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Updated: Jul 16, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
On a stable torus in a 3D system with a saddle-focus
Andrey L Shilnikov1, Leonid P Shilnikov2
1Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, 100 Piedmont Ave., Atlanta, Georgia 30303, USA.
Abstract:
This paper proposes a conceptual model for the onset of a stable torus near a saddle-focus equilibrium. This bifurcation scenario is typical of slow-fast systems that generate elliptic bursting in a variety of neuronal models in mathematical neuroscience. Variants of the model also capture other dynamical regimes recurring in a neighborhood of the saddle-focus. We also discuss homoclinic bifurcations for which the model assumptions are feasible.
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