Analysis of neural excitability and oscillations
Methods in neuronal modeling
Weakly connected neural networks
Weakly connected neural networks
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments (Springer Series in Synergetics)
Type i membranes, phase resetting curves, and synchrony
Neural Computation
Firing rate of the noisy quadratic integrate-and-fire neuron
Neural Computation
2005 Special Issue: Stochastic resonance in noisy spiking retinal and sensory neuron models
Neural Networks - 2005 Special issue: IJCNN 2005
Spike-timing error backpropagation in theta neuron networks
Neural Computation
Feature selection in simple neurons: How coding depends on spiking dynamics
Neural Computation
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We study the one-dimensional normal form of a saddle-node system under the influence of additive gaussian white noise and a static "bias current" input parameter, a model that can be looked upon as the simplest version of a type I neuron with stochastic input. This is in contrast with the numerous studies devoted to the noise-driven leaky integrate-and-fire neuron. We focus on the firing rate and coefficient of variation (CV) of the interspike interval density, for which scaling relations with respect to the input parameter and noise intensity are derived. Quadrature formulas for rate and CV are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model. We also show that caution must be used to extend these results to the Θ neuron model with multiplicative gaussian white noise. The correspondence between the first passage time statistics for the saddle-node model and the Θ neuron model is obtained only in the Stratonovich interpretation of the stochastic Θ neuron model, while previous results have focused only on the Ito interpretation. The correct Stratonovich interpretation yields CVs that are still relatively high, although smaller than in the Ito interpretation; it also produces certain qualitative differences, especially at larger noise intensities. Our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type I neurons from their firing statistics. We also briefly discuss the effect of finite boundaries (finite values of threshold and reset) on the firing statistics.