Critical fluctuations in cortical models near instability

Aburn, Matthew J., Holmes, C. A., Roberts, James A., Boonstra, Tjeerd W. and Breakspear, Michael (2012) Critical fluctuations in cortical models near instability. Frontiers in Physiology, 3 . doi:10.3389/fphys.2012.00331


Author Aburn, Matthew J.
Holmes, C. A.
Roberts, James A.
Boonstra, Tjeerd W.
Breakspear, Michael
Title Critical fluctuations in cortical models near instability
Journal name Frontiers in Physiology   Check publisher's open access policy
ISSN 1664-042X
Publication date 2012-08
Sub-type Article (original research)
DOI 10.3389/fphys.2012.00331
Open Access Status DOI
Volume 3
Total pages 17
Place of publication Lausanne, Switzerland
Publisher Frontiers Research Foundation
Language eng
Abstract Computational studies often proceed from the premise that cortical dynamics operate in a linearly stable domain, where fluctuations dissipate quickly and show only short memory. Studies of human electroencephalography (EEG), however, have shown significant autocorrelation at time lags on the scale of minutes, indicating the need to consider regimes where non-linearities influence the dynamics. Statistical properties such as increased autocorrelation length, increased variance, power law scaling, and bistable switching have been suggested as generic indicators of the approach to bifurcation in non-linear dynamical systems. We study temporal fluctuations in a widely-employed computational model (the Jansen-Rit model) of cortical activity, examining the statistical signatures that accompany bifurcations. Approaching supercritical Hopf bifurcations through tuning of the background excitatory input, we find a dramatic increase in the autocorrelation length that depends sensitively on the direction in phase space of the input fluctuations and hence on which neuronal subpopulation is stochastically perturbed. Similar dependence on the input direction is found in the distribution of fluctuation size and duration, which show power law scaling that extends over four orders of magnitude at the Hopf bifurcation. We conjecture that the alignment in phase space between the input noise vector and the center manifold of the Hopf bifurcation is directly linked to these changes. These results are consistent with the possibility of statistical indicators of linear instability being detectable in real EEG time series. However, even in a simple cortical model, we find that these indicators may not necessarily be visible even when bifurcations are present because their expression can depend sensitively on the neuronal pathway of incoming fluctuations.
Keyword Autocorrelation
Critical fluctuations
Hopf bifurcation
Neural mass model
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Article number 331

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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