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Title: Extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems

Abstract

The analysis of transitions in stochastic neurodynamical systems is essential to understand the computational principles that underlie those perceptual and cognitive processes involving multistable phenomena, like decision making and bistable perception. To investigate the role of noise in a multistable neurodynamical system described by coupled differential equations, one usually considers numerical simulations, which are time consuming because of the need for sufficiently many trials to capture the statistics of the influence of the fluctuations on that system. An alternative analytical approach involves the derivation of deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. However, the application of the method of moments is restricted by the assumption that the distribution of the state variables of the system takes on a unimodal Gaussian shape. We extend in this paper the classical moments method to the case of bimodal distribution of the state variables, such that a reduced system of deterministic coupled differential equations can be derived for the desired regime of multistability.

Authors:
;  [1]
  1. Computational Neuroscience Group, Universitat Pompeu Fabra, Passeig de Circumvallacio, 8, 08003 Barcelona (Spain)
Publication Date:
OSTI Identifier:
21072399
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevE.75.031913; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; COMPUTERIZED SIMULATION; DECISION MAKING; DIFFERENTIAL EQUATIONS; DISTRIBUTION; FLUCTUATIONS; MOMENTS METHOD; NOISE; STABILITY; STATISTICS; STOCHASTIC PROCESSES

Citation Formats

Deco, Gustavo, and Marti, Daniel. Extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems. United States: N. p., 2007. Web. doi:10.1103/PHYSREVE.75.031913.
Deco, Gustavo, & Marti, Daniel. Extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems. United States. doi:10.1103/PHYSREVE.75.031913.
Deco, Gustavo, and Marti, Daniel. Thu . "Extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems". United States. doi:10.1103/PHYSREVE.75.031913.
@article{osti_21072399,
title = {Extended method of moments for deterministic analysis of stochastic multistable neurodynamical systems},
author = {Deco, Gustavo and Marti, Daniel},
abstractNote = {The analysis of transitions in stochastic neurodynamical systems is essential to understand the computational principles that underlie those perceptual and cognitive processes involving multistable phenomena, like decision making and bistable perception. To investigate the role of noise in a multistable neurodynamical system described by coupled differential equations, one usually considers numerical simulations, which are time consuming because of the need for sufficiently many trials to capture the statistics of the influence of the fluctuations on that system. An alternative analytical approach involves the derivation of deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. However, the application of the method of moments is restricted by the assumption that the distribution of the state variables of the system takes on a unimodal Gaussian shape. We extend in this paper the classical moments method to the case of bimodal distribution of the state variables, such that a reduced system of deterministic coupled differential equations can be derived for the desired regime of multistability.},
doi = {10.1103/PHYSREVE.75.031913},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}