ArticleJournal of mathematical neuroscience2014
Large deviations for nonlocal stochastic neural fields.
Article in Journal of mathematical neuroscience, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- A gradient flow formulation for the stochastic Amari neural field model.Journal of mathematical biology · 2019Article
- Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis.Journal of mathematical biology · 2017Article
- Neural Field Models with Threshold Noise.Journal of mathematical neuroscience · 2016Article
- Stochastic neural field equations: a rigorous footing.Journal of mathematical biology · 2015Article
- Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks.Journal of mathematical neuroscience · 2015Article
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2 authors.
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Abstract
We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multiscale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations.Mathematics Subject Classification (2000): 60F10, 60H15, 65M60, 92C20.
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