The Impact of Chaos on Science and Society (UNU, 1997, 415 pages) |

(introduction...) |

Preface |

1. Chaotic dynamics |

(introduction...) |

Abstract |

I. Introduction |

II. Measuring Chaos |

III. Routes to chaos |

IV. Chaos in physical systems |

V. Noise and computer round-off errors |

VI. Hamiltonian systems |

VII. Symbolic dynamics |

VIII. Concluding remarks |

References |

2. Chaos and politics: applications of nonlinear dynamics to socio-political issues |

(introduction...) |

Abstract |

I. Introduction |

II. The evolution of simple models for population dynamics |

III. Predicting the weather: An intuitive example of chaotic dynamics |

IV. Chaotic dynamics and arms-race models |

V. Future outlook |

VI. Discussion and conclusions: The lessons of nonlinearity |

Notes |

References |

3. Is the EEG a strange attractor? Brain stem neuronal discharge patterns and electroencephalographic rhythms |

(introduction...) |

I. Introduction |

II. The EEG as a global nonlinear oscillator: Quasiperiodic, ( |

III. The neocortical source of the EEG signal |

IV. Hierarchical noise driving of the hierarchical modes of the EEG by brain stem neurons |

V. Deterministic and random models of hierarchical neuronal discharge patterns |

VI. Stochastic resonance and quasiperiodicity in single neuron-neocortical dynamics |

VII. Single neuron dynamics and the EEG: Two clinical examples |

VIII. Summary |

References |

4. The impact of chaos on mathematics |

(introduction...) |

Abstract |

I. Introduction: A historical view |

II. The Lorenz attractor |

III. The Feigenbaum bifurcation |

IV. Hydrodynamic turbulence |

V. Ergodic theory of differentiable dynamical systems: Axiom A systems |

VI. Ergodic theory of differentiable dynamical systems: General systems |

VII. Quadratic maps of the interval and the HÃ©non attractor |

VIII. Zeta functions |

IX. Conclusion |

References |

5. Chaos in neural networks |

(introduction...) |

Abstract |

I. Introduction |

II. Chaotic dynamics in nerve membranes |

III. Chaos in biological neural networks |

IV. Chaos in artificial neural networks |

V. Discussion |

References |

6. The impact of chaos on physics |

7. Chaos and physics |

(introduction...) |

Determinism versus probabilism |

A class of ubiquitous phenomena |

The impact of physics on chaos |

The problem of quantum chaos |

Is there new physics in chaos? |

Does chaos bring a new fundamental principle into physics? |

Acknowledgements |

Notes |

References |

8. Irreversibility and quantum chaos |

(introduction...) |

Abstract |

I. Introduction |

II. Quantum suppression of classical chaos |

III. Recovery of chaos |

IV. Stationary dissipation |

References |

9. Impact of high-dimensional chaos: A further step towards dynamical complexity |

(introduction...) |

I. From chaos to high-dimensional chaos |

II. From spatio-temporal chaos to turbulence |

III. High-dimensional chaos as the basis of statistical mechanics |

IV. Network of chaotic elements |

V. Neural information processing with high-dimensional chaos |

VI. Homeochaos in biological networks |

Acknowledgements |

Notes |

References |

10. The impact of chaos on biology: Promising directions for research |

(introduction...) |

Abstract |

Introduction |

Persistence and extinction in animal populations |

Periodicity in chaos |

Conclusion |

Acknowledgements |

Notes |

References |

Appendix. The difficulties of finding chaos in biological data |

11. Dynamical disease - The impact of nonlinear dynamics and chaos on cardiology and medicine |

(introduction...) |

Abstract |

I. Introduction - Chaos and dynamical disease |

II. Chaos in physiological experiments and medicine |

III. Nonlinear dynamics in cardiology |

IV. Summary and conclusions |

Acknowledgements |

References |

12. The impact of chaos on meteorology |

(introduction...) |

I. Introduction |

II. Local and global properties |

III. The middle-latitude jet as a dynamical system |

IV. Conclusions |

References |

13. The concept of chaos in the problem of earthquake prediction |

(introduction...) |

Abstract |

Nonlinear dynamics and earthquake-prone faults |

Modelling |

Prediction |

Conclusion |

References |

14. The impact of chaos on engineering |

(introduction...) |

Introduction |

The role of geometrical theory in applied mechanics |

Transient failure |

The influence of chaotic transients |

Conclusions |

Acknowledgements |

References |

15. The impact of chaos on economic theory |

(introduction...) |

I. Introduction |

