Basins with tentacles

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 $e^{-k{q}^2}.$ 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.

published version

References in corpus (3)

• Multi-node basin stability in complex dynamical networks
• The Size of the Sync Basin Revisited
• Critical Switching in Globally Attractive Chimeras