相关论文: Exact low-dimensional description for fast neural …

We investigate a large ensemble of Quadratic Integrate-and-Fire (QIF) neurons with heterogeneous input currents and adaptation variables. Our analysis reveals that for a specific class of adaptation, termed quadratic spike-frequency…

Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear…

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N tends to…

We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on…

Collective dynamics of spiking networks of neurons has been of central interest to both computation neuroscience and network science. Over the past years a new generation of neural population models based on exact reductions (ER) of spiking…

Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect…

Exact firing rate models, also known as next-generation neural mass models (NG-NMMs), provide a rigorous description of the dynamics of neural populations. While in its simplest form a single population only displays fixed-point activity,…

We introduce a two-phase quadratic integrate-and-fire (QIF) neuron whose membrane potential evolves according to two alternating Riccati equations within finite bounds. This simple extension removes the unphysical voltage divergence of the…

Starting from a spectral expansion of the Fokker-Plank equation for the membrane potential density in a network of spiking neurons, a low-dimensional dynamics of the collective firing rate is derived. As a result a $n$-order ordinary…

Low-dimensional descriptions of neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled…

Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are…

Realizations of low firing rates in neural networks usually require globally balanced distributions among excitatory and inhibitory links, while feasibility of temporal coding is limited by neuronal millisecond precision. We show that…

In large-scale neural networks, coherent limit cycle oscillations usually coexist with unstable incoherent equilibrium states, which are not observed experimentally. We implement a first-order dynamic controller to stabilize unknown…

Spiking Neural Networks (SNNs) have emerged as energy-efficient alternatives to traditional artificial neural networks, leveraging asynchronous and biologically inspired neuron dynamics. Among existing neuron models, the Leaky…

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic…

The dominant modeling framework for understanding cortical computations are heuristic firing rate models. Despite their success, these models fall short to capture spike synchronization effects, to link to biophysical parameters and to…

Over the last decade, next-generation neural mass models have become increasingly prominent in mathematical neuroscience. These models link microscopic dynamics with low-dimensional systems of so-called firing rate equations that exactly…

Stochastic integrate-and-fire (IF) neuron models have found widespread applications in computational neuroscience. Here we present results on the white-noise-driven perfect, leaky, and quadratic IF models, focusing on the spectral…

We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition…

Kinetics of a balanced network of neurons with a sparse grid of synaptic links is well representable by the stochastic dynamics of a generic neuron subject to an effective shot noise. The rate of delta-pulses of the noise is determined…