The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result

The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite...

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Bibliographic Details
Published in:Neural computation 2000-05, Vol.12 (5), p.1045-1055
Main Authors: Knight, B. W., Omurtag, A., Sirovich, L.
Format: Article
Language:English
Subjects:
Algorithms
Animal and plant ecology
Animal, plant and microbial ecology
Applied sciences
Artificial intelligence
Biological and medical sciences
Computer science
control theory
systems
Connectionism. Neural networks
Control theory. Systems
Demecology
Exact sciences and technology
Fundamental and applied biological sciences. Psychology
General aspects
General aspects. Models. Methods
Modelling and identification
Models, Neurological
Neurons - physiology
Population Dynamics
Synapses - physiology
Vertebrates: nervous system and sense organs
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Summary:The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upward shift in voltage in response to each synaptic event, we compare the theoretical prediction with the result of a direct simulation of 90,000 model neurons. The degree of agreement supports the applicability of the population dynamics equation. The theoretical prediction is in the form of a series. Convergence is rapid, so that the full result is well approximated by a few terms.
ISSN:0899-7667
1530-888X
DOI:10.1162/089976600300015493