Introduction and Outline

  • Wolfgang Weidlich
  • Günter Haag
Part of the Springer Series in Synergetics book series (SSSYN, volume 14)


We are going to develop a framework for the quantitative description of the dynamics of a wide class of sociological phenomena. The concepts of the theory used belong to the field of synergetics, a new interdisciplinary branch of science.


Entropy Dust Manifold Income Peaked 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.1
    H. Haken: Cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems. Rev. Mod. Phys. 47, 67 (1975)CrossRefADSMathSciNetGoogle Scholar
  2. 1.2
    H. Haken (ed.): Cooperative Effects, Progress in Synergetics, ( North-Holland, Amsterdam 1974 )Google Scholar
  3. 1.3
    H. Haken: Synergetics, an Introduction, 2nd ed., Springer Ser. Synergetics, Vol. 1 ( Springer, Berlin, Heidelberg, New York 1977 )Google Scholar
  4. 1.4
    H. Haken (ed.): Synergetics, a Workshop, Springer Ser. Synergetics, Vol. 2 ( Springer, Berlin, Heidelberg, New York 1977 )Google Scholar
  5. 1.5
    A. Pacault, C. Vidal (eds.): Synergetics far from Equilibrium, Springer Ser. Synergetics, Vol. 3 ( Springer, Berlin, Heidelberg, New York 1978 )Google Scholar
  6. 1.6
    W. Göttinger, H. Eikemeier (eds.): Structural Stability in Physics, Springer Ser. Synergetics, Vol. 4 ( Springer, Berlin, Heidelberg, New York 1978 )Google Scholar
  7. 1.7
    H. Haken (ed.): Pattern Formation by Dynamic Systems and Pattern Recognition, Springer Ser. Synergetics, Vol. 5 ( Springer, Berlin, Heidelberg, New York 1979 )Google Scholar
  8. 1.8
    H. Haken (ed.): Dynamics of Synergetic Systems, Springer Ser. Synergetics, Vol. 6 ( Springer, Berlin, Heidelberg, New York 1980 )Google Scholar
  9. 1.9
    G. Nicolis, I. Prigogine: Selforganisation in Non-Equilibrium System ( Wiley, New York 1977 )Google Scholar
  10. 1.10
    H. Haken: Generalized Ginzburg-Landau equations for phase transition-like phenomena in lasers, nonlinear optics, hydrodynamics and chemical reactions. Z. Phys. B21, 105 (1975)Google Scholar
  11. 1.11
    R. Bonifacio (ed.): Dissipative Systems in Quantum Optics, Topics Current Phys., Vol. 27 ( Springer, Berlin, Heidelberg, New York 1982 )Google Scholar
  12. 1.12
    H. Haken: Laser Theory, Encyclopedia of Physics, Vol. XXV/2 (Springer, Berlin, Heidelberg, New York 1970 )Google Scholar
  13. 1.13
    F. Schlögl: Chemical reaction models for non-equilibrium phase transitions. Z. Phys. 253, 147 (1972)CrossRefADSGoogle Scholar
  14. 1.14
    H. K. Janssen: Stochastic reaction model for a non-equilibium phase transition. Z. Phys. 270, 67 (1974)CrossRefADSGoogle Scholar
  15. 1.15
    S. Chaturvedi, C. W. Gardiner, I. S. Matheson, D. F. Walls: Stochastic analysis of a chemical reaction with spatial and temporal structures. J. Stat. Phys. 17, 469 (1977)CrossRefADSMathSciNetGoogle Scholar
  16. 1.16
    Y. Kuramoto: Diffusion Induced Chemical Turbulence, in [Ref. 1.8, p. 134] and Progr. Theor. Phys. Suppl. 64, 346 (1978)Google Scholar
  17. 1.17
    A. Nitzan: „The Critical Behavior of Non-Equilibrium Transitions in Reacting Diffusion Systems”, in [Ref. 1.8, p. 119]Google Scholar
  18. 1.18
    M. Eigen, P. Schuster: The hypercycle, a principle of natural self-organization, Naturwissenschaften 64, 541 (1977), 65, 7 (1978), 65, 341 (1978)CrossRefADSGoogle Scholar
  19. 1.19
    H. Kuhn: “Persistence of Organized Structures and Breakthrough of New Structures”, in [Ref. 1.4, p. 200]Google Scholar
  20. 1.20
    A. Babloyantz, L. K. Kaczmarek: Selforganization in multiply connected systems. Bull. Math. Biol. 41, 193 (1979)MATHMathSciNetGoogle Scholar
  21. 1.21
    J. S. Nicolis, E. N. Protonotarios: Bifurcation in non-negotiable games, a paradigm for self-organization in cognitive systems. Int. J. Bio-med. Comput. 10, 417 (1979)CrossRefGoogle Scholar
  22. 1.22
    J. S. Nicolis, M. Benrubi: Inadequate Communication Between Selforganizing Systems and Desynchronization of Physiological Rhythms, a Psychophysiological Study, General Systems, XXII, 119 (1977)Google Scholar
  23. 1.23
    A. Gierer, H. Meinhardt: Adaptation and application of a theory of biological pattern formation. J. Cell. Sci. 15, 321 (1974)Google Scholar
  24. 1.24
    S. K. Ma: Modern Theory of Critical Phenomena, (Benjamin, New York 1976 )Google Scholar
  25. 1.25
    C. Prins (ed.): Van der Waals Centennial Conference on Statistical Mechanics, ( North-Holland, Amsterdam 1974 )Google Scholar
