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Self-organization of a critical state on complex networks

  • Statistical, Nonlinear, and Soft Matter Physics
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Abstract

The critical dynamics of a two-threshold system with the law of conservation of the basic quantity z and in the absence of sink on a scale-free network has been studied. It has been shown that the critical state that is a set of metastable states appears in such a system. The structure of the metastable states is a set of stable clusters of nodes at which the z values are close to the positive and negative threshold values. Avalanches transforming the system from one metastable state to another state appear in the system. The absence of sink is effectively replaced by the annihilation process. The statistics of avalanches in such a system has been analyzed. It has been shown that the self-organized critical state can appear in the system.

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References

  1. S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. 51, 1079 (2002).

    Article  ADS  Google Scholar 

  2. S. N. Dorogovtsev, F. V. Goltsev, and J. F. F. Mendes, Rev. Mod. Phys. 80, 1275 (2008).

    Article  ADS  Google Scholar 

  3. R. Karmakar and S. S. Manna, J. Phys. A: Math. Gen. 38, L78 (2005).

    Article  Google Scholar 

  4. K.-L. Goh, D.-S. Lee, D. Kahgn, and D. Kim, Phys. Rev. Lett. 91, 148 701 (2003).

    Google Scholar 

  5. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  6. S. L. Ginzburg, V. A. Nakin, and N. E. Savitskaya, Zh. Éksp. Teor. Fiz. 130(5), 862 (2006) [JETP 103 (5), 747 (2006)].

    Google Scholar 

  7. S. L. Ginzburg, A. V. Nakin, and N. E. Savitskaya, Physica C (Amsterdam) 436, 7 (2006).

    ADS  Google Scholar 

  8. S. L. Ginzburg, M. A. Pustovoit, and N. E. Savitskaya, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 57, 1319 (1998).

    Google Scholar 

  9. S. L. Ginzburg and N. E. Savitskaya, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 66, 026128 (2002).

    ADS  Google Scholar 

  10. S. L. Ginzburg, Zh. Éksp. Teor. Fiz. 106(2), 607 (1994) [JETP 79 (2), 334 (1994)].

    MathSciNet  Google Scholar 

  11. D. Dhar, Phys. Rev. Lett. 64, 1613 (1990).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. A.-L. Barabasi and R. Albert, Science (Washington) 286, 509 (1999).

    Article  MathSciNet  Google Scholar 

  13. J. P. Sethna and C. R. Mayers, Phys. Rev. B: Condens. Matter 47, 11 171 (1993).

    Google Scholar 

  14. B. Tadi, U. Nowak, K. D. Usadel, R. Ramaswamy, and S. Padlewski, Phys. Rev. A: At., Mol., Opt. Phys. 45, 8536 (1992).

    ADS  Google Scholar 

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Authors and Affiliations

  1. Petersburg Nuclear Physics Institute, Russian Academy of Sciences, Gatchina, Leningradskaya oblast, 188300, Russia

    S. L. Ginzburg, A. V. Nakin & N. E. Savitskaya

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  1. S. L. Ginzburg
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  2. A. V. Nakin
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  3. N. E. Savitskaya
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Correspondence to N. E. Savitskaya.

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Original Russian Text © S.L. Ginzburg, A.V. Nakin, N.E. Savitskaya, 2009, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 136, No. 6, pp. 1183–1193.

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Ginzburg, S.L., Nakin, A.V. & Savitskaya, N.E. Self-organization of a critical state on complex networks. J. Exp. Theor. Phys. 109, 1022–1031 (2009). https://doi.org/10.1134/S1063776109120140

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  • DOI: https://doi.org/10.1134/S1063776109120140

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