Brain dynamics at multiple scales: can one reconcile the
apparent low-dimensional chaos of macroscopic variables with the
seemingly stochastic behavior of single neurons?
Sami El Boustani and Alain Destexhe
International Journal of Bifurcation and Chaos 20:
Nonlinear time series analyses have suggested that the human
electroencephalogram (EEG) may share statistical and dynamical
properties with chaotic systems. During slow-wave sleep or
pathological states like epilepsy, correlation dimension measurements
display low values, while in awake and attentive subjects, there is
not such low dimensionality, and the EEG is more similar to a
stochastic variable. We briefly review these results and contrast
them with recordings in cat cerebral cortex, as well as with
theoretical models. In awake or sleeping cats, recordings with
microelectrodes inserted in cortex show that global variables such as
local field potentials (local EEG) are similar to the human EEG.
However, in both cases, neuronal discharges are highly irregular and
exponentially distributed, similar to Poisson stochastic processes.
To attempt reconcile these results, we investigate models of
randomly-connected networks of integrate-and-fire neurons, and also
contrast global (averaged) variables, with neuronal activity. The
network displays different states, such as "synchronous regular" (SR)
or "asynchronous irregular" (AI) states. In SR states, the global
variables display coherent behavior with low dimensionality, while in
AI states, the global activity is high-dimensionally chaotic with
exponentially distributed neuronal discharges, similar to awake cats.
Scale-dependent Lyapunov exponents and epsilon-entropies show that
the seemingly stochastic nature at small scales (neurons) can coexist
with more coherent behavior at larger scales (averages). Thus, we
suggest that brain activity obeys similar scheme, with seemingly
stochastic dynamics at small scales (neurons), while large scales
(EEG) display more coherent behavior or high-dimensional chaos.
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