19 citations · 31 across the 4 of their papers we have counts for
4 papers
McKean-Vlasov Equations for Large Networks of Neurons with Adaptive Asymmetric Edges
Daniele Avitabile, James MacLaurin
Classical Mckean-Vlasov theory concerns high-dimensional particle systems for which the effect of one particle on another is instantaneous. However in many applications, particular…
Astrocytic resource diffusion stabilizes persistent activity in neural fields
Noah Palmer, Heather L. Cihak, Daniele Avitabile +1
Persistent neural activity underlying working memory requires sustained synaptic transmission, yet the metabolic and neurotransmitter support provided by astrocyte networks is larg…
Spatio-temporal canards in neural field equations
Daniele Avitabile, Mathieu Desroches, Edgar Knobloch
Canards are special solutions to ordinary differential equations that follow invariant repelling slow manifolds for long time intervals. In realistic biophysical single cell models…
Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system
Daniele Avitabile, Mathieu Desroches, Edgar Knobloch +1
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular per…