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Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document,…

Analysis of PDEs · Mathematics 2020-11-11 Grégory Dumont , Pierre Gabriel

This paper presents a comprehensive evaluation of Spiking Neural Network (SNN) neuron models for hardware acceleration by comparing event driven and clock-driven implementations. We begin our investigation in software, rapidly prototyping…

Neural and Evolutionary Computing · Computer Science 2025-12-24 Filippo Marostica , Alessio Carpegna , Alessandro Savino , Stefano Di Carlo

Reduced models of neuronal activity such as Integrate-and-Fire models allow a description of neuronal dynamics in simple, intuitive terms and are easy to simulate numerically. We present a method to fit an Integrate-and-Fire-type model of…

Neurons and Cognition · Quantitative Biology 2020-04-03 Renaud Jolivet , Wulfram Gerstner

For energy-efficient computation in specialized neuromorphic hardware, we present spiking neural coding, an instantiation of a family of artificial neural models grounded in the theory of predictive coding. This model, the first of its…

Neural and Evolutionary Computing · Computer Science 2022-08-09 Alexander Ororbia

We describe a new, computationally simple method for analyzing the dynamics of neuronal spike trains driven by external stimuli. The goal of our method is to test the predictions of simple spike-generating models against extracellularly…

Neurons and Cognition · Quantitative Biology 2007-05-23 Daniel S. Reich , Jonathan D. Victor , Bruce W. Knight

The computation performed by a neuron can be formulated as a combination of dimensional reduction in stimulus space and the nonlinearity inherent in a spiking output. White noise stimulus and reverse correlation (the spike-triggered average…

Biological Physics · Physics 2007-05-23 Blaise Aguera y Arcas , Adrienne Fairhall

In this paper we present a numerical study of a mathematical model of spiking neurons introduced by Ferrari et al. in an article entitled Phase transition forinfinite systems of spiking neurons. In this model we have a countable number of…

Neural and Evolutionary Computing · Computer Science 2019-11-11 Cecilia Romaro , Fernando Araujo Najman , Morgan André

A class of spiking neuronal models with threshold 2 is considered. It is defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire (LIF) or the binding neuron model and also for some…

Neurons and Cognition · Quantitative Biology 2019-08-20 Olha Shchur , Alexander Vidybida

We study the joint dynamics of membrane potential and time since the last spike in a population of integrate-and-fire neurons using a population density framework. This leads to a two-dimensional Fokker-Planck equation that captures the…

Disordered Systems and Neural Networks · Physics 2026-01-01 Luca Falorsi , Gianni V. Vinci , Maurizio Mattia

The action potential constitutes the digital component of the signaling dynamics of neurons. But the biophysical nature of the full-time course of the action potential associated with changes in membrane potential is mathematically distinct…

Neurons and Cognition · Quantitative Biology 2026-04-16 Gabriel A. Silva

In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh-Nagumo neuron model (FHN) in the excitable…

Dynamical Systems · Mathematics 2019-09-06 Marius E. Yamakou , Tat Dat Tran , Luu Hoang Duc , Juergen Jost

Neuromorphic computing targets energy-efficient event-driven information processing by placing artificial spiking-neurons at its core. Artificial neuron devices and circuits have multiple operating modes and produce region-dependent…

Applied Physics · Physics 2026-01-06 Zhiwei Li , Shi-Li Zhang , Chenyu Wen

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and…

Neurons and Cognition · Quantitative Biology 2022-09-16 Johanna Senk , Karolína Korvasová , Jannis Schuecker , Espen Hagen , Tom Tetzlaff , Markus Diesmann , Moritz Helias

We briefly review and highlight the consequences of rigorous and exact results obtained in \cite{cessac:10}, characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where…

Adaptation and Self-Organizing Systems · Physics 2010-08-31 Bruno Cessac , Hassan Nasser , Juan-Carlos Vasquez

We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…

Neurons and Cognition · Quantitative Biology 2007-05-23 H. Soula , C. C. Chow

Population equations for infinitely large networks of spiking neurons have a long tradition in theoretical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form…

Probability · Mathematics 2022-08-30 Valentin Schmutz , Eva Löcherbach , Tilo Schwalger

Spiking neural network models characterize the emergent collective dynamics of circuits of biological neurons and help engineer neuro-inspired solutions across fields. Most dynamical systems' models of spiking neural networks typically…

Computational Physics · Physics 2023-04-12 Georg Börner , Fabio Schittler Neves , Marc Timme

In this paper, we focus on efficiently and flexibly simulating the Fokker-Planck equation associated with the Nonlinear Noisy Leaky Integrate-and-Fire (NNLIF) model, which reflects the dynamic behavior of neuron networks. We apply the…

Numerical Analysis · Mathematics 2024-12-17 Ling Yan , Pei Zhang , Yanli Wang , Zhennan Zhou

In this work, we examine fundamental elements of spiking neural networks (SNNs) as well as how to tune them. Concretely, we focus on two different foundational neuronal units utilized in SNNs -- the leaky integrate-and-fire (LIF) and the…

Neural and Evolutionary Computing · Computer Science 2025-06-11 William Gebhardt , Alexander G. Ororbia , Nathan McDonald , Clare Thiem , Jack Lombardi

In this paper, we propose a shot noise-based leaky integrated and firing neuron model and provide a detailed analysis of the performance of this model compared to the traditional diffusion approximated model. In theoretical neuroscience,…

Neurons and Cognition · Quantitative Biology 2018-07-05 Zihao Xu