Measures of Complexity and Chaos

  • Neal B. Abraham
  • Alfonso M. Albano
  • Anthony Passamante
  • Paul E. Rapp

Part of the NATO ASI Series book series (NSSB, volume 208)

Table of contents

  1. Front Matter
    Pages i-x
  2. Complexity and Chaos

    1. N. B. Abraham, A. M. Albano, N. B. Tufillaro
      Pages 1-27
  3. Chaotic Metamorphoses

    1. Linda Caruso-Haviland, Paul E. Rapp
      Pages 29-31
  4. Characterizing Temporal Complexity: Chaos

    1. Measuring Dimensions, Entropies and Lyapunov Exponents

      1. H. Atmanspacher, V. Demmel, G. Morfill, H. Scheingraber, W. Voges, G. Wiedenmann
        Pages 33-49
      2. A. Goel, S. S. Rao, A. Passamante
        Pages 125-128
      3. K. Hartt, L. M. Kahn
        Pages 129-132
      4. U. Hübner, W. Klische, N. B. Abraham, C. O. Weiss
        Pages 133-136
      5. Daniel P. Lathrop, Eric J. Kostelich
        Pages 147-154
      6. W. M. Schaffer, L. F. Olsen
        Pages 187-190
      7. S. W. Tam, M. K. Devine
        Pages 193-197
      8. James Theiler
        Pages 199-202
    2. Other Measures

      1. Ditza Auerbach
        Pages 203-207
      2. Daniel Bensen, Michael Welge, Alfred Hübler, Norman Packard
        Pages 209-212
      3. Kenneth Chang, Alfred Hübler, Norman Packard
        Pages 225-228
      4. S. T. Gaito, G. P. King
        Pages 235-240
      5. R. Gilmore, G. Mindlin, H. G. Solari
        Pages 241-243
      6. M. Le Berre, E. Ressayre, A. Talllet
        Pages 245-248
      7. Thomas Meyer, Alfred Hübler, Norman Packard
        Pages 253-256
      8. M. A. Sepúlveda, R. Badii
        Pages 257-260
      9. Hernán G. Solari, R. Gilmore
        Pages 261-263
      10. Hernán G. Solari, Xin-Jun Hou, R. Gilmore
        Pages 265-268
    3. Characterizing Homoclinic Chaos

      1. F. T. Arecchi, A. Lapucci, R. Meucci
        Pages 281-294
      2. D. Hennequin, M. Lefranc, A. Bekkali, D. Dangoisse, P. Glorieux
        Pages 299-302
      3. Basil Nicolaenko, Zhen-Su She
        Pages 303-307
      4. F. Papoff, A. Fioretti, E. Arimondo, N. B. Abraham
        Pages 309-312
    4. Building Models from Data

      1. James P. Crutchfield
        Pages 327-338
      2. A. Destexhe, G. Nicolis, C. Nicolis
        Pages 339-343

About this book


This volume serves as a general introduction to the state of the art of quantitatively characterizing chaotic and turbulent behavior. It is the outgrowth of an international workshop on "Quantitative Measures of Dynamical Complexity and Chaos" held at Bryn Mawr College, June 22-24, 1989. The workshop was co-sponsored by the Naval Air Development Center in Warminster, PA and by the NATO Scientific Affairs Programme through its special program on Chaos and Complexity. Meetings on this subject have occurred regularly since the NATO workshop held in June 1983 at Haverford College only two kilometers distant from the site of this latest in the series. At that first meeting, organized by J. Gollub and H. Swinney, quantitative tests for nonlinear dynamics and chaotic behavior were debated and promoted [1). In the six years since, the methods for dimension, entropy and Lyapunov exponent calculations have been applied in many disciplines and the procedures have been refined. Since then it has been necessary to demonstrate quantitatively that a signal is chaotic rather than it being acceptable to observe that "it looks chaotic". Other related meetings have included the Pecos River Ranch meeting in September 1985 of G. Mayer­ Kress [2) and the reflective and forward looking gathering near Jerusalem organized by M. Shapiro and I. Procaccia in December 1986 [3). This meeting was proof that interest in measuring chaotic and turbulent signals is widespread.


Counter Diode Phase Signal bifurcation chaos complexity development dynamical systems entropy laser modeling

Editors and affiliations

  • Neal B. Abraham
    • 1
  • Alfonso M. Albano
    • 1
  • Anthony Passamante
    • 2
  • Paul E. Rapp
    • 3
  1. 1.Department of PhysicsBryn Mawr CollegeBryn MawrUSA
  2. 2.Naval Air Development CenterWarminsterUSA
  3. 3.Department of Physiology and BiochemistryThe Medical College of PennsylvaniaPhiladelphiaUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag US 1989
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-0625-3
  • Online ISBN 978-1-4757-0623-9
  • Series Print ISSN 0258-1221
  • Buy this book on publisher's site
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