II. Impediments to chaos in economics |

III. Empirical investigations |

IV. Theoretical investigations |

V. Conclusions |

References |

16. Chaos in society: Reflections on the impact of chaos theory on sociology |

(introduction...) |

I |

II |

III |

IV |

V |

Notes |

References |

17. Strange attractors and the origin of chaos |

(introduction...) |

I. Prologue |

II. The oldest chaos in a non-autonomous system - A shattered egg |

III. Encounter with the Japanese attractor |

IV. The Hayashi Laboratory at the time of the ''McGraw-Hill Book'' |

V. From the harmonic balance method to the mapping method |

VI. The true value of an advisor: A scion of chaos |

VII. The end of the Chihiro Hayashi Laboratory |

VIII. The original data that were preserved |

IX. Epilogue |

Acknowledgements |

References |

Panel discussion: The impact of chaos on science and society |

Opening address |

Contributors |

Other titles of interest |

**Technological Independence****The Asian Experience**

*Edited by Saneh Chamarik and Susantha Goonatilake*

Focusing on the importance of technology as a key to development, this volume examines the experiences, efforts, and perspectives of technological development in six Asian countries: China, India, Japan, Korea, the Philippines, and Thailand.

ISBN 92-808-0758-7

US$30

**Human Rights and Scientific and Technological Development**

*Edited by C. G. Weeramantry*

The present work represents an effort to develop a conceptual framework for the study of the interactions between human rights and scientific and technological development and review the current state of research in the area.

ISBN 92-808-0731-5

US$30

**The Impact of Technology on Human Rights****Global
Case-studies**

*Edited by C.G. Weeramantry*

This book is a sequel to *Human Rights and Scientific and
Technological Development* and follows on the theoretical discussion
concerning the interrelation between scientific and technological development
and human rights presented in the earlier volume. The present study comprises
five case-studies from Africa, Asia, Europe, and Latin America that look closely
at the impact of different technologies on human rights.

ISBN 92-808-0821-4

US$38

**Information Technology in Selected Countries****Reports
from Ireland, Ethiopia, Nigeria, and Tanzania**

*Edited by Eileen P. Drew and F. Gordon Foster*

Taking as a point of departure experiences in Ireland with processes of information technology innovation, this study explores in three country studies the main features of innovation in the 1970s and 1980s with the aim of providing insights and comparison tor further development.

ISBN 92-808-0831-1

US$27

WITHIN THE PAST DECADE there has been an explosion of interest in chaotic dynamics. Prompted by the growing body of knowledge about chaotic behaviour in an increasing number of scientific disciplines, a distinguished group of experts assemble in this volume to evaluate the impact that chaos has had on the conduct of science and on our understanding of society.

Presented here are contributions from mathematicians, physicists, biological and medical scientists, geoscientists, engineers, economists, and social scientists - including pioneers and world leaders in research on chaos. The result is a lively and stimulating international, interdisciplinary exchange of experiences and ideas on chaotic phenomena. The volume concludes with an exchange among the experts on the past and possible future impacts chaos has had in the physical and social sciences. This book offers an assessment of the general impact of chaos theory and, it is hoped, will further enhance the interaction among scientists who may discover that chaotic dynamics play an important part in their respective fields.

Readers will find here a unique documentation of the history of the development of chaos theory and record of a historic interaction among the founders of this field.

**Dr. Celso Grebogi** is Professor of Mathematics and
Distinguished Research Fellow at the University of Maryland, USA. He is a Fellow
of the American Physical Society and has been awarded the Senior Humboldt Prize,
the Toshiba Chair, and Fulbright Fellowship.

**Dr. James A. Yorke** is Distinguished Professor of
Mathematics and Director, the Institute for Physical Sciences and Technology, at
the University of Maryland, USA. He was awarded the Guggenheim Fellowship in
1980 and is widely known as the coiner of the term "chaos."

**United Nations University Press**

TOKYO · NEW YORK
· PARIS

UNUP-882

ISBN
92-808-0882-6