Computational Singular Perturbation Method for Nonstandard Slow-Fast Systems
From MaRDI portal
Publication:5109374
DOI10.1137/19M1242677zbMath1457.37102arXiv1906.06049MaRDI QIDQ5109374
Ian Lizarraga, Martin Wechselberger
Publication date: 11 May 2020
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1906.06049
Perturbations of ordinary differential equations (34D10) Singular perturbations of ordinary differential equations (34D15) Systems with slow and fast motions for nonlinear problems in mechanics (70K70) Computational methods for invariant manifolds of dynamical systems (37M21)
Related Items
Process-Oriented Geometric Singular Perturbation Theory and Calcium Dynamics, Discrete geometric singular perturbation theory, Algorithmic criteria for the validity of quasi-steady state and partial equilibrium models: the Michaelis-Menten reaction mechanism, A Surface of Heteroclinic Connections Between Two Saddle Slow Manifolds in the Olsen Model, Slow unfoldings of contact singularities in singularly perturbed systems beyond the standard form, Multiple timescales and the parametrisation method in geometric singular perturbation theory
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Parameterization of slow-stable manifolds and their invariant vector bundles: theory and numerical implementation
- Multiple time scale dynamics
- A constructive approach to quasi-steady state reductions
- Constraint-defined manifolds: a legacy code approach to low-dimensional computation
- Tikhonov's theorem and quasi-steady state
- Saddle slow manifolds and canard orbits in \(\mathbb{R}^{4}\) and application to the full Hodgkin-Huxley model
- Quasi-steady-state approximation in the mathematical modeling of biochemical reaction networks
- Quasi-steady-state approximation for chemical reaction networks
- Geometric singular perturbation theory for ordinary differential equations
- Mathematical physiology
- Dichotomic basis approach to solving hyper-sensitive optimal control problems
- Computer algebra derives correct initial conditions for low-dimensional dynamical models
- Analysis of the computational singular perturbation reduction method for chemical kinetics
- Coordinate-independent singular perturbation reduction for systems with three time scales
- Apparent discontinuities in the phase-resetting response of cardiac pacemakers
- Multiscale geometry of the Olsen model and non-classical relaxation oscillations
- Higher order corrections in the approximation of low-dimensional manifolds and the construction of simplified problems with the CSP method
- Geometry of the Computational Singular Perturbation Method
- When Shil'nikov Meets Hopf in Excitable Systems
- Computing the Stable Manifold of a Saddle Slow Manifold
- Fast and Slow Dynamics for the Computational Singular Perturbation Method
- Global reduced mechanisms for methane and hydrogen combustion with nitric oxide formation constructed with CSP data
- Computing Slow Manifolds of Saddle Type
- Geometric Singular Perturbation Theory Beyond the Standard Form
- Quasi-Steady State: Searching for and Utilizing Small Parameters
- Computation of Saddle-Type Slow Manifolds Using Iterative Methods
- Fenichel Theory for Multiple Time Scale Singular Perturbation Problems
- Two perspectives on reduction of ordinary differential equations
- Explicit time-scale splitting algorithm for stiff problems: Auto-ignition of gaseous mixtures behind a steady shock
