Highlights•Generalized integrate-and-fire (GIF) models permit efficient extraction of point
neuron parameters, which reproduce the spiking behavior of multiple cell types and are …

Phase transitions and critical behavior are crucial issues both in theoretical and
experimental neuroscience. We report analytic and computational results about phase …

We generalize multivariate Hawkes processes mainly by including a dependence with
respect to the age of the process, ie the delay since the last point. Within this class, we …

We consider multi-class systems of interacting nonlinear Hawkes processes modeling
several large families of neurons and study their mean field limits. As the total number of …

We consider spatially extended systems of interacting nonlinear Hawkes processes
modeling large systems of neurons placed in R d and study the associated mean field limits …

Networks of stochastic spiking neurons are interesting models in the area of theoretical
neuroscience, presenting both continuous and discontinuous phase transitions. Here, we …

Probabilistic cellular automata (PCA) are interacting discrete stochastic dynamical systems
used as a modeling tool for a wide range of natural and societal phenomena. Their key …

The macroscopic dynamics of large populations of neurons can be mathematically analyzed
using low-dimensional firing-rate or neural-mass models. However, these models fail to …

This paper shows that the heterogeneity in neuronal and synaptic dynamics reduces the
spiking activity of a Recurrent Spiking Neural Network (RSNN) while improving prediction …

We prove the existence of a phase transition for a stochastic model of interacting neurons.
The spiking activity of each neuron is represented by a point process having rate 1 …