Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
Firing patterns in the adaptive exponential integrate-and-fire model
Biological Cybernetics - Special Issue: Quantitative Neuron Modeling
Dynamics and bifurcations of the adaptive exponential integrate-and-fire model
Biological Cybernetics - Special Issue: Quantitative Neuron Modeling
Spike-timing error backpropagation in theta neuron networks
Neural Computation
Spiking neurons and the first passage problem
Neural Computation
On the simulation of nonlinear bidimensional spiking neuron models
Neural Computation
Which model to use for cortical spiking neurons?
IEEE Transactions on Neural Networks
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We derive conditions for continuous differentiability of inter-spike intervals ISIs of spiking neurons with respect to parameters decision variables of an external stimulating input current that drives a recurrent network of synaptically connected neurons. The dynamical behavior of individual neurons is represented by a class of discontinuous single-neuron models. We report here that ISIs of neurons in the network are continuously differentiable with respect to decision variables if 1 a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and 2 the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials. Our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models.