Cognitive Neurodynamics

, Volume 8, Issue 2, pp 143–149 | Cite as

Noise induced complexity: patterns and collective phenomena in a small-world neuronal network

  • Yanhong Zheng
  • Qingyun WangEmail author
  • Marius-F. Danca
Research Article


The effects of noise on patterns and collective phenomena are studied in a small-world neuronal network with the dynamics of each neuron being described by a two-dimensional Rulkov map neuron. It is shown that for intermediate noise levels, noise-induced ordered patterns emerge spatially, which supports the spatiotemporal coherence resonance. However, the inherent long range couplings of small-world networks can effectively disrupt the internal spatial scale of the media at small fraction of long-range couplings. The temporal order, characterized by the autocorrelation of a firing rate function, can be greatly enhanced by the introduction of small-world connectivity. There exists an optimal fraction of randomly rewired links, where the temporal order and synchronization can be optimized.


Small-world neural network Pattern Synchronization Coherence resonance 



This work was supported by the National Natural Science Foundation of China (Nos. 11102041 and 11172017) and the Research Fund for the Doctoral Program of Higher Education (No. 20121102110014).


  1. Bassett DS, Bullmore E (2006) Small-world brain networks. Neuroscientist 12:512–523PubMedCrossRefGoogle Scholar
  2. Chen H, Zhang JQ, Liu J (2008) Enhancement of neuronal coherence by diversity in coupled Rulkov-map models. Phys A 387:1071–1076CrossRefGoogle Scholar
  3. Gao Z, Hu B, Hu G (2001) Stochastic resonance of small-world networks. Phys Rev E 65:016209CrossRefGoogle Scholar
  4. García-Ojalvo J, Sancho JM (1999) Noise in spatially extended systems. Springer, New YorkCrossRefGoogle Scholar
  5. Gerstner W, Kistler WM (2002) Spiking neuron models. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  6. Gong YB, Xu B, Xu Q, Yang CL, Ren TQ, Hou ZH, Xin HW (2006) Ordering spatiotemporal chaos in complex thermosensitive neuron networks. Phys Rev E 73:046137CrossRefGoogle Scholar
  7. Izhikevich EM (2000) Neural excitability, spiking, and bursting. Int J Bifurcat Chaos 10:1171–1266CrossRefGoogle Scholar
  8. Kwon O, Moon HT (2002) Coherence resonance in small-world networks of excitable cells. Phys Lett A 298:319–324CrossRefGoogle Scholar
  9. Perc M (2005a) Spatial decoherence induced by small-world connectivity in excitable media. New J Phys 7(252):1–10Google Scholar
  10. Perc M (2005b) Spatial coherence resonance in excitable media. Phys Rev E 72:016207CrossRefGoogle Scholar
  11. Perc M (2005c) Persistency of noise-induced spatial periodicity in excitable media. Europhys Lett 72:712–718CrossRefGoogle Scholar
  12. Perc M (2007a) Effects of small-world connectivity on noise-induced temporal and spatial order in neural media. Chaos Solitons Fractals 31:280–291CrossRefGoogle Scholar
  13. Perc M (2007b) Spatial coherence resonance in neuronal media with discrete local dynamics. Chaos Solitons Fractals 31:64–69CrossRefGoogle Scholar
  14. Perc M (2007c) Stochastic resonance on excitable small-world networks via a pacemaker. Phys Rev E 76:066203CrossRefGoogle Scholar
  15. Perc M (2008) Stochastic resonance in soft matter systems: combined effects of static and dynamic disorder. Soft Matter 4:1861–1870CrossRefGoogle Scholar
  16. Perc M, Marhl M (2005) Minimal model for spatial coherence resonance. Phys Rev E 73:066205CrossRefGoogle Scholar
  17. Perc M, Ozer M, Uzuntarla M (2009) Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving. Phys Lett A 373:964–968CrossRefGoogle Scholar
  18. Pikovsky AS, Kurths J (1997) Coherence resonance in a noise-driven excitable system. Phys Rev Lett 78:775–778CrossRefGoogle Scholar
  19. Rulkov NF (2001) Regularization of synchronized chaotic bursts. Phys Rev Lett 86:183–186PubMedCrossRefGoogle Scholar
  20. Rulkov NF, Timofeev I, Bazhenov M (2004) Oscillations in large-scale cortical networks: map-based model. J Comput Neurosci 17:203–223PubMedCrossRefGoogle Scholar
  21. Savi MA (2007) Effects of randomness on chaos and order of coupled logistic maps. Phys Lett A 364:389–395CrossRefGoogle Scholar
  22. Sun XJ, Perc M, Lu QS, Kurths J (2008) Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons. Chaos 18:023102PubMedCrossRefGoogle Scholar
  23. Varela F, Lachaux IP, Rodriguez E, Martinerie J (2001) The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2:229–239PubMedCrossRefGoogle Scholar
  24. Wang QY, Duan ZS, Huang L, Chen GR, Lu QS (2007) Pattern formation and firing synchronization in networks of map neurons. New J Phys 9(383):1–11Google Scholar
  25. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442PubMedCrossRefGoogle Scholar
  26. Zheng YH, Lu QS (2008) Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network. Phys A 387:3719–3728CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Yanhong Zheng
    • 1
    • 2
  • Qingyun Wang
    • 1
    Email author
  • Marius-F. Danca
    • 3
    • 4
  1. 1.Department of Dynamics and ControlBeihang UniversityBeijingChina
  2. 2.School of Mathematics and Computer ScienceFujian Normal UniversityFuzhouChina
  3. 3.Department of Mathematics and Computer ScienceAvram Iancu UniversityCluj-NapocaRomania
  4. 4.Romanian Institute of Science and TechnologyCluj-NapocaRomania

Personalised recommendations