Clustering of Active Walkers: Phase Transition from Local Interactions

  • Frank Schweitzer
  • Lutz Schimansky-Geier
Part of the Institute for Nonlinear Science book series (INLS)


The emergence of complex behavior in a system consisting of interacting simple elements is among the most fascinating phenomena of our world. Examples of these emerging new features can be found in almost every field of today’s scientific interest, ranging from the behavior of social groups [1], to coherent pattern formation in physical and chemical systems [2], to the motion of swarms of animals in biology [3].


Density Fluctuation Effective Diffusion Coefficient Local Potential Biological Motion Nonlinear Feedback 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1a]
    E. Jantsch and C.H. Waddington, eds., Evolution and Consciousness. Human Systems in Transition (Addison-Wesley, Reading, MA, 1976)Google Scholar
  2. [1b]
    W. Weidlich, Phys. Rep. 204, 1 (1991).MathSciNetADSCrossRefGoogle Scholar
  3. [2]
    S. Kai, ed., Pattern Formation in Complex Dissipative Systems (World Scientific, Singapore, 1992).Google Scholar
  4. [3a]
    E.O. Wilson, The Insect Societies (Belknap, 1971)Google Scholar
  5. [3b]
    B. Pfistner, in Biological Motion, edited by W. Alt and G. Hoffmann, Lecture Notes in Biomathematics, vol. 89, (Springer-Verlag, Berlin, 1990), pp. 556–565.Google Scholar
  6. [4]
    See the numerous volumes of Springer Series in Synergetics, edited by H. Haken (Springer-Verlag, Berlin) or Santa Fe Institute Studies in the Sciences of Complexity (Addison-Wesley, Reading, MA).Google Scholar
  7. [5]
    D. Jefferson, R. Collins, C. Cooper, M. Dyer, M. Flowers, R. Korf, C. Taylor, and A. Wang, in Artificial Life II, edited by C. Langton, C. Taylor, J. Doyne Farmer, and S. Rasmussen (Addison-Wesley, Reading, MA, 1992), pp. 549–578.Google Scholar
  8. [6]
    J.H. Holland and J.H. Miller, AEA Papers Proc. 81(2), 365 (1991).Google Scholar
  9. [7]
    S. Bura, F. Guerin-Pace, H. Mathian, D. Pumain, and L. Sanders, preprint (P.A.R.I.S.), 1994.Google Scholar
  10. [8]
    D. R. Kayser, L.K. Aberle, R.D. Pochy, and L. Lam, Physica A 191, 17 (1992).ADSCrossRefGoogle Scholar
  11. [9]
    L. Lam, R.D. Freimuth, M.K. Pon, D.R. Kayser, J.T. Fredrick, and R.D. Pochy, in Pattern Formation in Complex Dissipative Systems, edited by S. Kai (World Scientific, Singapore, 1992), pp. 34–46.Google Scholar
  12. [10]
    F. Schweitzer, K. Lao, and F. Family (submitted for publication).Google Scholar
  13. [11]
    L. H’walisz, P. Jung, P. Hänggi, P. Talkner, and L. Schimansky-Geier, Z. Phys. B 77, 471 (1989).ADSCrossRefGoogle Scholar
  14. [12]
    F. Schweitzer and L. Schimansky-Geier, Physica A 206, 359 (1994).ADSCrossRefGoogle Scholar
  15. [13]
    W. Ebeling and R. Feistel, Physik der Selbstorganisation und Evolution (Akademie-Verlag, Berlin, 1986).Google Scholar
  16. [14]
    V. Calenbuhr and J.-L. Deneubourg, in Biological Motion, edited by W. Alt and G. Hoffmann, Lecture Notes in Biomathematics, vol. 89 (Springer-Verlag, Berlin, 1990), pp. 453–469.Google Scholar
  17. [15]
    M. Millonas, J. Theor. Biol. 159, 529 (1992).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Frank Schweitzer
  • Lutz Schimansky-Geier

There are no affiliations available

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