232 citations · 930 across the 41 of their papers we have counts for
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math.DS2014★ 2 cited
Canard explosion in delayed equations with multiple timescales
Maciej Krupa, Jonathan D. Touboul
We analyze canard explosions in delayed differential equations with a one-dimensional slow manifold. This study is applied to explore the dynamics of the van der Pol slow-fast syst…
math.DS2014★ 36 cited
Complex oscillations in the delayed Fitzhugh-Nagumo equation
Maciej Krupa, Jonathan Touboul
Motivated by the dynamics of neuronal responses, we analyze the dynamics of the Fitzhugh-Nagumo slow-fast system with delayed self-coupling. This system provides a canonical exampl…
math.DS2014
Pulsatile localized dynamics in delayed neural-field equations in arbitrary dimension
Grégory Faye, Jonathan Touboul
Neural field equations are integro-differential systems describing the macroscopic activity of spatially extended pieces of cortex. In such cortical assemblies, the propagation of…