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Self-consistent Formulations for Stochastic Nonlinear Neuronal Dynamics by Jonas Stapmanns; Tobias Kühn; David Dahmen; Thomas Luu; Carsten Honerkamp; Moritz Helias is a Physics and Astronomy article available to read on EtoBox.

What is Self-consistent Formulations for Stochastic Nonlinear Neuronal Dynamics about?

Neural dynamics is often investigated with tools from bifurcation theory. However, many neuron models are stochastic, mimicking fluctuations in the input from unknown parts of the brain or the spiking nature of signals. Noise changes the dynamics with respect to the deterministic model; in particular classical bifurcation theory cannot be applied. We formulate the stochastic neuron dynamics in the Martin-Siggia-Rose de Dominicis-Janssen (MSRDJ) formalism and present the fluctuation expansion of the effective action and the functional renormalization group (fRG) as two systematic ways to incorporate corrections to the mean dynamics and time-dependent statistics due to fluctuations in the presence of nonlinear neuronal gain. To formulate self-consistency equations, we derive a fundamental link between the effective action in the Onsager-Machlup (OM) formalism, which allows the study of phase transitions, and the MSRDJ effective action, which is computationally advantageous. These results in particular allow the derivation of an OM effective action for systems with non-Gaussian noise. This approach naturally leads to effective deterministic equations for the first moment of the stocha

Who reads Self-consistent Formulations for Stochastic Nonlinear Neuronal Dynamics?

Author

Jonas Stapmanns; Tobias Kühn; David Dahmen; Thomas Luu; Carsten Honerkamp; Moritz Helias

Publisher

The American Physical Society; American Physical Society; American Physical Society (APS) (ISSN 1063-651X)

Published

2020

Language

EN

Field

Physics and Astronomy (Physical Sciences)