Abstract
The field of quantitative sociodynamics is still a rather young and very thrilling interdisciplinary research area which deals with the mathematical modelling of the temporal evolution of social systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Uhlenbeck GE (1973) The validity and the limitations of the Boltzmann-equation. In: Cohen EGD, Thirring W (eds) The Boltzmann equation. Springer, Wien
Helbing D (1993) Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models. Physica A 196:546–573
Hofbauer J, Sigmund K (1984) Evolutionstheorie und dynamische Systeme. Paul Parey, Berlin
Axelrod R, Dion D (1988) The further evolution of cooperation. Science 242:1385–1390
Osgood CE, Tannenbaum PH (1955) The principle of congruity in the prediction of attitude change. Psychol Rev 62:42–55
Stratonovich RL (1963, 1967) Topics in the theory of random noise, vols 1, 2. Gordon and Breach, New York
Haken H (1983) Advanced synergetics. Springer, Berlin
Helbing D (1992) A mathematical model for attitude formation by pair interactions. Behav Sci 37:190–214
Langevin P (1908) On the theory of Brownian motion. Comptes Rendues Acad Sci Paris 146:530–533
Walls DF (1976) Non-equilibrium phase transitions in sociology. Collective Phenomena 2:125–130
Pauli H (1928) In: Debye P (ed) Probleme der Modernen Physik. Hirzel, Leipzig
Weidlich W (1991) Physics and social science—the approach of synergetics. Phys Rep 204:1–163
Weidlich W, Haag G (1983) Concepts and models of a quantitative sociology. The dynamics of interacting populations. Springer, Berlin
Helbing D (1992) A mathematical model for behavioral changes by pair interactions. In: Haag G, Mueller U, Troitzsch KG (eds) Economic evolution and demographic change. Formal models in social sciences. Springer, Berlin, pp 330–348
von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton, NJ
Schweitzer F, Bartels J, Pohlmann L (1991) Simulation of opinion structures in social systems. In: Ebeling W, Peschel M, Weidlich W (eds) Models of selforganization in complex systems (MOSES). Akademie, Berlin
Lewin K (1951) Field theory in social science. Harper & Brothers, New York, NY
Coleman JS (1964) Introduction to mathematical sociology. The Free Press of Glencoe, New York, NY
Malchow H (1988) Spatial patterning of interacting and dispersing populations. Mem Fac Sci Kyoto Univ (Ser Biol) 13:83–100
Festinger L (1957) A theory of cognitive dissonance. Row & Peterson, Evanston, IL
Bartholomew DJ (1967) Stochastic models for social processes. Wiley, London
Domencich TA, McFadden D (1975) Urban travel demand. A behavioral analysis. North-Holland, Amsterdam, pp 61–69
Lewenstein M, Nowak A, Latané B (1992) Statistical mechanics of social impact. Phys Rev A 45(2):763–776
Haag G (1989) Dynamic decision theory: applications to urban and regional topics. Kluwer Academic, Dordrecht
Feger H (1978) Konflikterleben und Konfliktverhalten. Huber, Bern
Weidlich W, Haag G (eds) (1988) Interregional migration. Springer, Berlin
Binney JJ, Dowrick NJ, Fisher AJ, Newman MEJ (1992) The theory of critical phenomena, Chap. 6: Mean-field theory. Clarendon Press, Oxford
Rapoport A (1983) Mathematical models in the social and behavioral sciences. Wiley, New York, NY
Helbing D (1993) Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory. Physica A 193:241–258
Reiner R, Weidlich W (1993) Der Beitrag der Synergetik zum Naturverständnis. In: Bien G, Gil Th, Wilke J (eds) Natur im Umbruch. Frommann-Holzboog, Stuttgart
Griffiths HB, Oldknow A (1993) Mathematics of models. Ellis Horwood, New York, NY
Haken H (1983) Advanced synergetics. Springer, Berlin
Haken H (1983) Synergetics, 3rd edn. Springer, Berlin
Haken H (1988) Information and self-organization: a macroscopic approach to complex systems. Springer, Berlin
Hamblin RL, Jacobsen RB, Miller JLL (1973) A mathematical theory of social change. Wiley, New York, NY
Hauk M (1994) Evolutorische Ökonomik und private Transaktionsmedien. Lang, Frankfurt/Main
Haus JW, Kehr KW (1987) Diffusion in regular and disordered lattices. Phys Rep 150(5, 6): 263–406
Heider F (1946) Attitudes and cognitive organization. J Psychol 21:107–112
Heider F (1958) The psychology of interpersonal relations. Wiley, New York, NY
Helbing D (1990) Physikalische Modellierung des dynamischen Verhaltens von Fußgängern. Master’s thesis, Georg-August University Göttingen
Helbing D (1991) A mathematical model for the behavior of pedestrians. Behav Sci 36: 298–310
