Parabolic bursting in an excitable system coupled with a slow oscillation
SIAM Journal on Applied Mathematics
Dynamics of the firing probability of noisy integrate-and-fire neurons
Neural Computation
A Phase Model of Temperature-Dependent Mammalian Cold Receptors
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
Computing and stability in cortical networks
Neural Computation
Minimal Models of Adapted Neuronal Response to In Vivo–lLike Input Currents
Neural Computation
Event-driven simulations of nonlinear integrate-and-fire neurons
Neural Computation
International Journal of Computer Mathematics - Computer Mathematics in Dynamics and Control
Spike-timing error backpropagation in theta neuron networks
Neural Computation
Semantic priming in a cortical network model
Journal of Cognitive Neuroscience
Feature selection in simple neurons: How coding depends on spiking dynamics
Neural Computation
First spiking dynamics of stochastic neuronal model with optimal control
ICONIP'08 Proceedings of the 15th international conference on Advances in neuro-information processing - Volume Part I
Journal of Cognitive Neuroscience
Finite-size and correlation-induced effects in mean-field dynamics
Journal of Computational Neuroscience
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We calculate the firing rate of the quadratic integrate-and-fire neuron in response to a colored noise input current. Such an input current is a good approximation to the noise due to the random bombardment of spikes, with the correlation time of the noise corresponding to the decay time of the synapses. The key parameter that determines the firing rate is the ratio of the correlation time of the colored noise, τs, to the neuronal time constant, τm. We calculate the firing rate exactly in two limits: when the ratio, τs/τm, goes to zero (white noise) and when it goes to infinity. The correction to the short correlation time limit is O(τs/τm), which is qualitatively different from that of the leaky integrate-and-fire neuron, where the correction is O(√τs/τm). The difference is due to the different boundary conditions of the probability density function of the membrane potential of the neuron at firing threshold. The correction to the long correlation time limit is O(τm/τs). By combining the short and long correlation time limits, we derive an expression that provides a good approximation to the firing rate over the whole range of τs/τm in the suprathreshold regime-- that is, in a regime in which the average current is sufficient to make the cell fire. In the subthreshold regime, the expression breaks down somewhat when τs becomes large compared to τm.