Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons
Neural Computation
Simplicity and efficiency of integrate-and-fire neuron models
Neural Computation
Stimulus-dependent correlations in threshold-crossing spiking neurons
Neural Computation
Stochastic properties of coincidence-detector neural cells
Neural Computation
Connection-centric network for spiking neural networks
NOCS '09 Proceedings of the 2009 3rd ACM/IEEE International Symposium on Networks-on-Chip
Input identification in the Ornstein-Uhlenbeck neuronal model with signal dependent noise
BVAI'07 Proceedings of the 2nd international conference on Advances in brain, vision and artificial intelligence
On a stochastic leaky integrate-and-fire neuronal model
Neural Computation
Mechanisms that modulate the transfer of spiking correlations
Neural Computation
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Letter to the editor: Neural networks including microRNAs
Neural Networks
Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process
Journal of Computational Neuroscience
Estimation of time-dependent input from neuronal membrane potential
Neural Computation
Advances in Artificial Neural Systems - Special issue on Advances in Unsupervised Learning Techniques Applied to Biosciences and Medicine
High-capacity embedding of synfire chains in a cortical network model
Journal of Computational Neuroscience
Information filtering by synchronous spikes in a neural population
Journal of Computational Neuroscience
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The integrate-and-fire neuron model is one of the most widely used models for analyzing the behavior of neural systems. It describes the membrane potential of a neuron in terms of the synaptic inputs and the injected current that it receives. An action potential (spike) is generated when the membrane potential reaches a threshold, but the actual changes associated with the membrane voltage and conductances driving the action potential do not form part of the model. The synaptic inputs to the neuron are considered to be stochastic and are described as a temporally homogeneous Poisson process. Methods and results for both current synapses and conductance synapses are examined in the diffusion approximation, where the individual contributions to the postsynaptic potential are small. The focus of this review is upon the mathematical techniques that give the time distribution of output spikes, namely stochastic differential equations and the Fokker–Planck equation. The integrate-and-fire neuron model has become established as a canonical model for the description of spiking neurons because it is capable of being analyzed mathematically while at the same time being sufficiently complex to capture many of the essential features of neural processing. A number of variations of the model are discussed, together with the relationship with the Hodgkin–Huxley neuron model and the comparison with electrophysiological data. A brief overview is given of two issues in neural information processing that the integrate-and-fire neuron model has contributed to – the irregular nature of spiking in cortical neurons and neural gain modulation.