Helbing D (1992) A fluid-dynamic model for the movement of pedestrians. Complex Systems 6:391–415
Helbing D (1992) Interrelations between stochastic equations for systems with pair interactions. Physica A 181:29–52
Helbing D (1992) A mathematical model for behavioral changes by pair interactions. In: Haag G, Mueller U, Troitzsch KG (eds) Economic evolution and demographic change. Formal models in social sciences. Springer, Berlin, pp 330–348
Helbing D (1992) Models for pedestrian behavior. In: Natural structures. Principles, strategies, and models in architecture and nature. Sonderforschungsbereich 230, tuttgart, Part II
Helbing D (1993) Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models. Physica A 196:546–573
Helbing D (1993) Stochastic and Boltzmann-like models for behavioral changes, and their relation to game theory. Physica A 193:241–258
Helbing D (1994) A mathematical model for behavioral changes by pair interactions and its relation to game theory. Angewandte Sozialforschung 18(3):117–132
Hilborn RC (1994) Chaos and nonlinear dynamics. Oxford University Press, New York, NY
Hofbauer J, Schuster P, Sigmund K (1979) A note on evolutionarily stable strategies and game dynamics. J Theor Biol 81:609–612
Hofbauer J, Sigmund K (1988) The theory of evolution and dynamical systems. Cambridge University Press, Cambridge
Horsthemke W, Lefever R (1984) Noise-induced transitions. Springer, Berlin
Huberman BA, Hogg T (1988) The behavior of computational ecologies. In: Huberman BA (ed) The ecology of computation. Elsevier, Amsterdam
Ising E (1925) Beitrag zur Theorie des Ferromagnetismus Zeitschrift der Physik. 31:253ff
van Kampen NG (1981) Stochastic processes in physics and chemistry. North-Holland, Amsterdam
Kennedy AM (1983) The adoption and diffusion of new industrial products: a literature review. Eur J Mark 17(3):31–88
Kruskal JB, Wish M (1978) Multidimensional scaling. Sage, Beverly Hills, CA
Luce RD (1959) Individual choice behavior, Chap. 2.A: Fechner’s problem. Wiley, New York, NY
Luce RD, Raiffa H (1957) Games and decisions. Wiley, New York, NY
Luhmann N (1991) Soziale Systeme, 4th edn. Suhrkamp, Frankfurt/Main
Ma S-K (1976) Modern theory of critical phenomena. Benjamin, Reading, MA
Mahajan V, Peterson RA (1985) Models for innovation diffusion. Sage, London
Malchow H (1988) Spatial patterning of interacting and dispersing populations. Mem Fac Sci Kyoto Univ (Ser Biol) 13:83–100
Matheson I, Walls DF, Gardiner CW (1975) Stochastic models of first-order nonequilibrium phase transitions in chemical reactions. J Stat Phys 12(1):21–34
McCauley JL (1993) Chaos dynamics and fractals. Cambridge University Press, Cambridge
Montroll EW (1965) Model making in biological and behavioral sciences. In: Eringen AC (ed) Recent advances in engineering science, vol. I. Gordon and Breach, New York, NY
Montroll EW (1978) On some mathematical models of social phenomena. In: Lakshmikantham V (ed) Nonlinear equations in abstract spaces. Academic Press, New York, NY
Montroll EW, Badger WW (1974) Introduction to quantitative aspects of social phenomena. Gordon and Breach, New York, NY
Montroll EW, Shlesinger MF (1984) On the wonderful world of random walks. In: Lebowitz JL, Montroll EW (eds) Nonequilibrium phenomena II: from stochastics to hydrodynamics. North-Holland, Amsterdam
Montroll EW, West BJ (1979) On an enriched collection of stochastic processes. In: Montroll EW, Lebowitz JL (eds) Fluctuation phenomena. North-Holland, Amsterdam
Mosekilde E, Larsen E, Sterman JD (1991) Coping with complexity: deterministic chaos in human decisionmaking behavior. In: Casti JL, Karlqvist A (eds) Beyond belief: randomness, prediction and explanation in science. CRC Press, Boca Raton, FL, pp 199–229
Mosekilde E, Thomsen JS, Larsen ER, Sterman J (1992) Nonlinear interactions in the economy. In: Haag G, Mueller U, Troitzsch KG (eds) Economic evolution and demographic change. Formal models in social sciences. Springer, Berlin
von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton, NJ
Nicolis G, Malek-Mansour M, van Nypelseer A, Kitahara K (1976) The onset of instabilities in nonequilibrium systems. J Stat Phys 14(5):417–432
Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. From dissipative structures to order through fluctuations. Wiley, New York, NY
Oeding D (1963) Verkehrsbelastung und Dimensionierung von Gehwegen und anderen Anlagen des Fußgängerverkehrs, vol 22, Straßenbau und Straßenverkehrstechnik, Bonn. p 8, Fig. 10.
