Pattern dynamics of the nonreciprocal Swift-Hohenberg model
Yuta Tateyama1, Hiroaki Ito1, Shigeyuki Komura2,3,4
1Department of Physics, Graduate School of Science, <a href="https://ror.org/01hjzeq58">Chiba University</a>, Chiba 263-8522, Japan.
Physical Review. E
|December 18, 2024
Summary
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.
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.
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