48 citations · 94 across the 36 of their papers we have counts for
7 papers · 1 filter
Threshold of front propagation in neural fields: An interface dynamics approach
Gregory Faye, Zachary P Kilpatrick
Neural field equations model population dynamics of large-scale networks of neurons. Wave propagation in neural fields is often studied by constructing traveling wave solutions in…
Ghosts of bump attractors in stochastic neural fields: Bottlenecks and extinction
Zachary P. Kilpatrick
We study the effects of additive noise on stationary bump solutions to spatially extended neural fields near a saddle-node bifurcation. The integral terms of these evolution equati…
Stochastic synchronization of neural activity waves
Zachary P. Kilpatrick
We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, travelin…
Stochastic motion of bumps in planar neural fields
Daniel Poll, Zachary P. Kilpatrick
We analyze the effects of spatiotemporal noise on stationary pulse solutions (bumps) in neural field equations on planar domains. Neural fields are integrodifferential equations wh…
Pulse bifurcations in stochastic neural fields
Zachary P Kilpatrick, Gregory Faye
We study the effects of additive noise on traveling pulse solutions in spatially extended neural fields with linear adaptation. Neural fields are evolution equations with an integr…
Coupling layers regularizes wave propagation in laminar stochastic neural fields
Zachary P. Kilpatrick
We study the effects of coupling between layers of stochastic neural field models with laminar structure. In particular, we focus on how the propagation of waves of neural activity…
Wandering bumps in stochastic neural fields
Zachary P. Kilpatrick, Bard Ermentrout
We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equat…