LEADER 03932nam 22006135 450 001 996418272803316 005 20200704210709.0 010 $a3-030-36399-6 024 7 $a10.1007/978-3-030-36399-4 035 $a(CKB)4100000010480363 035 $a(DE-He213)978-3-030-36399-4 035 $a(MiAaPQ)EBC6121774 035 $a(PPN)24298066X 035 $a(EXLCZ)994100000010480363 100 $a20200221d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Singular Perturbation Theory Beyond the Standard Form$b[electronic resource] /$fby Martin Wechselberger 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (X, 137 p. 42 illus., 40 illus. in color.) 225 1 $aFrontiers in Applied Dynamical Systems: Reviews and Tutorials,$x2364-4532 ;$v6 311 $a3-030-36398-8 320 $aIncludes bibliographical references. 327 $aIntroduction -- 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. 330 $aThis volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales. 410 0$aFrontiers in Applied Dynamical Systems: Reviews and Tutorials,$x2364-4532 ;$v6 606 $aDynamics 606 $aErgodic theory 606 $aOperator theory 606 $aDifferential equations 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aOperator theory. 615 0$aDifferential equations. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aOperator Theory. 615 24$aOrdinary Differential Equations. 676 $a515.39 676 $a515.48 700 $aWechselberger$b Martin$4aut$4http://id.loc.gov/vocabulary/relators/aut$01017959 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418272803316 996 $aGeometric Singular Perturbation Theory Beyond the Standard Form$92391156 997 $aUNISA