English
Related papers

Related papers: Spike-adding and reset-induced canard cycles in ad…

200 papers

Bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. These models…

Numerical Analysis · Computer Science 2012-11-07 Jonathan Touboul

The nonlinear noisy leaky integrate-and-fire (NNLIF) model is a popular mean-field description of a large number of interacting neurons, which has attracted mathematicians to study from various aspects. A core property of this model is the…

Analysis of PDEs · Mathematics 2022-06-15 Xu'an Dou , Zhennan Zhou

We have studied neuronal synchronisation in a random network of adaptive exponential integrate-and-fire neurons. We study how spiking or bursting synchronous behaviour appears as a function of the coupling strength and the probability of…

Spiking Neural Networks (SNNs) are seen as an energy-efficient alternative to traditional Artificial Neural Networks (ANNs), but the performance gap remains a challenge. While this gap is narrowing through ANN-to-SNN conversion, substantial…

Computer Vision and Pattern Recognition · Computer Science 2024-12-24 Ziqing Wang , Yuetong Fang , Jiahang Cao , Hongwei Ren , Renjing Xu

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…

Neural and Evolutionary Computing · Computer Science 2025-11-11 Ruyin Wan , George Em Karniadakis , Panos Stinis

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…

Neurons and Cognition · Quantitative Biology 2026-03-05 Rok Cestnik

In this work we consider a general non-autonomous hybrid system based on the integrate-and-fire model, widely used as simplified version of neuronal models and other types of excitable systems. Our unique assumption is that the system is…

Dynamical Systems · Mathematics 2013-11-25 Albert Granados , Martin Krupa , Frédérique Clément

Fast-slow systems are studied usually by "geometrical dissection". The fast dynamics exhibit attractors which may bifurcate under the influence of the slow dynamics which is seen as a parameter of the fast dynamics. A generic solution comes…

Dynamical Systems · Mathematics 2009-12-16 Alexandre Vidal , Jean-Pierre Françoise

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…

Neurons and Cognition · Quantitative Biology 2018-12-14 Antonio Politi , Ekkehard Ullner , Alessandro Torcini

Neural networks (NN) are implemented as sub-grid flame models in a large-eddy simulation of a single-injector liquid-propellant rocket engine with the aim to replace a look-up table approach. The NN training process presents an…

Fluid Dynamics · Physics 2022-01-11 Zeinab Shadram , Tuan M. Nguyen , Athanasios Sideris , William A. Sirignano

Adaptive behavior in volatile environments requires agents to switch among value-control regimes across latent contexts, but maintaining separate preferences, policy biases, and action-confidence parameters for every situation is…

Machine Learning · Computer Science 2025-12-16 Jacob Poschl

In this paper, the parameter estimation problem for a multi-timescale adaptive threshold (MAT) neuronal model is investigated. By manipulating the system dynamics, which comprise of a non-resetting leaky integrator coupled with an adaptive…

Neurons and Cognition · Quantitative Biology 2018-03-13 Amirhossein Jabalameli , Aman Behal

We consider double canard cycles including two canards in singularly perturbed planar systems with two canard points. Previous work studied the complex oscillations including relaxation oscillations and canard cycles in singularly perturbed…

Dynamical Systems · Mathematics 2021-09-08 Shuang Chen , Jinqiao Duan , Ji Li

Canard cycles are periodic orbits that appear as special solutions of fast-slow systems (or singularly perturbed Ordinary Differential Equations). It is well known that canard cycles are difficult to detect, hard to reproduce numerically,…

Dynamical Systems · Mathematics 2021-05-11 Hildeberto Jardon-Kojakhmetov , Christian Kuehn

Rapid action potential generation --- spiking --- and alternating intervals of spiking and quiescence --- bursting --- are two dynamic patterns observed in neuronal activity. In computational models of neuronal systems, the transition from…

Neurons and Cognition · Quantitative Biology 2011-07-15 John Burke , Mathieu Desroches , Anna M. Barry , Tasso J. Kaper , Mark A. Kramer

An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky…

Neurons and Cognition · Quantitative Biology 2009-11-13 Ruben Moreno-Bote , Nestor Parga

We propose a formulation of adaptive computation of free energy differences, in the ABF or nonequilibrium metadynamics spirit, using conditional distributions of samples of configurations which evolve in time. This allows to present a truly…

Statistical Mechanics · Physics 2015-06-25 Tony Lelievre , Mathias Rousset , Gabriel Stoltz

Model-based Reinforcement Learning and Control have demonstrated great potential in various sequential decision making problem domains, including in robotics settings. However, real-world robotics systems often present challenges that limit…

Machine Learning · Computer Science 2023-10-24 Achkan Salehi , Steffen Rühl , Stephane Doncieux

In this study, we investigate the effectiveness of using the PID (Proportional - Integral - Derivative) control loop factors for modifying response thresholds in a decentralized, non-communicating, threshold-based swarm. Each agent in our…

Multiagent Systems · Computer Science 2023-04-26 Maryam Kebari , Annie S. Wu , H. David Mathias

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…

Neurons and Cognition · Quantitative Biology 2013-11-06 Josef Ladenbauer , Moritz Augustin , LieJune Shiau , Klaus Obermayer