Older SJ (1968) Movement of pedestrians on footways in shopping streets. Traffic Eng Control 10:160–163
Olinick M (1978) An introduction to mathematical models in the social and life sciences. Addison-Wesley, Reading, MA, pp 59–65
Oppenheim I, Schuler KE, Weiss GH (eds) (1977) Stochastic processes in chemical physics: the master equation. MIT Press, Cambridge, MA
Ortúzar JdeD, Willumsen LG (1990) Modelling transport, Chap. 7: Discrete-choice models. Wiley, Chichester
Osgood CE, Tannenbaum PH (1955) The principle of congruity in the prediction of attitude change. Psychol Rev 62:42–55
Parsons T (1967) Sociological theory and modern society. Free Press, New York, NY
Pauli H (1928) In: Debye P (ed) Probleme der Modernen Physik. Hirzel, Leipzig
Pearl R (1924) Studies in human biology. Williams & Wilkins, Baltimore, MD
Planck M (1917) In: Ãœber einen Satz der statistischen Dynamik und seine Erweiterung in der Quantentheorie, Sitzungsber Preuss Akad Wiss, pp 324ff
Prigogine I (1976) Order through fluctuation: self-organization and social system. In: Jantsch E, Waddington CH (eds) Evolution and consciousness. Human systems in transition. Addison-Wesley, Reading, MA
Prigogine I, Herman R (1971) Kinetic theory of vehicular traffic. Elsevier, New York, NY
Rapoport A (1983) Mathematical models in the social and behavioral sciences. Wiley, New York, NY
Rapoport A (1986) General system theory. Essential concepts and applications. Abacus Press, Tunbridge Wells, Kent
Rapoport A, Chammah MA (1965) Prisoner’s dilemma. A study in conflict and cooperation. University of Michigan Press, Ann Arbor, MI
Ravenstein E (1876) The birthplaces of the people and the laws of migration. Geogr Mag III:173–177
Reiner R, Munz M (1990) Ranking regression analysis of spatiotemporal variables. Environ Plan A 22:507–526
Reiner R, Weidlich W (1993) Der Beitrag der Synergetik zum Naturverständnis. In: Bien G, Gil Th, Wilke J (eds) Natur im Umbruch. Frommann-Holzboog, Stuttgart
Schaffer WM, Olsen LF, Truty GL, Fulmer SL, Graser DJ (1988) Periodic and chaotic dynamics in childhood infections. In: Markus M, Müller StC, Nicolis G (eds) From chemical to biological organization. Springer, Berlin
Schüßler R (1989) Exit threats and cooperation under anonymity. J Conflict Resolut 33(4):728–749
Schüßler R (1990) Threshold effects and the decline of cooperation. J Conflict Resolut 34(3):476–494
Schuster HG (1988) Deterministic chaos, 2nd edn. VCH, Weinheim
Schuster P, Sigmund K, Hofbauer J, Wolff R (1981) Selfregulation of behavior in animal societies. Biol Cybern 40:1–25
Schweitzer F, Bartels J, Pohlmann L (1991) Simulation of opinion structures in social systems. In: Ebeling W, Peschel M, Weidlich W (eds) Models of selforganization in complex systems (MOSES). Akademie, Berlin
Stanley HE (1971) Introduction to phase transitions and critical phenomena. Oxford University Press, New York
Stratonovich RL (1963, 1967) Topics in the theory of random noise, vols 1, 2. Gordon and Breach, New York
Szép J, Forgó F (1985) Introduction to the theory of games. Akadémiai Kiadó, Budapest
Taylor P, Jonker L (1978) Evolutionarily stable strategies and game dynamics. Math Biosci 40:145–156
Thom R (1975) Structural stability and morphogenesis. Benjamin, Reading, MA
Tuma NB, Hannan MT (1984) Social dynamics. Models and methods. Academic Press, Orlando, FL
Uhlenbeck GE (1973) The validity and the limitations of the Boltzmann-equation. In: Cohen EGD, Thirring W (eds) The Boltzmann equation. Springer, Wien
Valentin L (1981) Subatomic physics: nuclei and particles. North-Holland, Amsterdam, pp 127–130, 342–349
Verhulst PF (1845) Nuov Mem Acad Roy Bruxelles 18:1ff
Vorob’ev NN (1977) Game theory. Lectures for economists and system scientists. Springer, New York, NY
Walls DF (1976) Non-equilibrium phase transitions in sociology. Collective Phenomena 2:125–130
Weidlich W (1971) The statistical description of polarization phenomena in society. Br J Math Stat Psychol 24:51
Weidlich W (1972) The use of statistical models in sociology. Collective Phenomena 1:51–59
Weidlich W (1987) Quantitative social science. Physica Scripta 35:380–387
Weidlich W (1991) Physics and social science—the approach of synergetics. Phys Rep 204:1–163
