On a stable torus in a 3D system with a saddle-focus
Dynamical Systems
2026-02-16 v1
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.
Keywords
Cite
@article{arxiv.2602.12451,
title = {On a stable torus in a 3D system with a saddle-focus},
author = {Andrey L. Shilnikov answered Leonid P. Shilnikov},
journal= {arXiv preprint arXiv:2602.12451},
year = {2026}
}