232 citations · 930 across the 41 of their papers we have counts for
13 papers · 1 filter
Spatial Dynamics with Heterogeneity
Denis D. Patterson, Simon A. Levin, A. Carla Staver +1
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling g…
Probabilistic Foundations of Spatial Mean-field Models in Ecology and Applications
Denis D. Patterson, Simon A. Levin, A. Carla Staver +1
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between t…
Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike adding and chaos
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul +1
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and…
Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan Touboul +1
This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation a…
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…
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…