Synergetics

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Foreword Series Preface Volume Preface Bibliography Contents About the Editor-in-Chief Biography Education About the Volume Editors Contributors Synergetics: An Introduction Synergetics: Basic Concepts Glossary The Role of Synergetics in Science The Laser Paradigm The Hierarchical Structure of Synergetics Basic Equations Method of Solution Instability of a Fixed Point Instability of a Limit Cycle, q0(t) (Haken 2004b) Instability of Tori (Haken 2004b) A Remark on the Method of Solution of Evolution Eq. (1) Quantum Theoretical Formulation Quantum-Classical Correspondence Regular Spatial and Spatio-Temporal Patterns Infinite Boundaries Theory, Representation Theory, Finite Boundaries A Further Mathematical Tool: Shannon Information and the Maximum (Information) Entropy Principle Phenomenological Synergetics Semantic Synergetics Some Selected Examples History and Relations to Other Fields Future Directions Bibliography Primary Literature Books and Reviews Laser Dynamics and Delayed Feedback Glossary Definition of the Subject Introduction Dynamic Timescales and Relaxation Oscillations Optical Feedback (Class-B Lasers) Optical Feedback of Class-C Lasers Optical Feedback of Two-State QD Lasers Future Directions Bibliography Fluid Dynamics, Pattern Formation Glossary Definition of the Subject Introduction The Basic Equations of Fluid Dynamics Continuity Equation Euler Equations Navier-Stokes Equations Incompressible Fluids with a Small Reynolds Number Transport Equations Surface Waves Gravity Waves Shallow Water Equations Numerical Solutions Instabilities Parametric Excitation of a Thin Bistable Fluid Layer Instabilities Mechanisms of Instability in Fluids Pattern Formation - Examples Types of Instabilities Order Parameter Equations Order Parameters The Ginzbur-Landau Eq. The Swift-Hohenberg Equation Conserved Order Parameter Fields Thin Films Phase Field Models The Fluid Density as Phase Field Future Directions Bibliography Primary Literature Books and Reviews Patterns and Interfaces in Dissipative Dynamics Glossary Definition of the Subject Introduction Stationary Patterns Symmetry-Breaking Transitions Selection of Stationary Patterns Modulated and Distorted Patterns Phase Dynamics Dynamics of Defects Moving Interfaces Stationary and Propagating Fronts Interfacial Instabilities Front Interactions and Coarsening Structures Built up of Fronts Interfaces of Patterns Wave Patterns Plane Waves Spiral and Scroll Waves Spiral Patterns and Turbulence Forced Systems Future Directions Bibliography Primary Literature Books and Reviews Fluid Dynamics: Turbulence Glossary Definition of the Subject Introduction The Basic Hydrodynamic Equations Ideal Fluids: Euler´s Equation Newtonian Fluids: Navier-Stokes Equation Vorticity Formulation of Incompressible Fluid Dynamics Lagrangian Formulation of Incompressible Fluid Dynamics Existence and Smoothness Results Vortex Solutions of the Navier-Stokes Equation Axisymmetric Vortices: Lamb-Oseen Vortex The Lundgren Spiral Stretched Vortices Vorticity Alignment Modeling Turbulent Fields by Random Vortex Distributions Patterns, Chaos, and Turbulence Pattern Formation and Routes to Chaos in Fluid Dynamics Point Vortex Motion Onsager´s Statistical Theory of Two-Dimensional Turbulence Extension to Three Dimensions Turbulence: Determinism and Stochasticity Statistical Averages Hierarchy of Moment Equations Evolution Equations for Probability Distributions Functional Equations Path Integral Formulation Reynolds Equation and Turbulence Modeling The Fine Structure of Turbulence Increments Length and Time Scales in Turbulent Flows The Integral Scale The Kolmogorov Scales Relation Between the Integral and the Kolmogorov Length Scale The Taylor Length and the Taylor-Based Reynolds Number Statistics of Increments: Structure Functions Kolmogorov´s 4/5 Law Phenomenological Theories of Turbulence Kolmogorov´s Theory K41: Self-Similarity