LEADER 03722nam 22005535 450 001 9910483695903321 005 20200706025519.0 010 $a3-030-35987-5 024 7 $a10.1007/978-3-030-35987-4 035 $a(CKB)4100000010480362 035 $a(DE-He213)978-3-030-35987-4 035 $a(MiAaPQ)EBC6120124 035 $a(PPN)242980651 035 $a(EXLCZ)994100000010480362 100 $a20200222d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aModeling with Nonsmooth Dynamics /$fby Mike R. Jeffrey 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (VIII, 104 p. 28 illus., 15 illus. in color.) 225 1 $aFrontiers in Applied Dynamical Systems: Reviews and Tutorials,$x2364-4532 ;$v7 311 $a3-030-35986-7 327 $aMathematics for a nonsmooth world -- 1930-2010: Nonsmooth dynamics? linear age -- Discontinuities to model missing knowledge -- Three experiments -- Layers and implementations -- Ideal and non-ideal sliding -- The three experiments revisited -- Further curiosities of hidden dynamics -- Closing remarks: open challenges. . 330 $aThis volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ?non-smooth? definition. A review of current ideas and introduction to key methods is given, with a view to opening discussion of a major open problem in our fundamental understanding of what nonsmooth models are. What does a nonsmooth model represent: an approximation, a toy model, a sophisticated qualitative capturing of empirical law, or a mere abstraction? Tackling this question means confronting rarely discussed indeterminacies and ambiguities in how we define, simulate, and solve nonsmooth models. The author illustrates these with simple examples based on genetic regulation and investment games, and proposes precise mathematical tools to tackle them. The volume is aimed at students and researchers who have some experience of dynamical systems, whether as a modelling tool or studying theoretically. Pointing to a range of theoretical and applied literature, the author introduces the key ideas needed to tackle nonsmooth models, but also shows the gaps in understanding that all researchers should be bearing in mind. Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics, specializing in dynamics, singularities, and asymptotics. 410 0$aFrontiers in Applied Dynamical Systems: Reviews and Tutorials,$x2364-4532 ;$v7 606 $aDynamics 606 $aErgodic theory 606 $aMathematical models 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aMathematical models. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aMathematical Modeling and Industrial Mathematics. 676 $a515.64 676 $a515.39 700 $aJeffrey$b Mike R$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768265 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483695903321 996 $aModeling with Nonsmooth Dynamics$92301696 997 $aUNINA