Fractal Analyses of Networks of Integrate-and-Fire Stochastic Spiking Neurons

  • Ariadne A. Costa
  • Mary Jean Amon
  • Olaf Sporns
  • Luis H. Favela
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


Although there is increasing evidence of criticality in the brain, the processes that guide neuronal networks to reach or maintain criticality remain unclear. The present research examines the role of neuronal gain plasticity in time-series of simulated neuronal networks composed of integrate-and-fire stochastic spiking neurons and the utility of fractal methods in assessing network criticality. Simulated time-series were derived from a network model of fully connected discrete-time stochastic excitable neurons. Monofractal and multifractal analyses were applied to neuronal gain time-series. Fractal scaling was greatest in networks with a mid-range of neuronal plasticity, versus extremely high or low levels of plasticity. Peak fractal scaling corresponded closely to additional indices of criticality, including average branching ratio. Networks exhibited multifractal structure, or multiple scaling relationships. Multifractal spectra around peak criticality exhibited elongated right tails, suggesting that the fractal structure is relatively insensitive to high-amplitude local fluctuations. Networks near critical states exhibited mid-range multifractal spectra width and tail length, which is consistent with the literature suggesting that networks poised at quasi-critical states must be stable enough to maintain organization but unstable enough to be adaptable. Lastly, fractal analyses may offer additional information about critical state dynamics of networks by indicating scales of influence as networks approach critical states.


1/f scaling Self-organized criticality Fractal analysis Multifractal analysis Neuronal networks 



This article was produced as part of the activities of FAPESP Research, Innovation and Dissemination Center for Neuromathematics (grant #2013/07699-0, S.Paulo Research Foundation). AAC also thanks grants \(\#\)2016/00430-3 and \(\#\)2016/20945-8 São Paulo Research Foundation (FAPESP).


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Ariadne A. Costa
    • 1
  • Mary Jean Amon
    • 1
  • Olaf Sporns
    • 1
  • Luis H. Favela
    • 2
  1. 1.Department of Psychological and Brain SciencesIndiana UniversityBloomingtonUSA
  2. 2.Department of Philosophy and Cognitive Sciences ProgramUniversity of Central FloridaOrlandoUSA

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