[HTML][HTML] Well-posedness and stability of a stochastic neural field in the form of a partial differential equation

JA Carrillo, P Roux, S Solem - Journal de Mathématiques Pures et …, 2025 - Elsevier
A system of partial differential equations representing stochastic neural fields was recently
proposed with the aim of modelling the activity of noisy grid cells when a mammal travels …

Multiscale motion and deformation of bumps in stochastic neural fields with dynamic connectivity

HL Cihak, ZP Kilpatrick - Multiscale Modeling & Simulation, 2024 - SIAM
The distinct timescales of synaptic plasticity and neural activity dynamics play an important
role in the brain's learning and memory systems. Activity-dependent plasticity reshapes …

Robustly encoding certainty in a metastable neural circuit model

HL Cihak, ZP Kilpatrick - Physical Review E, 2024 - APS
Localized persistent neural activity can encode delayed estimates of continuous variables.
Common experiments require that subjects store and report the feature value (eg …

Stability of wandering bumps for Hawkes processes interacting on the circle

Z Agathe-Nerine - arXiv preprint arXiv:2307.05982, 2023 - arxiv.org
We consider a population of Hawkes processes modeling the activity of $ N $ interacting
neurons. The neurons are regularly positioned on the circle $[-\pi,\pi] $, and the connectivity …

The Impact of Synaptic Dynamics on Working Memory in Neural Field Equations

HL Cihak - 2024 - search.proquest.com
Persistent neural activity in the non-human primate cortex can represent delayed estimates
of continuum variables in working memory. This activity appears as a “bump” that …