Fenichel Theory for Multiple Time Scale Singular Perturbation Problems
From MaRDI portal
Publication:5349314
DOI10.1137/16M1067202zbMath1373.34090OpenAlexW2742097411MaRDI QIDQ5349314
Marco Antonio Teixeira, Pedro Toniol Cardin
Publication date: 24 August 2017
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/16m1067202
Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Invariant manifolds for ordinary differential equations (34C45) Singular perturbations for ordinary differential equations (34E15)
Related Items
Canard solutions in neural mass models: consequences on critical regimes ⋮ Dynamics in diffusive Leslie–Gower prey–predator model with weak diffusion ⋮ Geometric singular perturbation theory for systems with symmetry ⋮ Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics ⋮ Coordinate-independent singular perturbation reduction for systems with three time scales ⋮ A general view on double limits in differential equations ⋮ Travelling waves in diffusive Leslie-Gower prey-predator model ⋮ Natural parameter conditions for singular perturbations of chemical and biochemical reaction networks ⋮ Quasi-neutral dynamics in a coinfection system with \(N\) strains and asymmetries along multiple traits ⋮ Traveling pulses of coupled Fitzhugh-Nagumo equations with doubly-diffusive effect ⋮ Complex oscillatory dynamics in a three-timescale El Niño southern oscillation model ⋮ Computational Singular Perturbation Method for Nonstandard Slow-Fast Systems ⋮ Reduction of Chemical Reaction Networks with Approximate Conservation Laws ⋮ Slow-fast normal forms arising from piecewise smooth vector fields ⋮ Structural stability for 2-dimensional piecewise smooth vector fields where the switching manifold is a double discontinuity ⋮ Singularly perturbed problems with multi-tempo fast variables ⋮ Geometric blow-up for folded limit cycle manifolds in three time-scale systems ⋮ Time delays and pollution in an open‐access fishery ⋮ Complex oscillatory patterns in a three-timescale model of a generalist predator and a specialist predator competing for a common prey ⋮ On slow-fast dynamics in a classical predator-prey system ⋮ Spike-Adding in a Canonical Three-Time-Scale Model: Superslow Explosion and Folded-Saddle Canards ⋮ Asymptotic behavior of periodic solutions in one-parameter families of Liénard equations ⋮ Quasi-periodic bursters and chaotic dynamics in a shallow arch subject to a fast-slow parametric excitation ⋮ Algorithmic reduction of biological networks with multiple time scales ⋮ Fisher-KPP dynamics in diffusive Rosenzweig–MacArthur and Holling–Tanner models ⋮ CORRIGENDUM: Fenichel Theory for Multiple Time Scale Singular Perturbation Problems ⋮ Multiple timescales and the parametrisation method in geometric singular perturbation theory ⋮ Qualitative dynamics of chemical reaction networks: an investigation using partial tropical equilibrations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multiple time scale dynamics
- Sector-delayed-Hopf-type mixed-mode oscillations in a prototypical three-time-scale model
- Geometric singular perturbation theory for ordinary differential equations
- Limit cycles in slow-fast forest-pest models
- Bifurcations of mixed-mode oscillations in a three-variable autonomous Van der Pol-Duffing model with a cross-shaped phase diagram
- Multimodal regimes in a compartmental model of the dopamine neuron
- Geometric singular perturbation theory in biological practice
- Food chain chaos due to junction-fold point
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Three-time scale singular perturbation control and stability analysis for an autonomous helicopter on a platform
- Mixed-Mode Oscillations with Multiple Time Scales
- Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example
- Low- and High-Frequency Oscillations in Three-Dimensional Food Chain Systems
- Multiscale Singularly Perturbed Control Systems: Limit Occupational Measures Sets and Averaging
- Canard cycles and center manifolds
- Mixed-Mode Oscillations in a Multiple Time Scale Phantom Bursting System
- Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron
- Canard Theory and Excitability
- Three time scale singular perturbation problems and nonsmooth dynamical systems
- Averaging of three time scale singularly perturbed control systems