# Generalized rate-code model for neuron ensembles with finite populations

## Abstract

We have proposed a generalized Langevin-type rate-code model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing a finite number N of neurons. Calculations using the Fokker-Planck equation have shown that, owing to the multiplicative noise, our rate model yields various kinds of stationary non-Gaussian distributions such as {gamma}, inverse-Gaussian-like, and log-normal-like distributions, which have been experimentally observed. The dynamical properties of the rate model have been studied with the use of the augmented moment method (AMM), which was previously proposed by the author from a macroscopic point of view for finite-unit stochastic systems. In the AMM, the original N-dimensional stochastic differential equations (DEs) are transformed into three-dimensional deterministic DEs for the means and fluctuations of local and global variables. The dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the AMM are in good agreement with those obtained by direct simulation. The synchronization in the neuronal ensemble is discussed. The variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise, which may be a conceivable origin of the observed large variability in cortical neurons.

- Authors:

- Department of Physics, Tokyo Gakugei University, Koganei, Tokyo 184-8501 (Japan)

- Publication Date:

- OSTI Identifier:
- 21072434

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevE.75.051904; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; BRAIN; COMPUTERIZED SIMULATION; DISTRIBUTION; FLUCTUATIONS; FOKKER-PLANCK EQUATION; GAUSS FUNCTION; MOMENTS METHOD; NERVE CELLS; NEURAL NETWORKS; NOISE; STOCHASTIC PROCESSES; SYNCHRONIZATION

### Citation Formats

```
Hasegawa, Hideo.
```*Generalized rate-code model for neuron ensembles with finite populations*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.051904.

```
Hasegawa, Hideo.
```*Generalized rate-code model for neuron ensembles with finite populations*. United States. doi:10.1103/PHYSREVE.75.051904.

```
Hasegawa, Hideo. Tue .
"Generalized rate-code model for neuron ensembles with finite populations". United States.
doi:10.1103/PHYSREVE.75.051904.
```

```
@article{osti_21072434,
```

title = {Generalized rate-code model for neuron ensembles with finite populations},

author = {Hasegawa, Hideo},

abstractNote = {We have proposed a generalized Langevin-type rate-code model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing a finite number N of neurons. Calculations using the Fokker-Planck equation have shown that, owing to the multiplicative noise, our rate model yields various kinds of stationary non-Gaussian distributions such as {gamma}, inverse-Gaussian-like, and log-normal-like distributions, which have been experimentally observed. The dynamical properties of the rate model have been studied with the use of the augmented moment method (AMM), which was previously proposed by the author from a macroscopic point of view for finite-unit stochastic systems. In the AMM, the original N-dimensional stochastic differential equations (DEs) are transformed into three-dimensional deterministic DEs for the means and fluctuations of local and global variables. The dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the AMM are in good agreement with those obtained by direct simulation. The synchronization in the neuronal ensemble is discussed. The variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise, which may be a conceivable origin of the observed large variability in cortical neurons.},

doi = {10.1103/PHYSREVE.75.051904},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 5,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}