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Nonlinear time series analyses have suggested that the humanelectroencephalogram (EEG) may share statistical and dynamical properties withchaotic systems. During slow-wave sleep or pathological states like epilepsy,correlation dimension measurements display low values, while in awake andattentive subjects, there is not such low dimensionality, and the EEG is moresimilar to a stochastic variable. We briefly review these results and contrastthem with recordings in cat cerebral cortex, as well as with theoreticalmodels. In awake or sleeping cats, recordings with microelectrodes inserted incortex show that global variables such as local field potentials (local EEG)are similar to the human EEG. However, in both cases, neuronal discharges arehighly irregular and exponentially distributed, similar to Poisson stochasticprocesses. To attempt reconcile these results, we investigate models ofrandomly-connected networks of integrate-and-fire neurons, and also contrastglobal (averaged) variables, with neuronal activity. The network displaysdifferent states, such as "synchronous regular" (SR) or "asynchronousirregular" (AI) states. In SR states, the global variables display coherentbehavior with low dimensionality, while in AI states, the global activity ishigh-dimensionally chaotic with exponentially distributed neuronal discharges,similar to awake cats. Scale-dependent Lyapunov exponents and epsilon-entropiesshow that the seemingly stochastic nature at small scales (neurons) can coexistwith more coherent behavior at larger scales (averages). Thus, we suggest thatbrain activity obeys similar scheme, with seemingly stochastic dynamics atsmall scales (neurons), while large scales (EEG) display more coherent behavioror high-dimensional chaos.

Does brain activity stem from high-dimensional chaotic dynamics?  Evidence from the human electroencephalogram, cat cerebral cortex and  artificial neuronal networks