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

Gustavo Deco and Daniel Martí
Phys. Rev. E 75, 031913 – Published 28 March 2007

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.

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  • Received 27 November 2006

DOI:https://doi.org/10.1103/PhysRevE.75.031913

©2007 American Physical Society

Authors & Affiliations

Gustavo Deco* and Daniel Martí

  • Computational Neuroscience Group, Universitat Pompeu Fabra, Passeig de Circumval∙lació, 8, 08003 Barcelona, Spain

  • *Also at Institució Catalana de Recerca i EstudisAvançats (ICREA), Barcelona, Spain. Electronic address: gustavo.deco@upf.edu

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Vol. 75, Iss. 3 — March 2007

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