Singular Perturbations : Introduction to System Order Reduction Methods with Applications.

Intro -- Foreword -- Preface -- Contents -- Chapter 1 Introduction -- 1.1 Regular and Singular Perturbations -- 1.1.1 Algebraic Equations -- 1.1.2 Asymptotic Expansions -- 1.1.3 Second Order Differential Equation -- 1.2 Method of Multiple Scales -- 1.2.1 Second Order Differential Equation -- 1.2.2 Second Order Differential System -- 1.2.3 A Note on the Initial Conditions -- 1.2.4 A Note on the Meaning of ``Small'' -- 1.3 Singularly Perturbed Differential Systems -- 1.3.1 Slow Surfaces and Slow Integral Manifolds -- 1.3.2 Integral Manifolds and Asymptotic Expansionsof Solutions -- Chapter 2 Slow Integral Manifolds -- 2.1 Introduction -- 2.2 Stability of Slow Integral Manifolds -- 2.3 Asymptotic Representation of Integral Manifolds -- 2.4 Two Mathematical Examples -- 2.5 Systems That Are Linear with Respect to the Fast Variables -- Chapter 3 The Book of Numbers -- 3.1 0+1 -- 3.2 1+1 -- 3.2.1 Theoretical Background -- 3.2.1.1 Asymptotic Expansions -- 3.2.2 Michaelis-Menten Kinetics -- 3.3 2+1 -- 3.3.1 Theoretical Background -- 3.3.2 Bimolecular Reaction System -- 3.4 1+2 -- 3.4.1 Theoretical Background -- 3.4.2 Cooperative Phenomenon -- 3.4.3 Cooperative Phenomenon: Another Approach -- 3.5 2+2 -- 3.5.1 Theoretical Background -- 3.5.2 Enzyme-Substrate-Inhibitor System -- 3.5.3 Enzyme-Substrate-Exhibitor: The Another Approach -- Chapter 4 Representations of Slow Integral Manifolds -- 4.1 Explicit and Implicit Slow Integral Manifolds -- 4.2 Parametric Representation of Integral Manifolds -- Chapter 5 Singular Singularly Perturbed Systems -- 5.1 Introduction -- 5.2 Construction of Slow Integral Manifold -- 5.3 Implicit Slow Integral Manifolds -- 5.4 Parametric Representation of Integral Manifolds -- 5.5 High-Gain Control -- 5.6 Reaction Kinetics of Organometallic Compounds -- Chapter 6 Reduction Methods for Chemical Systems.

6.1 Method of Intrinsic Manifolds -- 6.2 Iterative Method -- 6.3 Extending the Iterative Method -- Chapter 7 Specific Cases -- 7.1 Weakly Attractive Integral Manifolds -- 7.1.1 Gyroscopic Systems -- 7.1.2 Precessional Motions -- 7.1.3 Vertical Gyro with Radial Corrections -- 7.1.4 Heavy Gyroscope -- 7.1.5 Control of a One Rigid-Link Flexible-Joint Manipulator -- 7.2 Unstable Manifolds -- 7.3 Conditionally Stable Manifolds -- Chapter 8 Canards and Black Swans -- 8.1 Introduction -- 8.2 Singular Perturbations and Canards -- 8.2.1 Examples of Canards -- 8.2.2 Canards of Three-Dimensional Systems -- 8.2.2.1 Asymptotic Expansions for Canards -- 8.3 Canard Cascades -- 8.3.1 Simplest Canard Cascades -- 8.3.2 Canard Cascade for the van der Pol Model -- 8.3.3 Canard Cascades in Biological Models -- 8.4 Black Swans -- 8.5 Laser and Chemical Models -- 8.5.1 Lang-Kobayashi Equations -- 8.5.2 The Simple Laser -- 8.5.3 The Classical Combustion Model -- 8.5.4 Canards and Black Swan in a Model of a 3-DAutocatalator -- 8.5.4.1 Canard in the 3-D Autocatalator -- 8.5.4.2 Black Swan Construction -- 8.5.5 Gas Combustion in a Dust-Laden Medium -- 8.5.5.1 Autocatalytic Reaction -- 8.5.5.2 First-Order Reaction -- Chapter 9 Appendix: Proofs -- 9.1 The Existence and Properties of Bounded Solutions -- 9.1.1 Scalar Linear Equation -- 9.1.2 Scalar Nonlinear Equation -- 9.2 The Existence and Properties of Slow Integral Manifolds -- 9.3 Justification of Asymptotic Representation -- Bibliographical Remarks -- References -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.