Phase reduction of reaction-diffusion systems with delay
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918370575646720 |
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| author | Ozawa, Ayumi Kawamura, Yoji |
| author_facet | Ozawa, Ayumi Kawamura, Yoji |
| contents | We develop a phase reduction method for reaction-diffusion systems with a discrete delay. On the basis of the recent developments in the phase reduction theory for infinite-dimensional systems, we introduce a bilinear form tailored to spatially extended systems involving a discrete delay. By solving the adjoint equation associated with the bilinear form, we obtain the phase sensitivity function, which quantifies the shift of the phase in response to a given perturbation. The theory is verified numerically with the use of the Schnakenberg system with a discrete delay in one spatial dimension. We further demonstrate the utility of the theory by optimizing the interaction between a pair of the Schnakenberg systems, with the use of the phase equation, for maximizing the stability of in-phase synchronization. This study serves as a step towards establishing a theory for analyzing oscillatory systems that involve both spatial degrees of freedom and delay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase reduction of reaction-diffusion systems with delay Ozawa, Ayumi Kawamura, Yoji Adaptation and Self-Organizing Systems We develop a phase reduction method for reaction-diffusion systems with a discrete delay. On the basis of the recent developments in the phase reduction theory for infinite-dimensional systems, we introduce a bilinear form tailored to spatially extended systems involving a discrete delay. By solving the adjoint equation associated with the bilinear form, we obtain the phase sensitivity function, which quantifies the shift of the phase in response to a given perturbation. The theory is verified numerically with the use of the Schnakenberg system with a discrete delay in one spatial dimension. We further demonstrate the utility of the theory by optimizing the interaction between a pair of the Schnakenberg systems, with the use of the phase equation, for maximizing the stability of in-phase synchronization. This study serves as a step towards establishing a theory for analyzing oscillatory systems that involve both spatial degrees of freedom and delay. |
| title | Phase reduction of reaction-diffusion systems with delay |
| topic | Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2511.18360 |