Basins with Tentacles
Yuanzhao Zhang and Steven H. Strogatz
Phys. Rev. Lett. 127, 194101 – Published 2 November 2021
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 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.
Апдейт: по закону парных случаев, три дня спустя на Элементах появилась статья о змее с тентаклями:)))