The European Physical Journal Special Topics

, Volume 222, Issue 10, pp 2547–2557 | Cite as

Lattice limit cycle dynamics: Influence of long-distance reactive and diffusive mixing

  • A. ShabuninEmail author
  • A. Provata
Regular Article Applications in Chemistry, Physics and Engineering


The properties of global oscillations produced by coupled reactive stochastic discrete systems on a 2D lattice support are studied, taking into account the competitive influence of local and global mixing processes. Two types of global mixing are considered: reactive and diffusive. It is shown that in the case of diffusive mixing the increase in the diffusive coupling leads to a corresponding increase in the amplitude of the global oscillations. In the case of reactive mixing the competition of local-to-global effects leads to unexpected complex phenomena. Kinetic Monte Carlo simulations demonstrate that the amplitude of oscillations as a function of the mixing-reactive coupling presents an optimal value, which is attributed to the competitive effects between the local and global processes.


Hopf Bifurcation European Physical Journal Special Topic Local Reaction Limit Cycle Oscillation Kinetic Monte Carlo 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I.I. Blekhman, Synchronization in Science and Technology (American Society of Mechanical Engineers, New York, 1988), p. 255Google Scholar
  2. 2.
    A. Pikovsky, M. Rosenblum, J. Kurth, Synchronization: A universal concept in nonlinear dynamics (Cambridge University Press, Cambridge, 2003), p. 432Google Scholar
  3. 3.
    V.S. Anishchenko, V. Astakhov, A. Neiman, T. Vadivasova, L. Schimansky-Geier, Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments (Springer, Berlin, 2006), p. 450Google Scholar
  4. 4.
    D. Armbruster, K. Kaneko, A.S. Mikhailov, Networks of Interacting Machines: Production Organization in Complex Industrial Systems and Biological Cells (World Scientific, London, 2005), p. 280Google Scholar
  5. 5.
    Y. Kuramoto, Chemical oscillations, waves and turbulence (Springer, Berlin, 1984), p. 164Google Scholar
  6. 6.
    A.S. Mikhailov, G. Ertl, Engineering of Chemical Complexity (World Scientific, Singapure, 2012), p. 412Google Scholar
  7. 7.
    Y.M. Romanovsky, N.V. Stepanova, D.S. Chernavsky, Mathematical Biophysics (Nauka, Moscow, 1984), p. 304Google Scholar
  8. 8.
    A.S. Mikhailov, A.Y. Loskutov, Foundations of Synergetics (Springer, Berlin, 1996), p. 277Google Scholar
  9. 9.
    N. Kouvaris, A. Provata, D. Kugiumtzis, Phys. Lett. A 374, 507 (2010)ADSCrossRefzbMATHGoogle Scholar
  10. 10.
    M. Lihoreau, J.T. Costa, C. Rivault, Insectes Sociaux 59, 445 (2012)CrossRefGoogle Scholar
  11. 11.
    V.S. Anishchenko, S. Nikolaev, J. Kurths, Chaos 18, 037123 (2008)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    A. Shabunin, V. Astakhov, V.S. Anishchenko, Int. J. Bifurcation and Chaos 12, 1895 (2002)MathSciNetADSCrossRefzbMATHGoogle Scholar
  13. 13.
    I.I. Blekhman, P.S. Landa, M.G. Rosenblum, Appl. Mech. Rev. 11, 733 (1995)ADSCrossRefGoogle Scholar
  14. 14.
    V.S. Anishchenko, T.E. Vadivasova, J. Comm. Technol. Electr. 47, 117 (2002)Google Scholar
  15. 15.
    G.B. Ermentrout,J. Math. Biol. 23, 55 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    R. Imbihl, G. Ertl, Chem. Rev. 95, 697 (1995)CrossRefGoogle Scholar
  17. 17.
    C. Voss, N. Kruse, Ultramicroscopy 73, 211 (1998)CrossRefGoogle Scholar
  18. 18.
    R. Imbihl, Surface Sci. 603, 1671 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)ADSCrossRefzbMATHGoogle Scholar
  20. 20.
    V.P. Zhdanov, Phys. Rev. E 60, 7554 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    A.V. Shabunin, F. Baras, A. Provata,Phys. Rev. E 66, 036219 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    A. Efimov, A. Shabunin, A. Provata, Phys. Rev. E 78, 056201 (2008)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Department of PhysicsSaratov State UniversitySaratovRussia
  2. 2.Department of Physical ChemistryNational Center for Scientific Research “Demokritos”AthensGreece

Personalised recommendations