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  • Open Access

Phase reduction analysis of traveling breathers in reaction-diffusion systems

Takahiro Arai* and Yoji Kawamura

  • *Contact author: araitak@jamstec.go.jp
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Phys. Rev. Research 7, 043079 – Published 20 October, 2025

DOI: https://doi.org/10.1103/4nzq-9kr2

Abstract

We formulate a theory for phase reduction analysis of traveling breathers in reaction-diffusion systems with spatial translational symmetry. In this formulation, the spatial and temporal phases represent the position and oscillation of a traveling breather, respectively. We perform phase reduction analysis on a pair of FitzHugh-Nagumo models exhibiting standing breathers and a pair of Gray-Scott models exhibiting traveling breathers. The derived phase equations for the spatial and temporal phases indicate nontrivial spatiotemporal dynamics, where both phases are mutually coupled. Using the phase equations, we obtain the time evolution of the phase differences, which is consistent with that obtained from direct numerical simulations.

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Phys. Rev. Research 7, 043079– Published 20 October, 2025
  • Received 21 July 2025
  • Accepted 18 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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