
From Chaos to Complexity Science. 20 Years of Multidisciplinary Explorations
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Content
- Intro
- Contents
- Preface(
- Introduction
- Chapter 1
- Acceleration and Entropy: A Macroscopic Analogue of the Twin Paradox
- Chapter 2
- William James on Consciousness, Revisited(
- Abstract
- 1. Introduction
- 2. The Typology of Causality
- 3. Level 3 - Macroscopic: The Circular Causality of Intentionality
- 4. Level 2 - Mesoscopic: The Circular Causality of Reafference
- 5. Level 1 - Microscopic: Circular Causality among Neurons and Neural Masses
- 6. Circular Causality in Awareness
- 7. Consciousness Viewed as a System Parameter Controlling Chaos
- Conclusion
- Acknowledgments
- Ethical Compliance
- References
- Chapter 3
- The Structural Equations Technique for Testing Hypotheses in Nonlinear Dynamics: Catastrophes, Chaos and Related Dynamics(
- Abstract
- Overview
- Types and Amount of Data
- Statistical Power
- Optimal Time Lag
- Probability Density Functions
- Location
- Scale
- Structure of Behavioral Measurements
- Catastrophe Models
- Nonlinear Statistical Model
- Linear Comparison Models
- Exponential Model Series
- Lyapunov Models
- Bifurcation Models
- Linear Contrasts
- Tips for Using Nonlinear Regression
- Testing Catastrophes through Nonlinear Regression
- Examples on Record
- Ethical Compliance
- References
- Chapter 4
- Dynamical Prediction of Chaotic Time Series
- Chapter 5
- Synchronization of Oscillators in Complex Networks(
- Abstract
- 1. Introduction
- 2. Formal Development
- 2.1. Synchronization in Arbitrary, Coupled Systems
- 2.2. Beyond Linear Coupling
- 2.3. Networks and Graph Theory
- 3. Synchronization in Semirandom Smallworlds (Cycles)
- 3.1. Generation of Smallworld Cycles
- 3.2. Eigenvalues of Pristine Cycles
- 2.3. Eigenvalues of Smallworld Cycles
- 4. Synchronization in Scale-Free Networks
- 4.1. Generation of Scale-Free Networks
- 4.2. Eigenvalues of Pristine Scale-Free Networks
- 4.3. Eigenvalues of Scale-Free Networks
- 5. Hypercube Networks
- Conclusion
- Ethical Compliance
- References
- Chapter 6
- Contribution to the Debate on Linear and Nonlinear Analysis of the Electroencephalogram(
- Abstract
- Introduction
- Spectral Analysis
- Chaos and Noise in the Electroencephalogram
- Conclusion
- Acknowledgment
- Ethical Compliance
- References
- Chapter 7
- Detection of Transient Synchronization in Multivariate Brain Signals Application to Event-Related Potentials
- Chapter 8
- A Brief Note on Recurrence Quantification Analysis of Bipolar Disorder Performed by Using a Van Der Pol Oscillator Model
- Abstract
- 1. Introduction
- 2. The Bipolar Disorder
- 3. Qualitative Modeling of Bipolar Disorder by the Van Der Pol Mathematical Simulation
- 4. Quantitative Analysis of the Obtained Time Series Data
- 4.1. Gottschalk's Analysis of Correlation Dimension of Experimental Time Series
- 4.2. Analysis of Correlation Dimension of Van Der Pol Model Generated Time Series
- 4.3. Lyapunov Exponents Calculation
- 4.4. Recurrence Quantification Analysis
- 4.5. Coarse Graining Spectral Analysis
- 5. Discussion
- References
- Chapter 9
- Complex Dynamics of Visual Arts(
- Abstract
- 1. Introduction
- 2. Baker's Transform in -Space
- 3. Aesthetic Unstability Initiates Bifurcation
- 4. Self-Similarity in Art Space
- 5. Hierarchy of Complexity
- 5.1. Constancy
- 5.2. Linearity
- 5.3. Periodicity
- 5.4. Complexity
- 5.5. Chaos
- Conclusion
- Acknowledgments
- Appendix
- Artworks in Figure 12
- Artworks in Figure 13
- Artworks in Figure 14
- Ethical Compliance
- References
- Chapter 10
- Noninvertible Maps and Complex Basin Boundaries in Dynamic Economic Models with Coexisting Attractors
- Chapter 11
- Adaptive Synchronization of Two Different Uncertain Chaotic Systems
- Abstract
- 1. Introduction
- 2. System Definition and Problem Formulation
- 3. Adaptive Sliding Mode Controller Design
- 4. Numerical Simulations
- 4.1. Example 1
- 4.2. Example 2
- 4.3. Example 3
- Conclusion
- Acknowledgments
- Ethical Compliance
- References
- Chapter 12
- Extended Prigogine Theorem: Method for Universal Characterization of Complex System Evolution
- Abstract
- Abbreviations
- 1. Introduction
- 2. Entropy Demarcation Criterion
- 3. Universal Prigogine Theorem
- Conclusion
- Ethical Compliance
- References
- Chapter 13
- A Beginner's Guide to the Nature and Potentialities of Dynamical and Network Theory, Part I: A Very Very Brief Visual Introduction to the Theory of Dynamical Systems
- 1. Dynamical Systems
- 2. The Vectorfield
- 3. Trajectories
- 4. Basic Attractors
- 5. Basic Features Revealed in the Portrait: Attractors, Repellors, Saddles, Insets, Outsets, Basins, Separatrices
- 6. Response Diagrams
- 7. Bifurcations
- 8. Characteristic Properties in Portraits
- 9. Stability
- 10. Chaos
- 11. Dynamical Bifurcation Theory
- 12. Self-Organization, Networks, and Control Theory
- 13. Perspectives for Psychotherapy
- A. Stability, Instability, and Bifurcation
- B. Mid-Dimensional Chaos and Creativity
- C. Evaluation of Initial Conditions
- D. Evaluation of Research
- 14. The Antinomy of Dynamics
- Acknowledgments and Dedication
- Ethical Compliance
- References
- Chapter 14
- A Simple Model of Intermittent Chaos
- Chapter 15
- Synchronization of Fractals in Logarithmic Spirals
- Abstract
- Introduction
- Binding and Synchronization
- Three Ways of Representing Dynamics in Brain Activity
- Julia Sets Derived from Equations 1 and 2
- Discontinuities in Various Forms of Transient Synchronous Series
- Singularity in Time and in Processing
- Conclusion
- Ethical Compliance
- References
- Chapter 16
- Chaos in Returns and Volatilities of the London Gold Fix
- Abstract
- 1. Introduction
- 2. Data and Methodology
- 3. Empirical Results
- Conclusion
- References
- Editor Contact Information
- Index
- Blank Page
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