35 citations · 66 across the 3 of their papers we have counts for
3 papers
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…
Canards and curvature: nonsmooth approximation by pinching
Mathieu Desroches, Mike R. Jeffrey
In multiple time-scale (singularly perturbed) dynamical systems, canards are counterintuitive solutions that evolve along both attracting and repelling invariant manifolds. In two…