Critical fluctuations in cortical models near instability.

Area of Science:

• Computational neuroscience
• Non-linear dynamical systems
• Brain activity modeling

Background:

• Cortical dynamics are often assumed to be linearly stable.
• Human electroencephalography (EEG) data reveals long-term autocorrelation, suggesting non-linear influences.
• Statistical properties like power-law scaling and bistable switching may indicate bifurcations in non-linear systems.

Purpose of the Study:

• To investigate statistical signatures accompanying bifurcations in a computational model of cortical activity (Jansen-Rit model).
• To understand how non-linear dynamics and input fluctuations affect brain activity patterns.

Main Methods:

• Studied temporal fluctuations in the Jansen-Rit model of cortical activity.
• Tuned background excitatory input to approach supercritical Hopf bifurcations.
• Analyzed autocorrelation length, variance, and power-law scaling of fluctuations.

Main Results:

• A significant increase in autocorrelation length was observed near Hopf bifurcations.
• This increase was sensitive to the direction of input fluctuations in phase space.
• Power-law scaling in fluctuation size and duration was observed over four orders of magnitude at the bifurcation point.

Conclusions:

• The study demonstrates that statistical indicators of linear instability can be detected in computational models of brain activity.
• The expression of these indicators is sensitive to the neuronal pathway of incoming fluctuations.
• These findings have implications for interpreting electroencephalography (EEG) signals and understanding non-linear brain dynamics.