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Nonlinear Dynamics in Complex Systems: Theory and Applications for the Life-, Neuro- and Natural Sciences

Nonlinear Dynamics in Complex Systems: Theory and Applications for the Life-, Neuro- and Natural Sciences
Kataloginformation
Feldname Details
Vorliegende Sprache eng
Hinweise auf parallele Ausgaben 373254245 Buchausg. u.d.T.: ‡Fuchs, Armin: Nonlinear dynamics in complex systems
ISBN 978-3-642-33551-8
Name Fuchs, Armin
T I T E L Nonlinear Dynamics in Complex Systems
Zusatz zum Titel Theory and Applications for the Life-, Neuro- and Natural Sciences
Verlagsort Berlin ; Heidelberg
Verlag Springer
Erscheinungsjahr 2013
2013
Umfang Online-Ressource (XIV, 236 p. 117 illus, digital)
Reihe SpringerLink. Bücher
Notiz / Fußnoten Description based upon print version of record
Weiterer Inhalt Title; Foreword; Preface; Contents; Part INonlinear Dynamical Systems; Introduction; Complex Systems; Differential Equations - The Basics; First Steps; Terminology - Dynamical Systems Jargon; A First Encounter with Phase Space; Limitations of Linear Systems; One-dimensional Systems; Linear Stability Analysis; A Quantitative Measure of Stability; Bistability, Multistability and Qualitative Change; Exotic Cases: When Linear Stability Analysis Breaks Down; Potential Functions; Bifurcation Types; Saddle-Node Bifurcation; Transcritical Bifurcation; Supercritical Pitchfork Bifurcation. Subcritical Pitchfork BifurcationSystems with Hysteresis; Periodic One-Dimensional Systems; Problems for Chapter 2; Two-Dimensional Systems; The Harmonic Oscillator; Second Order Systems - A First Look; Second Order Systems - A Second Look; Damped Harmonic Oscillator; Classification of Two-Dimensional Linear Systems; Nonlinear Systems: Linear Stability Analysis in Two Dimensions; Limit Cycles; Hopf Bifurcation; Potential Functions in Two-Dimensional Systems; Generalization of Potentials: Lyapunov Functions; Nonlinear Oscillators; Van-der-Pol Oscillator: N(x,"705Fx) = x2 "705Fx. Rayleigh Oscillator: N(x,"705Fx) = "705Fx3Hybrid Oscillator: N(x,"705Fx) = { x2 "705Fx, "705Fx3}; Poincaré-Bendixon Theorem; Problems for Chapter 3; Higher-Dimensional Systems andChaos; Periodicity and Quasi-periodicity; Lorenz System; Rössler System; Fractal Dimension; Lyapunov Exponents; Time Series Analysis; Discrete Maps and Iterations in Space; Logistic Map; Geometric Approach; Lyapunov Exponents; Hénon Map; Feigenbaum Constants; Using Discrete Maps to Understand Continuous Systems; Iterated Function Systems; Mandelbrot Set; Stochastic Systems; Brownian Motion; Features of Noise. How to Describe KicksAverages; Distributions; Properties of the Gaussian Distribution; Correlations; Colors of Noise; Langevin and Fokker-Planck Equation; Reconstruction of Drift and Diffusion Term; Multiplicative Noise; Mean First Passage Time; Fingerprints of Stochasticity; Problems for Chapter 6; Part IIModel Systems; Haken-Kelso-Bunz (HKB) Model; Basic Law of Coordination: Relative Phase; Stability: Perturbations and Fluctuations; Oscillator Level; Symmetry Breaking Through the Components; Self-organization and Synergetics; Haken-Zwanzig System; Lorenz Revisited; Formalism of Synergetics. Neuronal ModelsHodgkin-Huxley Model; Fitzhugh-Nagumo Model; Hindmarsh-Rose Model; Part IIIMathematical Basics; Mathematical Basics; Complex Numbers; Linear Systems of Equations; Eigenvalues and Eigenvectors; Taylor Series; Delta and Sigmoid Functions; The Coupled HKB System; Numerical Procedures and Computer Simulations; Solutions; References; Index;
Titelhinweis Buchausg. u.d.T.: ‡Fuchs, Armin: Nonlinear dynamics in complex systems
ISBN ISBN 978-3-642-33552-5
Klassifikation TBJ
MAT003000
*37-01
37-02
37Gxx
37Nxx
003.75
519
003/.75
TA329-348
TA640-643
SK 810
Kurzbeschreibung With 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
1. Schlagwortkette Nichtlineares dynamisches System
Komplexes System
1. Schlagwortkette ANZEIGE DER KETTE Nichtlineares dynamisches System -- Komplexes System
2. Schlagwortkette Nichtlineares dynamisches System
Komplexes System
ANZEIGE DER KETTE Nichtlineares dynamisches System -- Komplexes System
SWB-Titel-Idn 373498489
Signatur Springer E-Book
Bemerkungen Elektronischer Volltext - Campuslizenz
Elektronische Adresse $uhttp://dx.doi.org/10.1007/978-3-642-33552-5
Internetseite / Link Volltext
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