Brain Dynamics at Multiple Scales: Can One Reconcile the Apparent Low-Dimensional Chaos of Macroscopic Variables with the seemingly Stochastic Behavior of Single Neurons?

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 ε-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 highdimensional chaos. Unité de Neurosciences Intégratives et Computationnelles (UNIC), CNRS, Gif-sur-Yvette, France ∗: Corresponding author at the following address: UNIC, Bat 33, CNRS, 1 Avenue de la Terrasse, 91198 Gif sur Yvette, France. E-mail: [email protected]