A nonequilibrium-potential approach to competition in neural populations

Deza, Roberto R.; Deza, Ignacio; Mart�nez, Nataniel; Mej�as, Jorge F.; Wio, Horacio S.

doi:10.3389/fphy.2018.00154

A nonequilibrium-potential approach to competition in neural populations

Deza, Roberto R.; Deza, Ignacio; Mart�nez, Nataniel; Mej�as, Jorge F.; Wio, Horacio S.

Authors

Ignacio Deza Ignacio.Deza@uwe.ac.uk
Associate Lecturer - CATE - CCT - UCCT0001

Ignacio Deza

Nataniel Mart�nez

Jorge F. Mej�as

Horacio S. Wio

Abstract

Energy landscapes are a highly useful aid for the understanding of dynamical systems, and a particularly valuable tool for their analysis. For a broad class of rate neural- network models of relevance in neuroscience, we derive a global Lyapunov function which provides an energy landscape without any symmetry constraint. This newly obtained “nonequilibrium potential” (NEP)—the first one obtained for a model of neural circuits—predicts with high accuracy the outcomes of the dynamics in the globally stable cases studied here. Common features of the models in this class are bistability—with implications for working memory and slow neural oscillations—and population bursts, associated with signal detection in neuroscience. Instead, limit cycles are not found for the conditions in which the NEP is defined. Their nonexistence can be proven by resorting to the Bendixson–Dulac theorem, at least when the NEP remains positive and in the (also generic) singular limit of these models. This NEP constitutes a powerful tool to understand average neural network dynamics from a more formal standpoint, and will also be of help in the description of large heterogeneous neural networks.

Journal Article Type	Article
Acceptance Date	Dec 17, 2018
Online Publication Date	Jan 10, 2019
Publication Date	Jan 10, 2019
Deposit Date	Mar 19, 2019
Publicly Available Date	Mar 19, 2019
Journal	Frontiers in Physics
Electronic ISSN	2296-424X
Publisher	Frontiers Media
Peer Reviewed	Peer Reviewed
Volume	6
Issue	154
DOI	https://doi.org/10.3389/fphy.2018.00154
Keywords	nonequilibrium potential, energy landscape, neural networks bistability, firing rate dynamics
Public URL	https://uwe-repository.worktribe.com/output/854186
Publisher URL	http://doi.org/10.3389/fphy.2018.00154
Related Public URLs	https://www.frontiersin.org/articles/10.3389/fphy.2018.00154/full
Contract Date	Mar 19, 2019