36 citations · 53 across the 5 of their papers we have counts for
6 papers
Heteroclinic cycles in Hopfield networks
Pascal Chossat, Martin Krupa
Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theo…
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…
The Period adding and incrementing bifurcations: from rotation theory to applications
Albert Granados, Lluís Alsedà, Martin Krupa
This survey article is concerned with the study of bifurcations of piecewise-smooth maps. We review the literature in circle maps and quasi-contractions and provide paths through t…
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…
Firing-rate, symbolic dynamics and frequency dependence in periodically driven spiking models: a piecewise-smooth approach
Albert Granados, Maciej Krupa
In this work we consider a periodically forced generic integrate-and-fire model with a unique attracting equilibrium in the subthreshold dynamics and study the dependence of the fi…
Noise-induced canard and mixed-mode oscillations in large stochastic networks with multiple timescales
Jonathan Touboul, Maciej Krupa, Mathieu Desroches
We investigate the dynamics of large stochastic networks with different timescales and nonlinear mean-field interactions. After deriving the limit equations for a general class of…