A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input
Biological Cybernetics
Exact Simulation of Integrate-and-Fire Models with Exponential Currents
Neural Computation
Event-driven simulations of nonlinear integrate-and-fire neurons
Neural Computation
Simple model of spiking neurons
IEEE Transactions on Neural Networks
Which model to use for cortical spiking neurons?
IEEE Transactions on Neural Networks
Consistent recovery of sensory stimuli encoded with MIMO neural circuits
Computational Intelligence and Neuroscience - Special issue on signal processing for neural spike trains
Fast and exact simulation methods applied on a broad range of neuron models
Neural Computation
Optimization methods for spiking neurons and networks
IEEE Transactions on Neural Networks
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For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model's rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation.