相关论文: Low-dimensional model for adaptive networks of spi…
Recently, low-dimensional models of neuronal activity have been exactly derived for large networks of deterministic, Quadratic Integrate-and-Fire (QIF) neurons. Such firing rate models (FRM) describe the emergence of fast collective…
Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking into account the fatigue due to spike emissions and the consequent reduction of the firing activity. We have studied the effect of this adaptation mechanism on the…
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…
Spiking neural networks (SNNs) offer biologically inspired computation but remain underexplored for continuous regression tasks in scientific machine learning. In this work, we introduce and systematically evaluate Quadratic…
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…
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…
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…
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…
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…
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…
The quadratic adaptive integrate-and-fire model (Izhikecih 2003, 2007) is recognized as very interesting for its computational efficiency and its ability to reproduce many behaviors observed in cortical neurons. For this reason it is…
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…
An exact low-dimensional system of mean-field equations for an infinite-size network of pulse coupled integrate-and-fire neurons with a bimodal distribution of an excitability parameter is derived. Bifurcation analysis of these equations…
Sequential neural activity is fundamental to cognition, yet how diverse sequences are recalled under biological constraints remains a key question. Existing models often struggle to balance biophysical realism and analytical tractability.…
Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony that underpin brain disorders and normal function. Exact…
Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic integrate and fire (QIF), among others. Unfortunately, the…
Spiking neural networks offer low energy consumption due to their event-driven nature. Beyond binary spike outputs, their intrinsic floating-point dynamics merit greater attention. Neuronal threshold levels and reset modes critically…
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…
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 capture spike synchronization effects of stochastic spiking…
Author summary: Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective…