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arXiv · 2504.07270

Instability of anchored spirals in geometric flows

Anthony Cortez·Nan Li·Nathan Mihm·Alice Xu·Xiaoxing Yu·Arnd Scheel
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Abstract

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.

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Anthony Cortez, Nan Li, Nathan Mihm, Alice Xu, Xiaoxing Yu, Arnd Scheel. 2025-04-09. Instability of anchored spirals in geometric flows. https://arxiv.org/abs/2504.07270

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