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arXiv · 2106.05709

Basins with tentacles

Yuanzhao Zhang·Steven H. Strogatz
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Abstract

To explore basin geometry in high-dimensional dynamical systems, we consider a ring of identical Kuramoto oscillators. Many attractors coexist in this system; each is a twisted periodic orbit characterized by a winding number $q$, with basin size proportional to $e^{-kq^2}.$ We uncover the geometry behind this size distribution and find the basins are octopus-like, with nearly all their volume in the tentacles, not the head of the octopus (the ball-like region close to the attractor). We present a simple geometrical reason why basins with tentacles should be common in high-dimensional systems.

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Yuanzhao Zhang, Steven H. Strogatz. 2021-11-02. Basins with tentacles. https://doi.org/10.1103/physrevlett.127.194101

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