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 |

David Ruelle