in the Inertial Range Failure of K41: Intermittency Kolmogorov´s Theory K62 The Multifractal Model Multiscale Analysis of Turbulent Fields Statistics Across Scales Markovian Properties Estimation of the Conditional Probability Distribution Path Integral Representation of the N-Scale Probability Distribution Statistics of Longitudinal and Transversal Components Lagrangian Fluid Dynamics Future Directions Further Reading Acknowledgments Bibliography Recent Advances in Quantum Chaos of Generic Systems Introduction Quantum Properties of Classically Integrable Systems Quantum Chaos of Classically Fully Chaotic (Ergodic) Systems Quantum Chaos of Classically Generic (Mixed-Type) Systems Quantum Phase Space: The Wigner Functions Principle of Uniform Semiclassical Condensation (PUSC) of Wigner Functions of Eigenstates Spectral Statistics in the Mixed-Type Phase Space Dynamical Localization of the Chaotic Eigenstates The Billiard Systems and Poincaré-Husimi Functions The Localization Measures Discussion and Conclusions Acknowledgments References Linear and Nonlinear Fokker-Planck Equations Glossary Definition of the Subject Introduction Desai-Zwanzig Model Liquid Crystal Model Winfree and Kuramoto Model Vlasov-Fokker-Planck Model Nonlinear Diffusion Equation, Nonextensive Thermostatistics, and Semiclassical Descriptions of Quantum Systems Time-Dependent Solutions and First-Order Statistics Linear Case Nonlinear Case Markov Property: Second-Order and Higher-Order Statistics Conditional Probability Densities Linear Fokker-Planck Equations Langevin Equations of Linear Fokker-Planck Equations Strongly Nonlinear Fokker-Planck Equations Langevin Equations of Strongly Nonlinear Fokker-Planck Equations Short-Time Propagator Chapman-Kolmogorov Equation, Kramers-Moyal Expansion, and Drift-Diffusion Estimates Chapman-Kolmogorov Equation Kramers-Moyal Expansion Drift-Diffusion Estimates Martingales From Strongly Nonlinear Fokker-Planck Equations to Martingales From Martingales to Strongly Nonlinear Fokker-Planck Equations Examples Shimizu-Yamada Model Dynamic Takatsuji Model Liquid Crystal Model Semiclassical Description of Quantum Systems Nonextensive Systems Linear Nonequilibrium Thermodynamics Summary and Future Directions Bibliography Additive Noise Tunes the Self-Organization in Complex Systems Glossary Introduction Slaving Principle and Center Manifold Theorem At the Stability Threshold About the Stability Threshold Additive Noise in Low-Dimensional Models: Stochastic Center Manifold Theory Nondelayed Systems Delayed Systems Additive Noise in Discrete Network Models Neural Mass Network Analysis of the Global Synchronization Coupling Induces Self-Organization in the Presence of Noise and Noise Affects System Frequency Noise Can Destruct Self-Organization While It Changes the System Frequency Synchronization in a Spiking Neural Network Future Directions Bibliography Chaotic Dynamics in Neural Systems Introduction Neuronal Activities and Transition Mechanisms Slow-Fast Decomposition Poincaré Mappings Classifications of Bursting Transition Routes Chaos in Neuron Models Leech Heart Interneuron Model: Period Doubling Cascades and the Blue Sky Catastrophe Period-Doubling in the Chay Model Torus Breakdown in the Bull Frog Hair Cell Model Chaotic Mixed-Mode Oscillations in the Extended Plant Model Acknowledgments Appendix Leech Heart Interneuron Model Chay Model Bibliography Shilnikov Chaos in Epilepsy Introduction Synergetics: Bottom-up Approach of Dimensionality Reduction DSBM: Data-Driven Method for Dimensionality Reduction Epileptic Seizures and Shilnikov Chaos An Ansatz to Model EEG Signals of Absence Seizures Shilnikov Chaos Shilnikov Chaos in Case of Epileptic Seizures? Data Dynamics Representation Shilnikov Condition Summary and Outlook Acknowledgments Bibliography Phase Synchronization in Neural Systems Glossary Definition of the Subject Introduction Micro- and Macroscopic Views Correlated Behavior and Phase