Asymptotic analysis of two reduction methods for systems of chemical reactions

DOI10.1016/S0167-2789(02)00386-XzbMath1036.80007arXivmath/0110159OpenAlexW2110841752MaRDI QIDQ1597264

Hans G. Kaper, Tasso J. Kaper

Publication date: 12 May 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0110159

zbMATH Keywords

iterative methodcombustionasymptotic expansionschemical kineticsenzyme kineticskinetic equationsslow manifoldgeometric singular perturbationmultiple time scalesreduction methodsatmospheric chemistryintrinsic low-dimensional manifoldsMichaelis-Menten-Henri mechanism

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Classical flows, reactions, etc. in chemistry (92E20) Chemical kinetics in thermodynamics and heat transfer (80A30) Qualitative investigation and simulation of ordinary differential equation models (34C60) Singular perturbations for ordinary differential equations (34E15) Multiple scale methods for ordinary differential equations (34E13)

Related Items (56)

Exponential estimates of symplectic slow manifolds ⋮ On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature ⋮ On the quasi-steady-state approximation in an open Michaelis-Menten reaction mechanism ⋮ Efficient implementation of chemistry in computational combustion ⋮ Geometry of the Computational Singular Perturbation Method ⋮ Bounds for the chaotic region in the Lorenz model ⋮ Asymptotic analysis of a target-mediated drug disposition model: algorithmic and traditional approaches ⋮ Stretching-based diagnostics and reduction of chemical kinetic models with diffusion ⋮ Slow integral manifolds for Lagrangian fluid dynamics in unsteady geophysical flows ⋮ Glycolysis in saccharomyces cerevisiae: algorithmic exploration of robustness and origin of oscillations ⋮ Coordinate-independent singular perturbation reduction for systems with three time scales ⋮ \textit{BCG} and \(IL-2\) model for bladder cancer treatment with fast and slow dynamics based on SPVF method -- stability analysis ⋮ Food sharing and time budgeting in predator-prey interaction ⋮ Methods of model reduction for large-scale biological systems: a survey of current methods and trends ⋮ Inertial effects and long-term transport properties of particle motion in washboard potential ⋮ Extension and justification of quasi-steady-state approximation for reversible bimolecular binding ⋮ Singularly perturbed vector field method (SPVF) applied to combustion of monodisperse fuel spray ⋮ Adaptive dynamical networks ⋮ Extending the zero-derivative principle for slow-fast dynamical systems ⋮ Analysis of the approximate slow invariant manifold method for reactive flow equations ⋮ Characterizing two-timescale nonlinear dynamics using finite-time Lyapunov exponents and subspaces ⋮ Asymptotics of conduction velocity restitution in models of electrical excitation in the heart ⋮ An epidemic model highlighting humane social awareness and vector-host lifespan ratio variation ⋮ Physical understanding of complex multiscale biochemical models via algorithmic simplification: glycolysis in saccharomyces cerevisiae ⋮ Comment on “Identification of low order manifolds: Validating the algorithm of Maas and Pope” [Chaos 9, 108–123 (1999)] ⋮ Response to “Comment on ‘Identification of low order manifolds: Validating the algorithm of Maas and Pope'” [Chaos 16, 048101 (2006)] ⋮ Biorthogonalization, geometric invariant properties and rate-based estimate of Lyapunov spectra ⋮ Quasi-equilibrium grid algorithm: geometric construction for model reduction ⋮ A constructive approach to quasi-steady state reductions ⋮ Properties of the Michaelis-Menten mechanism in phase space ⋮ A dengue epidemic model highlighting vertical-sexual transmission and impulsive control strategies ⋮ An in-host HIV-1 infection model incorporating quiescent and activated \(\mathrm{CD}4^+\) T cells as well as CTL response ⋮ Economic dynamics of reservoir sedimentation management: Optimal control with singularly perturbed equations of motion ⋮ The existence of solitary waves of singularly perturbed mKdV--KS equation ⋮ Higher order corrections in the approximation of low-dimensional manifolds and the construction of simplified problems with the CSP method ⋮ Transport-chemistry coupling in the reduced description of reactive flows ⋮ Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: a chemical explosive mode analysis ⋮ An efficient iterative algorithm for the approximation of the fast and slow dynamics of stiff systems ⋮ Multiple time-scales in nonlinear flight mechanics: diagnosis and modeling ⋮ Natural tangent dynamics with recurrent biorthonormalizations: a geometric computational approach to dynamical systems exhibiting slow manifolds and periodic/chaotic limit sets ⋮ Causes for ``ghost manifolds ⋮ About non-coincidence of invariant manifolds and intrinsic low dimensional manifolds (ILDM) ⋮ Analysis of the accuracy and convergence of equation-free projection to a slow manifold ⋮ Operator splitting for chemical reaction systems with fast chemistry ⋮ Effective reduction of a three-dimensional circadian oscillator model ⋮ On unifying concepts for trajectory-based slow invariant attracting manifold computation in kinetic multiscale models ⋮ Mechanism analysis with ILDMs for H<sub>2</sub>combustion on Pd catalysts ⋮ Unbounded dynamics in dissipative flows: Rössler model ⋮ Singular perturbed vector field method applied to combustion in diesel engine: continuous case with thermal runaway ⋮ Bifurcation analysis of a model for atherosclerotic plaque evolution ⋮ Parameterisations of slow invariant manifolds: application to a spray ignition and combustion model ⋮ A CSP and tabulation-based adaptive chemistry model ⋮ The parameterization method for invariant manifolds. III: Overview and applications ⋮ Phase transitions for the Brusselator model ⋮ Computation of Saddle-Type Slow Manifolds Using Iterative Methods ⋮ The ``hidden dynamics of the Rössler attractor

