Parabolic bursting in an excitable system coupled with a slow oscillation
SIAM Journal on Applied Mathematics
Diffusion approximation of the neuronal model with synaptic reversal potentials
Biological Cybernetics
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Shunting inhibition does not have a divisive effect on firing rates
Neural Computation
Linearization of F-1 curves by adaptation
Neural Computation
Neuronal Networks of the Hippocampus
Neuronal Networks of the Hippocampus
Dynamics of the firing probability of noisy integrate-and-fire neurons
Neural Computation
Rate models for conductance-based cortical neuronal networks
Neural Computation
Firing rate of the noisy quadratic integrate-and-fire neuron
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
2008 Special Issue: The state of MIIND
Neural Networks
Population models of temporal differentiation
Neural Computation
Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process
Journal of Computational Neuroscience
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Rate models are often used to study the behavior of large networks of spiking neurons. Here we propose a procedure to derive rate models that take into account the fluctuations of the input current and firing-rate adaptation, two ubiquitous features in the central nervous system that have been previously overlooked in constructing rate models. The procedure is general and applies to any model of firing unit. As examples, we apply it to the leaky integrate-and-fire (IF) neuron, the leaky IF neuron with reversal potentials, and to the quadratic IF neuron. Two mechanisms of adaptation are considered, one due to an afterhyperpolarization current and the other to an adapting threshold for spike emission. The parameters of these simple models can be tuned to match experimental data obtained from neocortical pyramidal neurons. Finally, we show how the stationary model can be used to predict the time-varying activity of a large population of adapting neurons.