LEADER 05926nam 22008775 450 001 9910437767103321 005 20200702051739.0 010 $a3-642-33552-7 024 7 $a10.1007/978-3-642-33552-5 035 $a(CKB)3400000000086118 035 $a(EBL)1082697 035 $a(OCoLC)811563989 035 $a(SSID)ssj0000767120 035 $a(PQKBManifestationID)11429479 035 $a(PQKBTitleCode)TC0000767120 035 $a(PQKBWorkID)10733010 035 $a(PQKB)10703322 035 $a(DE-He213)978-3-642-33552-5 035 $a(MiAaPQ)EBC1082697 035 $a(MiAaPQ)EBC6312271 035 $a(PPN)168324822 035 $a(EXLCZ)993400000000086118 100 $a20120923d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNonlinear Dynamics in Complex Systems$b[electronic resource] $eTheory and Applications for the Life-, Neuro- and Natural Sciences /$fby Armin Fuchs 205 $a1st ed. 2013. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013. 215 $a1 online resource (236 p.) 300 $aDescription based upon print version of record. 311 $a3-642-33551-9 320 $aIncludes bibliographical references (pages [229]-230) and index. 327 $aPart I Nonlinear Dynamical Systems -- Introduction -- One-dimensional Systems -- Two-Dimensional Systems -- Higher-Dimensional Systems and Chaos -- Discrete Maps and Iterations in Space -- Stochastic Systems -- Part II: Model Systems -- Haken-Kelso-Bunz (HKB) Model -- Self-organization and Synergetics -- Neuronal Models -- Part III: Mathematical Basics -- Mathematical Basics -- The Coupled HKB System -- Numerical Procedures and Computer Simulations -- Solutions. 330 $aWith many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz model), self-organization and pattern formation in complex systems (Synergetics), and models of dynamical properties of neurons (Hodgkin-Huxley, Fitzhugh-Nagumo and Hindmarsh-Rose). Part III may serve as a refresher and companion of some mathematical basics that have been forgotten or were not covered in basic math courses. Finally, the appendix contains an explicit derivation and basic numerical methods together with some programming examples as well as solutions to the exercises provided at the end of certain chapters. Throughout this book all derivations are as detailed and explicit as possible, and everybody with some knowledge of calculus should be able to extract meaningful guidance follow and apply the methods of nonlinear dynamics to their own work.?This book is a masterful treatment, one might even say a gift, to the interdisciplinary scientist of the future.??With the authoritative voice of a genuine practitioner, Fuchs is a master teacher of how to handle complex dynamical systems.??What I find beautiful in this book is its clarity, the clear definition of terms, every step explained simply and systematically.?(J.A.Scott Kelso, excerpts from the foreword). 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aStatistical physics 606 $aDynamical systems 606 $aDynamics 606 $aErgodic theory 606 $aVibration 606 $aSystem theory 606 $aNeurosciences 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aNeurosciences$3https://scigraph.springernature.com/ontologies/product-market-codes/B18006 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aVibration. 615 0$aSystem theory. 615 0$aNeurosciences. 615 14$aMathematical and Computational Engineering. 615 24$aComplex Systems. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aVibration, Dynamical Systems, Control. 615 24$aSystems Theory, Control. 615 24$aNeurosciences. 676 $a003/.75 700 $aFuchs$b Armin$4aut$4http://id.loc.gov/vocabulary/relators/aut$01064325 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437767103321 996 $aNonlinear Dynamics in Complex Systems$92537398 997 $aUNINA