Phase reduction analysis of traveling breathers in reaction--diffusion systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918168793972736 |
|---|---|
| author | Arai, Takahiro Kawamura, Yoji |
| author_facet | Arai, Takahiro Kawamura, Yoji |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase reduction analysis of traveling breathers in reaction--diffusion systems Arai, Takahiro Kawamura, Yoji Adaptation and Self-Organizing Systems Pattern Formation and Solitons 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. |
| title | Phase reduction analysis of traveling breathers in reaction--diffusion systems |
| topic | Adaptation and Self-Organizing Systems Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2507.14942 |