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A Quantitative Measure, Mechanism and Attractor for Self-Organization in Networked Complex Systems

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Part of the Lecture Notes in Computer Science book series (LNCCN,volume 7166)


Quantity of organization in complex networks here is measured as the inverse of the average sum of physical actions of all elements per unit motion multiplied by the Planck’s constant. The meaning of quantity of organization is the number of quanta of action per one unit motion of an element. This definition can be applied to the organization of any complex system. Systems self-organize to decrease the average action per element per unit motion. This lowest action state is the attractor for the continuous self-organization and evolution of a dynamical complex system. Constraints increase this average action and constraint minimization by the elements is a basic mechanism for action minimization. Increase of quantity of elements in a network, leads to faster constraint minimization through grouping, decrease of average action per element and motion and therefore accelerated rate of self-organization. Progressive development, as self-organization, is a process of minimization of action.


  • network
  • self-organization
  • complex system
  • organization
  • quantitative measure
  • principle of least action
  • principle of stationary action
  • attractor
  • progressive development
  • acceleration


  1. Georgiev, G., Georgiev, I.: The least action and the metric of an organized system. Open Syst. Inf. Dyn. 9(4), 371 (2002)

    MathSciNet  CrossRef  Google Scholar 

  2. de Maupertuis, P.: Essai de cosmologie (1750)

    Google Scholar 

  3. Goldstein, H.: Classical Mechanics. Addison Wesley (1980)

    Google Scholar 

  4. Feynman, R.: The Principle of Least Action in Quantum Mechanics. Ph.D. thesis (1942)

    Google Scholar 

  5. Gauss, J.: Über ein neues allgemeines Grundgesetz der Mechanik (1831)

    Google Scholar 

  6. Taylor, J.: Hidden unity in nature’s laws. Cambridge University Press (2001)

    Google Scholar 

  7. Kaku, M.: Quantum Field Theory. Oxford University Press (1993)

    Google Scholar 

  8. Hoskins, D.A.: A least action approach to collective behavior. In: Parker, L.E. (ed.) Proc. SPIE, Microrob. and Micromech. Syst., vol. 2593, pp. 108–120 (1995)

    Google Scholar 

  9. Piller, O., Bremond, B., Poulton, M.: Least Action Principles Appropriate to Pressure Driven Models of Pipe Networks. In: ASCE Conf. Proc. 113 (2003)

    Google Scholar 

  10. Willard, L., Miranker, A.: Neural network wave formalism. Adv. in Appl. Math. 37(1), 19–30 (2006)

    MathSciNet  MATH  CrossRef  Google Scholar 

  11. Wang, J., Zhang, K., Wang, E.: Kinetic paths, time scale, and underlying landscapes: A path integral framework to study global natures of nonequilibrium systems and networks. J. Chem. Phys. 133, 125103 (2010)

    CrossRef  Google Scholar 

  12. Annila, A., Salthe, S.: Physical foundations of evolutionary theory. J. Non-Equilib. Thermodyn., 301–321 (2010)

    Google Scholar 

  13. Devezas, T.C.: Evolutionary theory of technological change: State-of-the-art and new approaches. Tech. Forec. & Soc. Change 72, 1137–1152 (2005)

    CrossRef  Google Scholar 

  14. Chaisson, E.J.: The cosmic Evolution. Harvard (2001)

    Google Scholar 

  15. Bar-Yam, Y.: Dynamics of Complex Systems. Addison Wesley (1997)

    Google Scholar 

  16. Smart, J.M.: Answering the Fermi Paradox. J. of Evol. and Tech. (June 2002)

    Google Scholar 

  17. Vidal, C.: Computational and Biological Analogies for Understanding Fine-Tuned Parameters in Physics. Found. of Sci. 15(4), 375–393 (2010)

    MathSciNet  CrossRef  Google Scholar 

  18. Gershenson, C., Heylighen, F.: When Can We Call a System Self-Organizing? In: Banzhaf, W., Ziegler, J., Christaller, T., Dittrich, P., Kim, J.T. (eds.) ECAL 2003. LNCS (LNAI), vol. 2801, pp. 606–614. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

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Georgiev, G.Y. (2012). A Quantitative Measure, Mechanism and Attractor for Self-Organization in Networked Complex Systems. In: Kuipers, F.A., Heegaard, P.E. (eds) Self-Organizing Systems. IWSOS 2012. Lecture Notes in Computer Science, vol 7166. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-642-28582-0

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