Fast sigmoidal networks via spiking neurons
Neural Computation
Dynamics of neuronal populations: the equilibrium solution
SIAM Journal on Applied Mathematics
A population study of integrate-and-fire-or-burst neurons
Neural Computation
2008 Special Issue: The state of MIIND
Neural Networks
Modeling cortex network: a spatio-temporal population approach
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Analytical solution for dynamic of neuronal populations
ICANN'05 Proceedings of the 15th international conference on Artificial Neural Networks: biological Inspirations - Volume Part I
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A population density description of large populations of neurons has generated considerable interest recently. The evolution in time of the population density is determined by a partial differential equation (PDE). Most of the algorithms proposed to solve this PDE have used finite difference schemes. Here, I use the method of characteristics to reduce the PDE to a set of ordinary differential equations, which are easy to solve. The method is applied to leaky-integrate-and-fire neurons and produces an algorithm that is efficient and yields a stable and manifestly nonnegative density. Contrary to algorithms based directly on finite difference schemes, this algorithm is insensitive to large density gradients, which may occur during evolution of the density.