English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study coarse pattern formation in a cellular automaton modelling aspatially-extended stochastic neural network. The model, originally proposed byGong and Robinson [36], is known to support stationary and travelling bumps oflocalised activity. We pose the model on a ring and study the existence andstability of these patterns in various limits using a combination of analyticaland numerical techniques. In a purely deterministic version of the model, posedon a continuum, we construct bumps and travelling waves analytically usingstandard interface methods from neural fields theory. In a stochastic versionwith Heaviside firing rate, we construct approximate analytical probabilitymass functions associated with bumps and travelling waves. In the fullstochastic model posed on a discrete lattice, where a coarse analyticdescription is unavailable, we compute patterns and their linear stabilityusing equation-free methods. The lifting procedure used in the coarsetime-stepper is informed by the analysis in the deterministic and stochasticlimits. In all settings, we identify the synaptic profile as a mesoscopicvariable, and the width of the corresponding activity set as a macroscopicvariable. Stationary and travelling bumps have similar meso- and macroscopicprofiles, but different microscopic structure, hence we propose liftingoperators which use microscopic motifs to disambiguate between them. We providenumerical evidence that waves are supported by a combination of high synapticgain and long refractory times, while meandering bumps are elicited by shortrefractory times.

Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation analysis