Chaos, Catastrophe, and Human Affairs: Applications of Nonlinear Dynamics to Work, Organizations, and Social Evolution

By Stephen J. Guastello | Go to book overview

Yilmaz, 1992), and are based on the analysis of residuals from a linear time series. There is another nonparametric approach as well that is based on a different principle ( Cheng & Tong, 1992). The catastrophes and discontinuous change dynamics appear to have been forgotten, meanwhile.

The next chapter addresses the conceptual issues underlying hypothesis testing for both chaos and catastrophe models. Methods are also presented for detecting chaos, dimensionality, and catastrophes, and for extracting model equations that are based on a strong parametric foundation for multimodal frequency distributions. The choice of time intervals is drawn from the substance or content of the application. As one might anticipate, there are issues to address concerning the counterpoint among chance, randomness, and determinism. Many, but not all, of the applications contained in Chapters 4-12 are based on those techniques.


SUMMARY

This chapter introduced the central concepts of nonlinear dynamics. Attractors range in complexity from fixed points to chaotic attractors. Attractors are structurally stable, while repellors and saddles are unstable. Chaotic attractors are stable in a global sense, but unstable in a local sense. Bifurcation mechanisms can transform attractors from fixed points to a chaotic regime, and the logistic map is a frequently observed route to chaos. Multiple couplings of period attractors are also frequently responsible for producing chaotic behavior.

Fractals are geometric forms in fractional dimensions. Although they were initially studied as independent lines of thought, it was eventually recognized that fractal geometry and nonlinear dynamics concerning chaos offered similar deterministic explanations for apparently random behavior. The basin of chaotic attractors was later found to be fractal.

Catastrophes are sudden discontinuous changes of events. The classification theorem for catastrophe models shows that there are 11 singular models, which range in complexity from one to five control parameters with one or two behavioral output variables. The topology of their response surfaces show that a complex manifold produces a continuity between apparently discontinuous states. Catastrophe models are configurations of stability and instability dynamics and usually involve fixed- point or limit cycle attractors, although boundary and chaotic attractors can be accommodated within the same framework. Catastrophe dynamics can be applied to understanding sudden changes in entire dynamical schemes as well.

Self-organization is a principle by which a living system in the state of chaos reorganizes its elements to produce a more stable structure and

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Chaos, Catastrophe, and Human Affairs: Applications of Nonlinear Dynamics to Work, Organizations, and Social Evolution
Table of contents

Table of contents

  • Title Page iii
  • Contents vii
  • Preface ix
  • Acknowledgments x
  • 1 - An Invitation to Chaos 1
  • Summary 10
  • 2 - Nonlinear Dynamical Systems Theory 11
  • Summary 57
  • 3 - Metaphors, Easter Bunnies, Modeling, and Verification 59
  • Summary 97
  • 4 - Nds, Human Decision Making, and Cognitive Processes 99
  • Summary 123
  • 5 - Dynamics of Motivation and Conflict 124
  • Summary 173
  • 6 - Stress and Human Performance 175
  • 7 - Accidents and Risk Analysis 205
  • Summary 231
  • 8 - Stress-Related Illness 232
  • Summary 256
  • 9 - The Evolution of Human Systems 257
  • Summary 298
  • 10 - Innovation, Creativity, and Complexity 301
  • Summary 328
  • 11 - The Dynamical Nature of Organizational Development 329
  • Summary 365
  • 12 - Chaos, Revolution, and War 367
  • Epilogue: Nothing Stops These Elephants 395
  • References 402
  • Author Index 426
  • Subject Index 435
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