On a stable torus in a 3D system with a saddle-focus
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.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Nonlinear Dynamics and Pattern Formation
Differential Equations and Numerical Methods
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 12 February 2026
- Language
- EN
- Document type
- Preprint