Advertisement

The European Physical Journal Special Topics

, Volume 227, Issue 10–11, pp 1231–1241 | Cite as

The mean complexities in the regimes of dynamical networks with full oscillations binding

  • Valentin Afraimovich
  • Aleksei DmitrichevEmail author
  • Dmitry Shchapin
  • Vladimir Nekorkin
Regular Article
Part of the following topical collections:
  1. Advances in Nonlinear Dynamics of Complex Networks: Adaptivity, Stochasticity, Delays

Abstract

We continue to apply the notion of mean complexities to study dynamical networks. We show that the mean complexities can help to single out the nodes with similar features (and dynamical behavior) and to reveal some properties of the topology of the networks. We found that the nodes with the same degree (number of connections) have equal values of the mean complexities in the regime of full binding. At the same time, the mean complexities of nodes with different degree follow a descending order with respect to the degree.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Albert, A.L. Barabasi, Rev. Mod. Phys. 74, 47 (2002) ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    M.E.J. Newman, SIAM Rev. 45, 167 (2003) ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Phys. Rep. 424, 175 (2006) ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    M.E.J. Newman, A.L. Barabasi, D.J. Watts, The Structure and Dynamics of Networks (Princeton University Press, Princeton, 2006) Google Scholar
  5. 5.
    E. Prisner, Graph Dynamics (CRC Press, Boca Raton, FL, 1995) Google Scholar
  6. 6.
    O.V. Maslennikov, V.I. Nekorkin, Phys. Usp. 60, 694 (2017) ADSCrossRefGoogle Scholar
  7. 7.
    V. Afraimovich, A. Dmitrichev, D. Shchapin, V. Nekorkin, Commun. Nonlinear Sci. Numer. Simul. 55, 166 (2018) ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    V.S. Afraimovich, L.A. Bunimovich, S.V. Moreno, Regul. Chaotic Dyn. 15, 127 (2010) ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    V.S. Afraimovich, L.A. Bunimovich, Nonlinearity 20, 1761 (2007) ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    V. Afraimovich, G.M. Zaslavsky, Chaos 18, 519 (2003) ADSCrossRefGoogle Scholar
  11. 11.
    X. Leoncini, Hamiltonian chaos and anomalous transport in two dimensional flows, in Hamiltonian chaos beyond the KAM theory: dedicated to George M. Zaslavsky, edited by C.J. Luo Albert, V. Afraimovich (Springer-Verlag, Berlin, Heidelberg, 2011), pp. 143–192 Google Scholar
  12. 12.
    V. Afraimovich, R. Rechtman, Commun. Nonlinear Sci. Num. Simul. 14, 1454 (2009) CrossRefGoogle Scholar
  13. 13.
    V.I. Nekorkin, L.V. Vdovin, Prikl. Nelin. Dina. 15, 36 (2007) (in Russian) Google Scholar
  14. 14.
    M. Courbage, V.I. Nekorkin, L.V. Vdovin, Chaos 17, 043109 (2007) ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    M. Courbage, V.I. Nekorkin, Int. J. Bifurc. Chaos 20, 1631 (2010) CrossRefGoogle Scholar
  16. 16.
    O.V. Maslennikov, V.I. Nekorkin, Chaos 26, 073104 (2016) ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Valentin Afraimovich
    • 1
    • 2
  • Aleksei Dmitrichev
    • 2
    Email author
  • Dmitry Shchapin
    • 2
  • Vladimir Nekorkin
    • 2
  1. 1.Instituto de Investigacion en Comunicacion Optica, Universidad Autonoma de San Luis PotosiSan Luis PotosiMexico
  2. 2.Institute of Applied Physics RASNizhny NovgorodRussia

Personalised recommendations