We deal with the problem of bridging the gap between two scales in neuronal modeling. At
the first (microscopic) scale, neurons are considered individually and their behavior …

The timing of cortical neurogenesis has a major effect on the size and organization of the
mature cortex. The deletion of the LIM-homeodomain transcription factor Lhx2 in cortical …

Numerous studies have proposed that specific brain activity statistics provide evidence that
the brain operates at a critical point, which could have implications for the brain’s information …

In such different domains as statistical physics, neurosciences, spin glasses, social science,
economics and finance, large ensemble of interacting individuals evolving following (…

We study the nonlinear dynamics of a surprising phenomenon arising in large networks of
excitable elements in response to noise: while at low noise, solutions remain in the vicinity of …

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 …

The brain’s activity is characterized by the interaction of a very large number of neurons that
are strongly affected by noise. However, signals often arise at macroscopic scales …

We investigate the dynamics of a limit of interacting FitzHugh--Nagumo neurons in the
regime of large interaction coefficients. We consider the dynamics described by a mean-field …

Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature,
and soil gradients controlling vegetation growth to morphogen gradients controlling gene …

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 …