Linear response in neuronal networks: from neurons dynamics to collective response

Abstract

We review two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitely, including network parameters dependence. This is done in a statistical physics-like approach where one associates to the spontaneous dynamics of the model a natural notion of Gibbs distribution inherited from ergodic theory or stochastic processes. These two examples are the Amari-Wilson-Cowan model and a conductance based Integrate and Fire model.

23 pages, 17 figures, to appear

References in corpus (3)

• An update on nonequilibrium linear response
• On the susceptibility function of piecewise expanding interval maps
• Linear response, susceptibility and resonances in chaotic toy models

Cited by in corpus (7)

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• Spectroscopy of phase transitions for multiagent systems
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• Understanding Recurrent Neural Networks Using Nonequilibrium Response Theory
• Rigorous justification for the space-split sensitivity algorithm to compute linear response in Anosov systems
• Predictors and Predictands of Linear Response in Spatially Extended Systems