Isochronal Phase Reduction and Speed Correction of a Pulse in a Stochastic Kinematic Model
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arXiv
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| Format: | Preprint |
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2025
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| author | McGinnis, Joshua A. Li, Xinbo Ogawa, Toshiyuki Mori, Yoichiro |
| author_facet | McGinnis, Joshua A. Li, Xinbo Ogawa, Toshiyuki Mori, Yoichiro |
| contents | We develop a method for computing the stochastic wave speed of pulse solutions in kinematic equations subject to small stochastic forcing based on the isochronal phase reduction. These kinematic equations arise as the singular limit of sharp pulse solutions in the FitzHugh-Nagumo system, and our approach contributes a new perspective and method to the growing body of work on stochastic wave propagation in excitable media. The method yields an effective Itô process for the wave's position. The coefficients of the Itô process can be computed deterministically allowing for efficient computation. We demonstrate the efficiency and accuracy of our method through numerical demonstrations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_09455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isochronal Phase Reduction and Speed Correction of a Pulse in a Stochastic Kinematic Model McGinnis, Joshua A. Li, Xinbo Ogawa, Toshiyuki Mori, Yoichiro Dynamical Systems Probability 35R60, 60H15, 60H35 We develop a method for computing the stochastic wave speed of pulse solutions in kinematic equations subject to small stochastic forcing based on the isochronal phase reduction. These kinematic equations arise as the singular limit of sharp pulse solutions in the FitzHugh-Nagumo system, and our approach contributes a new perspective and method to the growing body of work on stochastic wave propagation in excitable media. The method yields an effective Itô process for the wave's position. The coefficients of the Itô process can be computed deterministically allowing for efficient computation. We demonstrate the efficiency and accuracy of our method through numerical demonstrations. |
| title | Isochronal Phase Reduction and Speed Correction of a Pulse in a Stochastic Kinematic Model |
| topic | Dynamical Systems Probability 35R60, 60H15, 60H35 |
| url | https://arxiv.org/abs/2508.09455 |