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Nicolas Brunel : Collective states with irregular single neuron activity in brain networks

Electrophysiological recordings of neurons in the cortex of mammals reveal a ubiquitous high degree of irregularity of single neuron activity. The mechanisms and functional role of this irregular activity remain the subject of debate. Here, I will describe simplified models of networks of neurons, and analytical tools that can be used to understand their dynamics. Under some conditions, such networks can be described using a system of coupled Fokker-Planck equations (one for each class of neurons composing the network), in which the drift and diffusion terms depend on the probability flux at firing threshold. Provided specific conditions on network connectivity are satisfied, these models reproduce some of the landmark features observed in experiments (highly irregular firing at low rates, weak correlations between neurons, wide distributions of firing rates). Interestingly, these networks show a rich diversity of irregular states (chaotic or not, asynchronous or synchronous).

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