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Kinouchi O, Brochini L, Costa AA, et al. Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems. Sci Rep. 2019;9(1):3874doi: 10.1038/s41598-019-40473-1.
Kinouchi, O., Brochini, L., Costa, A. A., Campos, J. G. F., & Copelli, M. (2019). Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems. Scientific reports, 9(1), 3874. https://doi.org/10.1038/s41598-019-40473-1
Kinouchi, Osame, et al. "Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems." Scientific reports vol. 9,1 (2019): 3874. doi: https://doi.org/10.1038/s41598-019-40473-1
Kinouchi O, Brochini L, Costa AA, Campos JGF, Copelli M. Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems. Sci Rep. 2019 Mar 07;9(1):3874. doi: 10.1038/s41598-019-40473-1. PMID: 30846773; PMCID: PMC6405991.
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Sci Rep. 2019 Mar 07;9(1):3874. doi: 10.1038/s41598-019-40473-1.

Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems.

Scientific reports

Osame Kinouchi, Ludmila Brochini, Ariadne A Costa, João Guilherme Ferreira Campos, Mauro Copelli

Affiliations

  1. Universidade de São Paulo, Departamento de Física-FFCLRP, Ribeirão Preto, SP, Brazil. [email protected].
  2. Universidade de São Paulo, Instituto de Matemática e Estatística, São Paulo, SP, Brazil.
  3. Universidade Federal de Goiás, Unidade Acadêmica Especial de Ciências Exatas, Jataí, GO, Brazil.
  4. Universidade Federal de Pernambuco, Departamento de Física, Recife, PE, Brazil.
  5. Universidade de São Paulo, Departamento de Física-FFCLRP, Ribeirão Preto, SP, Brazil.

PMID: 30846773 PMCID: PMC6405991 DOI: 10.1038/s41598-019-40473-1

Abstract

In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. Here we make a linear stability analysis of the mean field fixed points of two self-organized quasi-critical systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism interrupts the oscillations, producing both power law avalanches and dragon king events, which appear as bands of synchronized firings in raster plots. Our approach differs from standard SOC models in that it predicts the coexistence of these different types of neuronal activity.

References

  1. Hum Brain Mapp. 2008 Jul;29(7):770-7 - PubMed
  2. Phys Rev Lett. 2014 Apr 4;112(13):138103 - PubMed
  3. Nat Neurosci. 2013 Jul;16(7):942-8 - PubMed
  4. Phys Rev E. 2017 Jan;95(1-1):012310 - PubMed
  5. PLoS One. 2011 May 06;6(5):e14804 - PubMed
  6. Nature. 1976 Sep 23;263(5575):319-20 - PubMed
  7. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Dec;80(6 Pt 1):061917 - PubMed
  8. Phys Rev Lett. 2005 Jun 3;94(21):218102 - PubMed
  9. Phys Rev Lett. 2009 Mar 20;102(11):118110 - PubMed
  10. Sci Rep. 2018 Feb 21;8(1):3417 - PubMed
  11. Neural Comput. 1998 May 15;10(4):821-35 - PubMed
  12. Nat Commun. 2013;4:2521 - PubMed
  13. Philos Trans A Math Phys Eng Sci. 2008 Feb 13;366(1864):329-43 - PubMed
  14. Neuron. 2012 Jan 26;73(2):235-47 - PubMed
  15. Sci Rep. 2016 Jul 20;6:29561 - PubMed
  16. J R Soc Interface. 2013 Jan 6;10(78):20120558 - PubMed
  17. Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Aug;86(2 Pt 1):021909 - PubMed
  18. Phys Rev Lett. 2006 Jan 20;96(2):028107 - PubMed
  19. Phys Rev E. 2017 Apr;95(4-1):042303 - PubMed
  20. Phys Rev Lett. 2016 Jun 17;116(24):240601 - PubMed
  21. J Neurosci. 2012 Jul 18;32(29):9817-23 - PubMed
  22. Phys Rev Lett. 2000 Jun 26;84(26 Pt 1):6114-7 - PubMed
  23. Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):032135 - PubMed
  24. Phys Rev Lett. 2011 Feb 4;106(5):058101 - PubMed
  25. Proc Natl Acad Sci U S A. 1997 Jan 21;94(2):719-23 - PubMed
  26. Sci Rep. 2016 Nov 07;6:35831 - PubMed
  27. Neural Comput. 2018 Apr;30(4):1132-1149 - PubMed
  28. Chaos. 2018 Jan;28(1):013103 - PubMed
  29. PLoS Comput Biol. 2012 Jan;8(1):e1002312 - PubMed
  30. J Comput Neurosci. 2000 May-Jun;8(3):183-208 - PubMed
  31. J Neurosci. 2003 Dec 3;23(35):11167-77 - PubMed
  32. Front Physiol. 2012 Mar 28;3:62 - PubMed
  33. Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012712 - PubMed
  34. J Math Biol. 2011 Sep;63(3):433-57 - PubMed

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