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

Hartley, Caroline, Taylor, Timothy J, Kiss, Istvan Z, Farmer, Simon F and Berthouze, Luc (2014) Identification of criticality in neuronal avalanches: II. A theoretical and empirical investigation of the Driven case. Journal of Mathematical Neuroscience, 4 (9). pp. 1-42. ISSN 2190-8567

PDF - Published Version
Available under License Creative Commons Attribution.

Download (1MB) | Preview


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.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Informatics
School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Q Science > QP Physiology > QP0351 Neurophysiology and neuropsychology
R Medicine > RC Internal medicine > RC0321 Neurosciences. Biological psychiatry. Neuropsychiatry
Depositing User: Luc Berthouze
Date Deposited: 28 Apr 2014 08:17
Last Modified: 20 Nov 2020 15:35

View download statistics for this item

📧 Request an update