Uses Software

• HQR3
• HQR3 EXCHNG

Cites Work

• Quasi-steady-state approximation in the mathematical modeling of biochemical reaction networks
• Invariant manifolds of singularly perturbed ordinary differential equations
• Quasi-steady-state approximation for chemical reaction networks
• Geometric singular perturbation theory for ordinary differential equations
• Numerical integration of stiff ODE's of singular perturbation type
• Singular perturbation methods for ordinary differential equations
• Normally hyperbolic invariant manifolds in dynamical systems
• An efficient storage scheme for reduced chemical kinetics based on orthogonal polynomials
• Forced-convergence iterative schemes for the approximation of invariant manifolds
• The use of algebraic sets in the approximation of inertial manifolds and lumping in chemical kinetic systems
• Coupling of chemical reaction with flow and molecular transport
• Nonlinear singular perturbation phenomena: theory and applications
• Perturbations of discontinuous solutions of non-linear systems of differential equations
• Invariant manifold methods for metabolic model reduction
• Viscous detonation in H₂‒O₂‒Ar using intrinsic low-dimensional manifolds and wavelet adaptive multilevel representation
• Asymptotic Solution of Stiff PDEs with the CSP Method: The Reaction Diffusion Equation
• Intrinsic low-dimensional manifolds of strained and unstrained flames
• Identification of low order manifolds: Validating the algorithm of Maas and Pope
• The Quasi-Steady-State Assumption: A Case Study in Perturbation
• Tracking Invariant Manifolds up to Exponentially Small Errors
• Global reduced mechanisms for methane and hydrogen combustion with nitric oxide formation constructed with CSP data
• Invariant manifolds in singular perturbation problems for ordinary differential equations
• Invariant manifolds
• Efficient calculation of intrinsic low-dimensional manifolds for the simplification of chemical kinetics
• Explicit time-scale splitting algorithm for stiff problems: Auto-ignition of gaseous mixtures behind a steady shock
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Asymptotic analysis of two reduction methods for systems of chemical reactions