Skip to main content
Erschienen in: Cognitive Neurodynamics 2/2014

01.04.2014 | Research Article

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

verfasst von: Yanhong Zheng, Qingyun Wang, Marius-F. Danca

Erschienen in: Cognitive Neurodynamics | Ausgabe 2/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Chen H, Zhang JQ, Liu J (2008) Enhancement of neuronal coherence by diversity in coupled Rulkov-map models. Phys A 387:1071–1076CrossRef Chen H, Zhang JQ, Liu J (2008) Enhancement of neuronal coherence by diversity in coupled Rulkov-map models. Phys A 387:1071–1076CrossRef
Zurück zum Zitat Gao Z, Hu B, Hu G (2001) Stochastic resonance of small-world networks. Phys Rev E 65:016209CrossRef Gao Z, Hu B, Hu G (2001) Stochastic resonance of small-world networks. Phys Rev E 65:016209CrossRef
Zurück zum Zitat García-Ojalvo J, Sancho JM (1999) Noise in spatially extended systems. Springer, New YorkCrossRef García-Ojalvo J, Sancho JM (1999) Noise in spatially extended systems. Springer, New YorkCrossRef
Zurück zum Zitat Gerstner W, Kistler WM (2002) Spiking neuron models. Cambridge University Press, CambridgeCrossRef Gerstner W, Kistler WM (2002) Spiking neuron models. Cambridge University Press, CambridgeCrossRef
Zurück zum Zitat 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 73:046137CrossRef 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 73:046137CrossRef
Zurück zum Zitat Izhikevich EM (2000) Neural excitability, spiking, and bursting. Int J Bifurcat Chaos 10:1171–1266CrossRef Izhikevich EM (2000) Neural excitability, spiking, and bursting. Int J Bifurcat Chaos 10:1171–1266CrossRef
Zurück zum Zitat Kwon O, Moon HT (2002) Coherence resonance in small-world networks of excitable cells. Phys Lett A 298:319–324CrossRef Kwon O, Moon HT (2002) Coherence resonance in small-world networks of excitable cells. Phys Lett A 298:319–324CrossRef
Zurück zum Zitat Perc M (2005a) Spatial decoherence induced by small-world connectivity in excitable media. New J Phys 7(252):1–10 Perc M (2005a) Spatial decoherence induced by small-world connectivity in excitable media. New J Phys 7(252):1–10
Zurück zum Zitat Perc M (2005b) Spatial coherence resonance in excitable media. Phys Rev E 72:016207CrossRef Perc M (2005b) Spatial coherence resonance in excitable media. Phys Rev E 72:016207CrossRef
Zurück zum Zitat Perc M (2005c) Persistency of noise-induced spatial periodicity in excitable media. Europhys Lett 72:712–718CrossRef Perc M (2005c) Persistency of noise-induced spatial periodicity in excitable media. Europhys Lett 72:712–718CrossRef
Zurück zum Zitat Perc M (2007a) Effects of small-world connectivity on noise-induced temporal and spatial order in neural media. Chaos Solitons Fractals 31:280–291CrossRef Perc M (2007a) Effects of small-world connectivity on noise-induced temporal and spatial order in neural media. Chaos Solitons Fractals 31:280–291CrossRef
Zurück zum Zitat Perc M (2007b) Spatial coherence resonance in neuronal media with discrete local dynamics. Chaos Solitons Fractals 31:64–69CrossRef Perc M (2007b) Spatial coherence resonance in neuronal media with discrete local dynamics. Chaos Solitons Fractals 31:64–69CrossRef
Zurück zum Zitat Perc M (2007c) Stochastic resonance on excitable small-world networks via a pacemaker. Phys Rev E 76:066203CrossRef Perc M (2007c) Stochastic resonance on excitable small-world networks via a pacemaker. Phys Rev E 76:066203CrossRef
Zurück zum Zitat Perc M (2008) Stochastic resonance in soft matter systems: combined effects of static and dynamic disorder. Soft Matter 4:1861–1870CrossRef Perc M (2008) Stochastic resonance in soft matter systems: combined effects of static and dynamic disorder. Soft Matter 4:1861–1870CrossRef
Zurück zum Zitat Perc M, Marhl M (2005) Minimal model for spatial coherence resonance. Phys Rev E 73:066205CrossRef Perc M, Marhl M (2005) Minimal model for spatial coherence resonance. Phys Rev E 73:066205CrossRef
Zurück zum Zitat Perc M, Ozer M, Uzuntarla M (2009) Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving. Phys Lett A 373:964–968CrossRef Perc M, Ozer M, Uzuntarla M (2009) Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving. Phys Lett A 373:964–968CrossRef
Zurück zum Zitat Pikovsky AS, Kurths J (1997) Coherence resonance in a noise-driven excitable system. Phys Rev Lett 78:775–778CrossRef Pikovsky AS, Kurths J (1997) Coherence resonance in a noise-driven excitable system. Phys Rev Lett 78:775–778CrossRef
Zurück zum Zitat Rulkov NF, Timofeev I, Bazhenov M (2004) Oscillations in large-scale cortical networks: map-based model. J Comput Neurosci 17:203–223PubMedCrossRef Rulkov NF, Timofeev I, Bazhenov M (2004) Oscillations in large-scale cortical networks: map-based model. J Comput Neurosci 17:203–223PubMedCrossRef
Zurück zum Zitat Savi MA (2007) Effects of randomness on chaos and order of coupled logistic maps. Phys Lett A 364:389–395CrossRef Savi MA (2007) Effects of randomness on chaos and order of coupled logistic maps. Phys Lett A 364:389–395CrossRef
Zurück zum Zitat Sun XJ, Perc M, Lu QS, Kurths J (2008) Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons. Chaos 18:023102PubMedCrossRef Sun XJ, Perc M, Lu QS, Kurths J (2008) Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons. Chaos 18:023102PubMedCrossRef
Zurück zum Zitat Varela F, Lachaux IP, Rodriguez E, Martinerie J (2001) The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2:229–239PubMedCrossRef Varela F, Lachaux IP, Rodriguez E, Martinerie J (2001) The brainweb: phase synchronization and large-scale integration. Nat Rev Neurosci 2:229–239PubMedCrossRef
Zurück zum Zitat 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):1–11 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):1–11
Zurück zum Zitat Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442PubMedCrossRef Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442PubMedCrossRef
Zurück zum Zitat Zheng YH, Lu QS (2008) Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network. Phys A 387:3719–3728CrossRef Zheng YH, Lu QS (2008) Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network. Phys A 387:3719–3728CrossRef
Metadaten
Titel
Noise induced complexity: patterns and collective phenomena in a small-world neuronal network
verfasst von
Yanhong Zheng
Qingyun Wang
Marius-F. Danca
Publikationsdatum
01.04.2014
Verlag
Springer Netherlands
Erschienen in
Cognitive Neurodynamics / Ausgabe 2/2014
Print ISSN: 1871-4080
Elektronische ISSN: 1871-4099
DOI
https://doi.org/10.1007/s11571-013-9257-x

Weitere Artikel der Ausgabe 2/2014

Cognitive Neurodynamics 2/2014 Zur Ausgabe

Neuer Inhalt