  26. 1.26
    H. Haken: Licht und Materie, Vol. 1-3 (B. I.-Wissenschaftsverlag, Mannheim, Wien, Zürich, 1979, 1980, 1981 )Google Scholar
  27. 1.27
    H. Paul: Lasertheorie, Vol. 53, 54 ( Akademie, Berlin WTB, 1969 )Google Scholar
  28. 1.28
    M. Sargent, M. O. Scully, W. E. Lamb, jr.: Laser Physics, ( Addison Wesley, Reading, MA 1974 )Google Scholar
  29. 1.29
    F. Haake: Treatment of Open Systems by Generalized Master Equations, Springer Tracts Mod. Phys., Vol. 66 ( Springer, Berlin, Heidelberg, New York 1973 )Google Scholar
  30. 1.30
    H. Grabert: Projection Operator Techniques in Nonequilibrium Statistical Mechanics, Springer Tracts Mod. Phys., Vol. 95 ( Springer, Berlin, Heidelberg, New York 1982 )Google Scholar
  31. 1.31
    R. Landauer: The Role of Fluctuations in Multistable Systems and in the Transition to Multi-stability, in Bifurcation Theory and Applications in Scientific Disciplines, ed. by O. Gurel, O. E. Rössler ( N. Y. Acad. Sci., New York 1979 ) p. 433Google Scholar
  32. 1.32
    D. A. McQuarrie: Stochastic approach to chemical kinetics. J. Appl. Prob. 4, 413 (1967)CrossRefMATHMathSciNetGoogle Scholar
  33. 1.33
    R. Kubo, K. Matsuo, K. Kitahara: Fluctuation and relaxation of macrovariables. J. Stat. Phys. 9, 51 (1973)CrossRefADSGoogle Scholar
  34. 1.34
    J. T. Hynes, R. Kapral, M. Weinberg: Microscopic theory of Brownian motion: Nonlinear Langevin equations. Physica 81 A, 485 (1975)Google Scholar
  35. 1.35
    V. Daniel: Physical Principles in Human Cooperation, The Sociological Rev. 44, 107 (1952)CrossRefGoogle Scholar
  36. 1.36
    W. Weidlich: The statistical description of polarization phenomena in society. Br. J. Math. Stat. Psychol. 24, 251 (1971)CrossRefMATHGoogle Scholar
  37. 1.37
    W. Weidlich: The use of statistical models in sociology. Collect. Phenom. 1, 51 (1972)Google Scholar
  38. 1.38
    W: Weidlich: Dynamics of Interacting Social Groups”, in [Ref. 1.2, p. 269]Google Scholar
  39. 1.39
    E. Callen, M. Scully, D. Shapero: J. Math. Psychol. (1975)Google Scholar
  40. 1.40
    D. F. Walls: Non-equilibrium phase transition in sociology. Collect. Phenom. 2, 125 (1976)MathSciNetGoogle Scholar
  41. 1.41
    W. Weidlich, G. Haag: Dynamics of Interacting Groups in Society with Application to the Migration of Population”, in [Ref. 1.8, p. 235]Google Scholar
  42. 1.42
    W. Weidlich, G. Haag: Migration behavior of mixed population in a town. Collect. Phenom. 3, 89 (1980)MathSciNetGoogle Scholar
  43. 1.43
    J. S. Coleman: Introduction to Mathematical Sociology, ( The Free Press, New York 1964 )Google Scholar
  44. 1.44
    D. J. Bartholomew: Stochastic Models for Social Processes ( Wiley, London 1967 )Google Scholar
  45. 1.45
    E. W. Montroll, W. W. Badger: Introduction to Quantitative Aspècts of Social Phenomena ( Gordon and Breach, New York 1974 )Google Scholar
  46. 1.46
    A. Nitschke: Revolutionen in Naturwissenschaft und Gesellschaft, Problemata 83, Stuttgart-Bad Cannstatt (1979)Google Scholar
  47. 1.47
    A. Nitschke: “Systems and Changes of Systems in History, in [Ref. 1.7, p. 234]Google Scholar
  48. 1.48
    T. Poston, I. N. Stewart, Catastrophe Theory and Its Applications ( Pitman, London 1978 )MATHGoogle Scholar
  49. 1.49
    R. Abraham, C. Shaw: Dynamics, The Geometry of Behaviour Vol. 0-3 ( Aerial Press, Santa Cruz 1982 )Google Scholar
  50. 1.50
    M. W. Hirsch, S. Smale: Differential Equations, Dynamical Systems and Linear Algebra ( Academic, New York 1974 )Google Scholar
  51. 1.51
    R. L. Stratonovich: Topics in the Theory of Random Noise, Vols. 1 and 2 (Gordon and Breach, New York 1963 and 1967 )Google Scholar
  52. 1.52
    A. T. Bharucha-Reid: Elements of the Theory of Markov Processes and Their Applications ( Mc-Graw Hill, New York 1960 )MATHGoogle Scholar
  53. 1.53
    N. Wax (ed.): Selected Papers on Noise and Stochastic Processes ( Dover, New York 1954 )MATHGoogle Scholar
  54. 1.54
    D. H. Sattinger: Topics in Stability and Bifurcation Theory”, Lecture Notes Math., Vol. 309 ( Springer, Berlin, Heidelberg, New York 1973 )Google Scholar
  55. 1.55
    J. E. Marsden, M. Mc Cracken: The Hopf Bifurcation and Its Applications, Appl. Math. Sc. Vol. 19 ( Springer, New York 1976 )Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Wolfgang Weidlich
    • 1
  • Günter Haag
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

Personalised recommendations