Fenichel Theory for Multiple Time Scale Singular Perturbation Problems

This paper is concerned with a geometric study of singularly perturbed systems of ordinary differential equations expressed by ($n-1$)-parameter families of smooth vector fields on $\mathbb{R}^l$, ...

[1]  John Guckenheimer,et al.  Mixed-Mode Oscillations with Multiple Time Scales , 2012, SIAM Rev..

[2]  Vladimir Gaitsgory,et al.  Averaging of three time scale singularly perturbed control systems , 2001 .

[3]  John Rinzel,et al.  Canard theory and excitability , 2013 .

[4]  Nancy Kopell,et al.  Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example , 2008, SIAM J. Appl. Dyn. Syst..

[5]  Freddy Dumortier,et al.  Canard Cycles and Center Manifolds , 1996 .

[6]  Sergio Rinaldi,et al.  Low- and high-frequency oscillations in three-dimensional food chain systems , 1992 .

[7]  Frédérique Clément,et al.  Mixed-Mode Oscillations in a Multiple Time Scale Phantom Bursting System , 2012, SIAM J. Appl. Dyn. Syst..

[8]  Marco Antonio Teixeira,et al.  THREE TIME SCALE SINGULAR PERTURBATION PROBLEMS AND NONSMOOTH DYNAMICAL SYSTEMS , 2014 .

[9]  Sergio Rinaldi,et al.  Slow-fast limit cycles in predator-prey models , 1992 .

[10]  Peter Szmolyan,et al.  Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points - Fold and Canard Points in Two Dimensions , 2001, SIAM J. Math. Anal..

[11]  G. Hek Geometric singular perturbation theory in biological practice , 2010 .

[12]  Georgi S. Medvedev,et al.  Multimodal regimes in a compartmental model of the dopamine neuron , 2004 .

[13]  Vladimir Gaitsgory,et al.  Multiscale Singularly Perturbed Control Systems: Limit Occupational Measures Sets and Averaging , 2002, SIAM J. Control. Optim..

[14]  Nikola Popović,et al.  Sector-delayed-Hopf-type mixed-mode oscillations in a prototypical three-time-scale model , 2016, Appl. Math. Comput..

[15]  Christopher Jones,et al.  Geometric singular perturbation theory , 1995 .

[16]  N. Kopell,et al.  Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron. , 2008, Chaos.

[17]  J. Aracil,et al.  Three‐time scale singular perturbation control and stability analysis for an autonomous helicopter on a platform , 2013 .