Modeling the functional organization of the visual cortex
MSTD '95 Proceedings of the workshop on Measures of spatio-temporal dynamics
Dynamics of neuronal populations: the equilibrium solution
SIAM Journal on Applied Mathematics
A population study of integrate-and-fire-or-burst neurons
Neural Computation
A simple and stable numerical solution for the population density equation
Neural Computation
Modeling Neuronal Assemblies: Theory and Implementation
Neural Computation
Populations of tightly coupled neurons: The rgc/lgn system
Neural Computation
Spiking neurons and the first passage problem
Neural Computation
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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The use of a population dynamics approach promises efficient simulation of large assemblages of neurons. Depending on the issues addressed and the degree of realism incorporated in the simulated neurons, a wide range of different population dynamics formulations can be appropriate. Here we present a common mathematical structure that these various formulations share and that implies dynamical behaviors that they have in common. This underlying structure serves as a guide toward efficient means of simulation. As an example, we derive the general population firing-rate frequency-response and show how it may be used effectively to address a broad range of interacting-population response and stability problems. A few specific cases will be worked out. A summary of this work appears at the end, before the appendix.