03930nam 22006255 450 991048324940332120200704210709.03-030-36399-610.1007/978-3-030-36399-4(CKB)4100000010480363(DE-He213)978-3-030-36399-4(MiAaPQ)EBC6121774(PPN)24298066X(EXLCZ)99410000001048036320200221d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierGeometric Singular Perturbation Theory Beyond the Standard Form /by Martin Wechselberger1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (X, 137 p. 42 illus., 40 illus. in color.) Frontiers in Applied Dynamical Systems: Reviews and Tutorials,2364-4532 ;63-030-36398-8 Includes bibliographical references.Introduction -- Motivating examples -- A coordinate-independent setup for GSPT -- Loss of normal hyperbolicity -- Relaxation oscillations in the general setting -- Pseudo singularities & canards -- What we did not discuss.This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.Frontiers in Applied Dynamical Systems: Reviews and Tutorials,2364-4532 ;6DynamicsErgodic theoryOperator theoryDifferential equationsDynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XOperator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Ordinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Dynamics.Ergodic theory.Operator theory.Differential equations.Dynamical Systems and Ergodic Theory.Operator Theory.Ordinary Differential Equations.515.39515.48515.39Wechselberger Martinauthttp://id.loc.gov/vocabulary/relators/aut1017959MiAaPQMiAaPQMiAaPQBOOK9910483249403321Geometric Singular Perturbation Theory Beyond the Standard Form2391156UNINA