of a reduced dynamical system using spatial Fourier series expansion.
  • Bifurcation analysis around fixed points.

Main Results:

  • Observed characteristic spatiotemporal patterns: disordered, aligned, swap, chiral-swap, and chiral phases.
  • Classified patterns based on their spatiotemporal Fourier spectra.
  • Identified Turing and wave bifurcations destabilizing the disordered phase into aligned and chiral phases, respectively.
  • Revealed a pitchfork bifurcation connecting the aligned and chiral phases.

Conclusions:

  • The one-dimensional nonreciprocal Swift-Hohenberg model exhibits rich pattern dynamics.
  • Phase transitions are governed by specific bifurcations (Turing, wave, pitchfork).
  • The study provides a detailed classification and understanding of emergent patterns and their transitions.