We propose an overview of the modeling approaches for the mathematical description and
analysis of processes that combine continuous and discontinuous behavior, namely …

Finite-size effects may significantly influence the collective dynamics of large populations of
neurons. Recently, we have shown that in globally coupled networks these effects can be …

According to many experimental observations, neurons in cerebral cortex tend to operate in
an asynchronous regime, firing independently of each other. In contrast, many other …

Dynamic excitatory-inhibitory (EI) balance is a paradigmatic mechanism invoked to explain
the irregular low firing activity observed in the cortex. However, we will show that the EI …

Reduction of collective dynamics of large heterogeneous populations to low-dimensional
mean-field models is an important task of modern theoretical neuroscience. Such models …

We study synchronization phenomena in a multiplex network composed of two rings with
identical Leaky Integrate-and-Fire (LIF) oscillators located on the nodes of the rings. Within …

Understanding the magnitude and structure of interneuronal correlations and their
relationship to synaptic connectivity structure is an important and difficult problem in …

Цель настоящей работы-обзор исследований коллективной динамики в сетях
активных элементов с импульсными связями. Для многих сетевых колебательных …

We revisit the dynamics of a prototypical model of balanced activity in networks of spiking
neurons. A detailed investigation of the thermodynamic limit for fixed density of connections …

The idealization of neuronal pulses as δ-spikes is a convenient approach in neuroscience
but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse …