Synergetics

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