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020 _a9783642335525
_9978-3-642-33552-5
082 _a620
_223
100 _aFuchs, Armin.
_920112
245 _aNonlinear Dynamics in Complex Systems
_h[electronic resource] :
_bTheory and Applications for the Life-, Neuro- and Natural Sciences /
_cby Armin Fuchs.
250 _a1st ed. 2013.
260 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXIV, 238 p.
_bonline resource.
505 _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.
520 _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).
650 _aEngineering mathematics.
_920113
650 _aEngineering-Data processing.
_920114
650 _aSystem theory.
_920115
650 _aDynamical systems.
_920116
650 _aMultibody systems.
_920117
650 _aVibration.
_920118
650 _aMechanics, Applied.
_920119
650 _aControl theory.
_920120
650 _aNeurosciences.
_920121
650 _aMathematical and Computational Engineering Applications.
_920122
650 _aComplex Systems.
_920123
650 _aDynamical Systems.
_920124
650 _aMultibody Systems and Mechanical Vibrations.
_920125
650 _aSystems Theory, Control .
_920126
650 _aNeuroscience.
_920127
856 _uhttps://doi.org/10.1007/978-3-642-33552-5
942 _cEBK
999 _c13605
_d13605