Instability of anchored spirals in geometric flows
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908813827768320 |
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| author | Cortez, Anthony Li, Nan Mihm, Nathan Xu, Alice Yu, Xiaoxing Scheel, Arnd |
| author_facet | Cortez, Anthony Li, Nan Mihm, Nathan Xu, Alice Yu, Xiaoxing Scheel, Arnd |
| contents | We investigate existence, stability, and instability of anchored rotating spiral waves in a model for geometric curve evolution. We find existence in a parameter regime limiting on a purely eikonal curve evolution. We study stability and instability theoretically, in the aforementioned limiting regime, and numerically. We find convective and absolute oscillatory instability, as well as saddle-node bifurcations. Our results in particular shed light on the instability of spiral waves in reaction-diffusion systems caused by an instability of wave trains against transverse modulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Instability of anchored spirals in geometric flows Cortez, Anthony Li, Nan Mihm, Nathan Xu, Alice Yu, Xiaoxing Scheel, Arnd Pattern Formation and Solitons Analysis of PDEs We investigate existence, stability, and instability of anchored rotating spiral waves in a model for geometric curve evolution. We find existence in a parameter regime limiting on a purely eikonal curve evolution. We study stability and instability theoretically, in the aforementioned limiting regime, and numerically. We find convective and absolute oscillatory instability, as well as saddle-node bifurcations. Our results in particular shed light on the instability of spiral waves in reaction-diffusion systems caused by an instability of wave trains against transverse modulations. |
| title | Instability of anchored spirals in geometric flows |
| topic | Pattern Formation and Solitons Analysis of PDEs |
| url | https://arxiv.org/abs/2504.07270 |