We review two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitly, including network parameters dependence. This is done in a statistical physicslike 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 [S. Amari, Syst. Man Cybernet. SMC-2, 643–657 (1972); H. R. Wilson and J. D. Cowan, Biophys. J. 12, 1–24 (1972)] and a conductance based Integrate and Fire model [M. Rudolph and A. Destexhe, Neural Comput. 18, 2146–2210 (2006); M. Rudolph and A. Destexhe, Neurocomputing 70(10–12), 1966–1969 (2007)].
Linear response in neuronal networks: From neurons dynamics to collective response
Note: This paper is part of the Focus Issue, Linear Response Theory: Potentials and Limits.
Bruno Cessac; Linear response in neuronal networks: From neurons dynamics to collective response. Chaos 1 October 2019; 29 (10): 103105. https://doi.org/10.1063/1.5111803
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