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 Hénon 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