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Identification of criticality in neuronal avalanches: II. A theoretical and empirical investigation of the Driven case

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posted on 2023-06-08, 17:05 authored by Caroline Hartley, Timothy J Taylor, Istvan Kiss, Simon F Farmer, Luc BerthouzeLuc Berthouze
The observation of apparent power laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a separation of timescales is thought to be crucial for the observation of power-law dynamics and computational models are often constructed with this property. However, this is not necessarily a characteristic of physiological neural networks—external input does not only occur when the network is at rest/a steady state. In this paper we study a simple neuronal network model driven by a continuous external input (i.e. the model does not have an explicit separation of timescales from seeding the system only when in the quiescent state) and analytically tuned to operate in the region of a critical state (it reaches the critical regime exactly in the absence of input—the case studied in the companion paper to this article). The system displays avalanche dynamics in the form of cascades of neuronal firing separated by periods of silence. We observe partial scale-free behaviour in the distribution of avalanche size for low levels of external input. We analytically derive the distributions of waiting times and investigate their temporal behaviour in relation to different levels of external input, showing that the system’s dynamics can exhibit partial long-range temporal correlations. We further show that as the system approaches the critical state by two alternative ‘routes’, different markers of criticality (partial scale-free behaviour and long-range temporal correlations) are displayed. This suggests that signatures of criticality exhibited by a particular system in close proximity to a critical state are dependent on the region in parameter space at which the system (currently) resides.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Mathematical Neuroscience

ISSN

2190-8567

Publisher

SpringerOpen

Issue

9

Volume

4

Page range

1-42

Department affiliated with

  • Informatics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2014-04-28

First Open Access (FOA) Date

2014-04-28

First Compliant Deposit (FCD) Date

2014-04-25

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