• Open Access

Basins with Tentacles

Yuanzhao Zhang and Steven H. Strogatz
Phys. Rev. Lett. 127, 194101 – Published 2 November 2021

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 ekq2. We uncover the geometry behind this size distribution and find the basins are octopuslike, 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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  • Received 10 June 2021
  • Revised 3 August 2021
  • Accepted 14 October 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.194101

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsNetworks

Authors & Affiliations

Yuanzhao Zhang1,2 and Steven H. Strogatz1,3

  • 1Center for Applied Mathematics, Cornell University, Ithaca, New York 14853, USA
  • 2Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
  • 3Department of Mathematics, Cornell University, Ithaca, New York 14853, USA

Article Text

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Issue

Vol. 127, Iss. 19 — 5 November 2021

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