相关论文: Global-in-time classical solutions and qualitative…

Networks in the brain consist of different types of neurons. Here we investigate the influence of neuron diversity on the dynamics, phase space structure and computational capabilities of spiking neural networks. We find that already a…

In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant delay. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant…

We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for…

Spiking neural networks (SNNs) have attracted much attention due to their ability to process temporal information, low power consumption, and higher biological plausibility. However, it is still challenging to develop efficient and…

Spiking Neural Networks (SNNs) offer a biologically plausible and energy-efficient framework for temporal information processing. However, existing studies overlook a fundamental property widely observed in biological neurons-synaptic…

Spiking Neural Networks (SNNs) have gained increasing attention as energy-efficient neural networks owing to their binary and asynchronous computation. However, their non-linear activation, that is Leaky-Integrate-and-Fire (LIF) neuron,…

We investigate numerically the dynamics of large networks of $N$ globally pulse-coupled integrate and fire neurons in a noise-induced synchronized state. The powerspectrum of an individual element within the network is shown to exhibit in…

We extensively explore networks of weakly unbalanced, leaky integrate-and-fire (LIF) neurons for different coupling strength, connectivity, and by varying the degree of refractoriness, as well as the delay in the spike transmission. We find…

Idealized networks of integrate-and-fire neurons with impulse-like interactions obey McKean-Vlasov diffusion equations in the mean-field limit. These equations are prone to blowups: for a strong enough interaction coupling, the mean-field…

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…

The population activity of random networks of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons has been studied extensively. In particular, a state of asynchronous activity with low firing rates and low pairwise correlations…

Deep Neural Networks (DNNs) are the current state-of-the-art models in many speech related tasks. There is a growing interest, though, for more biologically realistic, hardware friendly and energy efficient models, named Spiking Neural…

Spiking Neural Networks (SNNs) capture the information processing mechanism of the brain by taking advantage of spiking neurons, such as the Leaky Integrate-and-Fire (LIF) model neuron, which incorporates temporal dynamics and transmits…

Motor imagery, an important category in electroencephalogram (EEG) research, often intersects with scenarios demanding low energy consumption, such as portable medical devices and isolated environment operations. Traditional deep learning…

Accurate and efficient time-series forecasting remains a challenging problem for both classical and quantum neural architectures, particularly in multivariate environmental settings. This work adapts the Quantum Leaky Integrate-and-Fire…

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…

Spike correlations between neurons are ubiquitous in the cortex, but their role is at present not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input…

The elapsed time model has been widely studied in the context of mathematical neuroscience with many open questions left. The model consists of an age-structured equation that describes the dynamics of interacting neurons structured by the…

In large-scale excitatory neuronal networks, rapid synchronization manifests as {multiple firing events (MFEs)}, mathematically characterized by a finite-time blow-up of the neuronal firing rate in the mean-field Fokker-Planck equation.…

In order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of neurons structured by the distribution of times elapsed since…