Synchronization From Single Cell Dynamics to Neural Masses: Synchronization in a Neural Population Synchronization Between Neural Populations: Coupled Neural Masses Predicting Effects of Phase Synchronization Final Notes Summary Acknowledgments Bibliography Brain Pacemaker Glossary Definition of the Subject Introduction Standard High-Frequency Stimulation Coordinated Reset Stimulation Multisite Linear Delayed Feedback Nonlinear Delayed Feedback Mixed Nonlinear Delayed Feedback Proportional-Integro-Differential Feedback Plasticity Closed-Loop DBS Summary Bibliography Self-Organization in Clinical Psychology Definition of the Subject Introduction Dynamic Diseases Self-Organized Synchronization Patterns in Peripheral Physiological Systems Nonlinear Dynamics in the Communication of Patient and Therapist Self-Organization in Human Change Processes The Concept of Self-Organization Promotes New Information Technologies in Clinical Psychology - The Synergetic Navigation Syst... The Self-Organizing Brain Future Directions Bibliography Movement Coordination Glossary Definition of the Subject Introduction The Basic Law of Coordination: Relative Phase Stability: Perturbations and Fluctuations The Oscillator Level Oscillators for Limb Movements The Coupling Breaking and Restoring Symmetries Symmetry Breaking Through the Components Asymmetry in the Mode of Coordination Transitions to Anti-phase Conclusions Extensions of the HKB Model Future Directions Acknowledgments Bibliography Primary Literature Books and Reviews Determinisms of Behavior and Synergetics Glossary Definition of Subject Introduction Skinner and Determinism Synergetics, Amplitude Equations, and Behavior Application 1: Grasping of Objects with Different Sizes Application 2: Walk-Run Transitions Application 3: Action Chains and Child Play General Aspects of the Modeling Framework Conclusions Future Directions Bibliography Intentionality: Steps Towards Naturalization on the Basis of Complex Dynamical Systems Glossary Definition of the Subject Introduction Intentionality and Representation Synergetics Discussion: A Structural Science Concept of Intentionality Aboutness Functionality Mental-Likeness Future Directions Bibliography Primary Literature Books and Reviews Self-Organization and the City Glossary Definition of the Subject Introduction What Is a City? Explicit Attempts to Define a City Images of Cities The Economic City The City as a Central Place The City as a Node in a System of Cities The Ecological City The City as a Representation of Society The City as a Sociocultural Force The Postmodern City The Self-Organizing City In What Sense Are Cities Self-Organized Systems? The Inconsistency Between Self-Organization and Planning Complexity Theories of Cities: An Overview Dissipative Cities Synergetic Cities Slow Cities and Fast Regions Pattern Formation and Pattern Recognition in the City Chaotic Cities Fractal Cities Cellular Automata Cities AB and FACS Cities Sandpile Cities Small World Cities Self-Organization and the City SIRN: Synergetic Inter-representation Networks The Basic SIRN Model The City Game Cognition and the City Information Compression, Inflation, and Adaptation CogCity Planning and Design Planning Design A Self-Planned/Self-Designed City Prediction, Planning, Self-Organization and Cities Urbanism Complexity and Urbanism Future Directions Bibliography Financial Market Dynamics: A Synergetic Perspective Glossary Introduction Price Dynamics Data Stylized Facts of Markets Financial Market Modeling Predator-Prey, Many Interacting Agents, and Spin Models Statistical Feedback Models Multi-timescale Models Cross-Sectional Dynamics Simulations Final Comments Future Directions Bibliography Industrial Society´s Natural Future Introduction Industry Economy Human Nature Finance Details Outlook Conclusion Acknowledgments Appendix Natural Constants of the Human Species Main Variables of the Industrial Society Evaluating National Policy Bibliography Index