Weidlich W (1994) Synergetic modelling concepts for sociodynamics with application to collective political opinion formation. J Math Sociol 18:267–291
Weidlich W, Braun M (1992) The master equation approach to nonlinear economics. J Evol Econ 2:233–265
Weidlich W, Haag G (1983) Concepts and models of a quantitative sociology. The dynamics of interacting populations. Springer, Berlin
Weidlich W, Haag G (eds) (1988) Interregional migration. Springer, Berlin
Williams HCWL (1977) On the formation of travel demand models and economic evaluation measures of user benefit. Environ Plan A 9(3):285–344
Williams WSC (1991) Nuclear and particle physics. Clarendon Press, Oxford, pp 56–61
Wunderlin A, Haken H (1984) Some applications of basic ideas and models of synergetics to sociology. In: Frehland E (ed) Synergetics—from microscopic to macroscopic order. Springer, Berlin
Young FW, Hamer RM (1987) Multidimensional scaling: history, theory, and applications. Lawrence Erlbaum Associates, Hillsdale, NJ
Zeeman EC (ed) (1977) Catastrophe theory. Addison-Wesley, London
Zeeman EC (1980) Population dynamics from game theory. In: Nitecki A, Robinson C (eds) Global theory of dynamical systems, Springer, Berlin
Ziman JM (1972) Principles of the theory of solids. Cambridge University Press, London
Zipf GK (1946) The P1P2/D hypothesis on the intercity movement of persons. Am Sociol Rev 11:677–686
Varian HR (1992) Microeconomic analysis, 3rd edn. Norton, New York, NY
Coleman J (1973) The mathematics of collective action. Heinemann Educational Books, London
Coleman JS (1990) Foundations of social theory. Belknap (Harvard University), Cambridge, MA
Daly AJ, Zachary S (1978) Improved multiple choice models. In: Hensher DA, Dalvi MQ (eds) Determinants of travel choice. Saxon House, Westmead
Buckley W (1967) Sociology and modern systems theory. Prentice-Hall, Englewood Cliffs, NJ
Coleman JS (1964) Introduction to mathematical sociology. The Free Press of Glencoe, New York, NY
Diekmann A (1992) The log-logistic distribution as a model for social diffusion processes. J Sci Ind Res 51:285–290
Diekmann A, Mitter P (eds) (1984) Stochastic modelling of social processes. Academic Press, Orlando, FL
Domencich TA, McFadden D (1975) Urban travel demand. A behavioral analysis. North-Holland, Amsterdam, pp 61–69
Ebeling W (1991) Dynamics of competition and valuation in non-physical systems. In: Sydow A (ed) Handbook on computational systems analysis. Elsevier, Amsterdam
Ebeling W (1991) Stochastic models of competition processes in non-physical systems. Syst Anal Model Simul 8:3
Ebeling W, Jiménez-Montaño MA, Bruckner E, Scharnhorst A (1992) A stochastic model of technological evolution. In: Haag G, Mueller U, Troitzsch KG (eds) Economic evolution and demographic change. Formal models in social sciences. Springer, Berlin
Eigen M (1971) The selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58:465
Eigen M, Schuster P (1979) The hypercycle. Springer, Berlin
Fisher RA (1930) The genetical theory of natural selection. Oxford University Press, Oxford
Fokker AD (1914) Die mittlere Energie rotierender elektrischer Dipole im Strahlungsfeld. Annalen der Physik 348:810–820
Gardiner CW (1985) Handbook of stochastic methods, 2nd edn. Springer, Berlin
Gardiner CW, McNeil KJ, Walls DF, Matheson IS (1976) Correlations in stochastic theories of chemical reactions. J Stat Phys 14(4):307–331
Glance N, Hogg T, Huberman BA (1991) Computational ecosystems in a changing environment. Int J Mod Phys C 2(3):735–753
Glance NS, Huberman BA (1992) Dynamics with expectations. Phys Lett A 165:432–440
Goel NS, Maitra SC, Montroll EW (1971) On the Volterra and other nonlinear models of interacting populations. Rev Mod Phys 43(2):231–276
Goel NS, Richter-Dyn N (1974) Stochastic models in biology. Academic Press, New York, NY
Granovetter M, Soong R (1983) Threshold models of diffusion and collective behavior. J Math Sociol 9:165–179
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Helbing, D. (2010). Introduction and Summary. In: Quantitative Sociodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11546-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-11546-2_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11545-5
Online ISBN: 978-3-642-11546-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)