CHAOS AND COMPLEXITY RESEARCH PROGRESS

CHAOS AND COMPLEXITY RESEARCH PROGRESS

Library of Congress Cataloging-in-Publication Data

CONTENTS

PREFACE

Chapter 1: DYNAMICAL PREDICTION OF CHAOTIC TIME SERIES

1. Introduction

2. Dynamical Networks

3. Prediction of future evolution

4. Cross prediction

5. Conclusion

6. Acknowledgement

7. References

Chapter 2: DYNAMICS AS A HEURISTIC FRAMEWORK FOR PSYCHOPATHOLOGY

Abstract

1. Introduction

1.1. Explanation levels in psychopathology

1.2. How dynamic are mental diseases?

1.3. From dynamical diseases to psychopathology

2. Metaphors

2.1. The ’Self’ as a dynamical system

2.2. Dynamical metaphors for the psychotherapeutic processes

2.3. Conclusion

3. Qualitative

3.1. Gradient systems

3.2. Neural networks

3.2.1. Models of syndromes

3.2.2. Time-course of affective disorders

3.3. Conclusion

4. Quantitative

4.1. Data fitting

4.2. Time series analysis

4.2.1. Brain dynamics

4.2.2. Symptoms dynamics and therapies

4.2.3. Dynamics of cognitive processes

4.2.4. Clinical Interviews

4.2.5. Family system

4.3. Conclusion

5. Conclusion

References

Chapter 3: COLLECTIVE PHENOMENA IN LIVING SYSTEMS AND IN SOCIAL ORGANIZATIONS

Abstract

1. INTRODUCTION

2. SOME MODELS OF COLLECTIVE BEHAVIOURS IN BIOLOGICAL SYSTEMS

3. A NEW APPROACH TO COLLECTIVE BEHAVIOUR DESCRIPTION AND A PROTOTYPICAL EXAMPLE

CONCLUSION

REFERENCES

Chapter 4: CONTRIBUTION TO THE DEBATE ON LINEAR AND NONLINEAR ANALYSIS OF THE ELECTROENCEPHALOGRAM

ABSTRACT

INTRODUCTION

SPECTRAL ANALYSIS

CHAOS AND NOISE IN THE ELECTROENCEPHALOGRAM

CONCLUDING REMARKS

ACKNOWLEDGMENTS

REFERENCES

Chapter 5: COMPLEX DYNAMICS OF VISUAL ARTS

ABSTRACT

1. INTRODUCTION

2. BAKER’S TRANSFORM IN Ψ -SPACE

3. AESTHETIC UNSTABILITY INITIATES BIFURCATION

4. SELF-SIMILARITY IN ART SPACE

5. HIERARCHY OF COMPLEXITY

6. CONCLUSION

ACKNOWLEDGEMENT

7. REFERENCES

APPENDIX

Artworks in Figure 12

Artworks in Figure 13

Artworks in Figure 14

Chapter 6: THE MYTH OF THE TOWER OF BABYLON AS A SYMBOL OF CREATIVE CHAOS

Chapter 7: MEASURES OF COUPLING STRENGTH AND SYNCHRONIZATION IN NON LINEAR INTERACTION OF HEART RATE AND SYSTOLIC BLOOD PRESSURE IN THE CARDIOVASCULAR CONTROL SYSTEM

ABSTRACT

1. INTRODUCTION

2. MATERIALS AND METHODS

2.1. Experimental Protocol and Data Acquisition

2.2. Preprocessing Data. Testing for Non Stationarity and Non Linearity

3. ANALYSIS OF THE DATA

3.1. Estimate of Coupling between R-R Intervals and SBP

3.2. Recurrence Quantification Analysis and Cross Recurrence Quantification Analysis

4. RESULTS AND CONCLUSION

ACKNOWLEDGEMENTS

REFERENCES

Chapter 8: FILTERING TIME SERIES USING POINT-WISE DIMENSION: APPLICATION TO THE STUDY OF ELECTROCARDIOGRAMS

ABSTRACT

1. INTRODUCTION

2. METHOD

2.1. The Filtering Procedure

3. SIGNALS

4. RESULTS AND DISCUSSION

5. CONCLUSION

REFERENCES

Chapter 9: NON PERIODIC CYCLES IN ITALIAN FINANCIAL MARKET

INTRODUCTION

1. PROCEDURE

2. AN APPLICATION

3. FURTHER RESEARCH

REFERENCES

Chapter 10: NONINVERTIBLE MAPS AND COMPLEX BASIN BOUNDARIES IN DYNAMIC ECONOMIC MODELS WITH COEXISTING ATTRACTORS

Abstract

1. Introduction

2. Discrete Dynamical Systems, Noninvertible Maps and Critical Curves

3. A Nonlinear Duopoly Game with Multiple Nash Equilibria

3.1. Nash Equilibria and their Local Stability

3.2. Critical Curves and Structure of the Basins

3.2.1. Basin of Infinity

3.2.2. Basins of Coexisting Bounded Attractors and their Global Bifurcations

3.2.3. More Complex Attractors

4. Conclusions

Appendix A. The attractivity of infinity

Appendix B. Local stability analysis of the fixed points

B.1. Homogeneous case

B.2. Non homogeneous case

References

Chapter 11: PHASE-PORTRAIT IN CONVERSATION-PROCESSES

ABSTRACT

1. INTRODUCTION

2. DELAY COORDINATES

3. RESULTS

4. CONCLUSION

REFERENCES

Chapter 12: OPTION PRICING: A STRAIGHTFORWARD PROCEDURE

ABSTRACT

1. INTRODUCTION

2. THE DISCRETE TIME HOMOGENEOUS SEMI-MARKOV MODEL

3. THE EVOLUTION EQUATION SOLUTION

4. DESCRIPTION OF DATA

5. THE CONSTRUCTION OF THE INPUT MODEL

6. RESULTS AND CONCLUDING REMARKS

ACKNOWLEDGEMENTS

REFERENCES

Chapter 13: THE RIEMANN MAGNETON OF THE PRIMES*

ABSTRACT

1. INTRODUCTION

2. THE FORMULATION AND THE COMPUTATIONS

3. ANALYTICAL COMPUTATIONS

4. CONCLUDING REMARKS AND FUTURE WORK

ACKNOWLEDGEMENTS

REFERENCES

Chapter 14: SELF-ORGANIZED POWER-LAW EQUILIBRIUM DISTRIBUTIONS IN STRUCTURED DYNAMICAL SYSTEMS

Abstract

1. Introduction

2. Power Laws: The Signature of Self-Organization

2.1. Example I: Size-Abundance Distributions in Plant Communities

2.2. Example II: Species Packing in Hierarchical Competition-Colonization Models

3. Concluding Remarks

References

Chapter 15: CLIMATIC MEMORY

ABSTRACT

REFERENCES

Chapter 16: ON THE COMPLEX FOUNDATION OF ETHICS

INDEX