  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.
