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Spontaneous Scaling Emergence In Generic Stochastic Systems

Author

Listed:
  • SORIN SOLOMON

    (Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel)

  • MOSHE LEVY

    (Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel)

Abstract

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom.While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction.The systems present power laws with exponents which in a wide range(α −2there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos, and bursts/intermittency.

Suggested Citation

  • Sorin Solomon & Moshe Levy, 1996. "Spontaneous Scaling Emergence In Generic Stochastic Systems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 745-751.
    • Handle: RePEc:wsi:ijmpcx:v:07:y:1996:i:05:n:s0129183196000624
    DOI: 10.1142/S0129183196000624
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    Citations

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    Cited by:

    1. Domenico Delli Gatti & Edoardo Gaffeo & Mauro Gallegati, 2008. "A look at the relationship between industrial dynamics and aggregate fluctuations," Department of Economics Working Papers 0803, Department of Economics, University of Trento, Italia.
    2. Sorin Solomon & Nataša Golo, 2015. "Microeconomic structure determines macroeconomic dynamics: Aoki defeats the representative agent," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 5-30, April.
    3. Segarra, Agustí & Teruel, Mercedes, 2012. "An appraisal of firm size distribution: Does sample size matter?," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 314-328.
    4. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    5. Predrag R. Jelenković & Jian Tan, 2010. "Modulated Branching Processes, Origins of Power Laws, and Queueing Duality," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 807-829, November.
    6. Solomon, Sorin & Richmond, Peter, 2001. "Power laws of wealth, market order volumes and market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 188-197.
    7. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    8. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    9. Wataru Souma, 2002. "Physics of Personal Income," Papers cond-mat/0202388, arXiv.org.
    10. Honjo, Haruo & Sano, Masaki & Miki, Hiroshi & Sakaguchi, Hidetsugu, 2015. "Statistical properties of approval ratings for governments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 266-272.
    11. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press, vol. 11(5), pages 895-953, November.
    12. Sorin Solomon & Moshe Levy, 2000. "Market Ecology, Pareto Wealth Distribution and Leptokurtic Returns in Microscopic Simulation of the LLS Stock Market Model," Papers cond-mat/0005416, arXiv.org.

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