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arXiv · 1808.07850

A nonequilibrium-potential approach to competition in neural populations

R. R. Deza·J. I. Deza·N. Martinez·J. F. Mejias·H. S. Wio
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Abstract

Energy landscapes are a useful aid for the understanding of dynamical systems, and a valuable tool for their analysis. For a broad class of rate models of neural networks, we derive a global Lyapunov function which provides an energy landscape without any symmetry constraint. This newly obtained `nonequilibrium potential' (NEP) 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 burst', also relevant in neuroscience. Instead, limit cycles are not found. Their nonexistence can be proven by resort to the Bendixson--Dulac theorem, at least when the NEP remains positive and in the (also generic) singular limit of these models. Hopefully, this NEP will help understand average neural network dynamics from a more formal standpoint, and will also be of help in the description of large heterogeneous neural networks.

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R. R. Deza, J. I. Deza, N. Martinez, J. F. Mejias, H. S. Wio. 2018-08-23. A nonequilibrium-potential approach to competition in neural populations. https://arxiv.org/abs/1808.07850

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